Generalized magnetofluid connections in relativistic magnetohydrodynamics.
Asenjo, Felipe A; Comisso, Luca
2015-03-20
The concept of magnetic connections is extended to nonideal relativistic magnetohydrodynamical plasmas. Adopting a general set of equations for relativistic magnetohydrodynamics including thermal-inertial, thermal electromotive, Hall, and current-inertia effects, we derive a new covariant connection equation showing the existence of generalized magnetofluid connections that are preserved during the dissipationless plasma dynamics. These connections are intimately linked to a general antisymmetric tensor that unifies the electromagnetic and fluid fields, allowing the extension of the magnetic connection notion to a much broader concept.
HARM A Numerical Scheme for General Relativistic Magnetohydrodynamics
Gammie, C F; Tóth, G; Gammie, Charles F.; Kinney, Jonathan C. Mc
2003-01-01
We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, and van Leer scheme. A variant of constrained transport, proposed earlier by T\\'oth, is used to maintain a divergence free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.
Relativistic magnetohydrodynamics
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
WhiskyMHD: Numerical Code for General Relativistic Magnetohydrodynamics
Baiotti, Luca; Giacomazzo, Bruno; Hawke, Ian; et al.
2010-10-01
Whisky is a code to evolve the equations of general relativistic hydrodynamics (GRHD) and magnetohydrodynamics (GRMHD) in 3D Cartesian coordinates on a curved dynamical background. It was originally developed by and for members of the EU Network on Sources of Gravitational Radiation and is based on the Cactus Computational Toolkit. Whisky can also implement adaptive mesh refinement (AMR) if compiled together with Carpet. Whisky has grown from earlier codes such as GR3D and GRAstro_Hydro, but has been rewritten to take advantage of some of the latest research performed here in the EU. The motivation behind Whisky is to compute gravitational radiation waveforms for systems that involve matter. Examples would include the merger of a binary system containing a neutron star, which are expected to be reasonably common in the universe and expected to produce substantial amounts of radiation. Other possible sources are given in the projects list.
General relativistic magnetohydrodynamic simulations of collapsars: Rotating black hole cases
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Mizuno, Y. [Kyoto Univ., Kyoto (Japan). Department of Astronomy; Yamada, S. [Waseda Univ., Tokyo (Japan). Science and Engineering; Koide, S. [Toyama Univ., Toyama (Japan). Department of Engineering; Shibata, K. [Kyoto Univ., Kyoto (Japan). Kwasan and Hida Observatory
2005-06-01
We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of coIIapsars including a rotating black hole. InitiaIIy, we assume that the care collapse has failed in this star. A rotating black hole of a few solar masses is inserted by hand into the calculation. The simulation results show the formation of a diskIike structure and the generation of a jetIike outflow near the central black hole. The jetIike outflow propagates and accelerated mainly by the magnetic field. The total jet velocity is {approx} 0.3c. When the rotation of the black hole is faster, the magnetic field is twisted strongly owing to the frame-dragging effect. The magnetic energy stored by the twisting magnetic field is directly converted to kinetic energy of the jet rather than propagating as an Alfven wave. Thus, as the rotation of the black hole becomes faster, the poloidal velocity of the jet becomes faster.
General-Relativistic Resistive Magnetohydrodynamics in three dimensions: formulation and tests
Dionysopoulou, Kyriaki; Palenzuela, Carlos; Rezzolla, Luciano; Giacomazzo, Bruno
2013-01-01
We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of Implicit-Explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for small electrical conductivities. Using tests in one, two, and three dimensions, we show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing physical setups in all ranges of conductivities. In addition to tests in flat spacetime, we report simulations of magnetized nonrotating relativistic stars, both in the Cowling approximation and in dynamical spacetimes. Finally, because of its astrophysical relevance and because it provides a severe testbed for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that als...
Relativistic magnetohydrodynamics in one dimension.
Lyutikov, Maxim; Hadden, Samuel
2012-02-01
We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation.
GRHydro: A new open source general-relativistic magnetohydrodynamics code for the Einstein Toolkit
Moesta, Philipp; Faber, Joshua A; Haas, Roland; Noble, Scott C; Bode, Tanja; Loeffler, Frank; Ott, Christian D; Reisswig, Christian; Schnetter, Erik
2013-01-01
We present the new general-relativistic magnetohydrodynamics (GRMHD) capabilities of the Einstein Toolkit, an open-source community-driven numerical relativity and computational relativistic astrophysics code. The GRMHD extension of the Toolkit builds upon previous releases and implements the evolution of relativistic magnetised fluids in the ideal MHD limit in fully dynamical spacetimes using the same shock-capturing techniques previously applied to hydrodynamical evolution. In order to maintain the divergence-free character of the magnetic field, the code implements both hyperbolic divergence cleaning and constrained transport schemes. We present test results for a number of MHD tests in Minkowski and curved spacetimes. Minkowski tests include aligned and oblique planar shocks, cylindrical explosions, magnetic rotors, Alfv\\'en waves and advected loops, as well as a set of tests designed to study the response of the divergence cleaning scheme to numerically generated monopoles. We study the code's performanc...
RAISHIN: A High-Resolution Three-Dimensional General Relativistic Magnetohydrodynamics Code
Mizuno, Yosuke; Nishikawa, Ken-Ichi; Koide, Shinji; Hardee, Philip; Fishman, Gerald J.
2006-01-01
We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high resolution shock-capturing scheme. The numerical fluxes are calculated using the Harten, Lax, & van Leer (HLL) approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. In order to examine the numerical accuracy and the numerical efficiency, the code uses four different reconstruction methods: piecewise linear methods with Minmod and MC slope-limiter function, convex essentially non-oscillatory (CENO) method, and piecewise parabolic method (PPM) using multistep TVD Runge-Kutta time advance methods with second and third-order time accuracy. We describe code performance on an extensive set of test problems in both special and general relativity. Our new GRMHD code has proven to be accurate in second order and has successfully passed with all tests performed, including highly relativistic and magnetized cases in both special and general relativity.
RAISHIN: A High-Resolution Three-Dimensional General Relativistic Magnetohydrodynamics Code
Mizuno, Y; Koide, S; Hardee, P; Fishman, G J; Mizuno, Yosuke; Nishikawa, Ken-Ichi; Koide, Shinji; Hardee, Philip; Fishman, Gerald J.
2006-01-01
We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high resolution shock-capturing scheme. The numerical fluxes are calculated using the Harten, Lax, & van Leer (HLL) approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. In order to examine the numerical accuracy and the numerical efficiency, the code uses four different reconstruction methods: piecewise linear methods with Minmod and MC slope-limiter function, convex essentially non-oscillatory (CENO) method, and piecewise parabolic method (PPM) using multistep TVD Runge-Kutta time advance methods with second and third-order time accuracy. We describe code performance on an extensive set of test problems in both special and general relativity. Our new GRMHD code has proven to be accurate in second order and has successfully passed with all tests performed, including highly relativistic and mag...
General-relativistic resistive magnetohydrodynamics in three dimensions: Formulation and tests
Dionysopoulou, Kyriaki; Alic, Daniela; Palenzuela, Carlos; Rezzolla, Luciano; Giacomazzo, Bruno
2013-08-01
We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of implicit-explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for large electrical conductivities. Using tests in one, two, and three dimensions, we show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing scenarios in a very wide range of conductivities. In addition to tests in flat spacetime, we report simulations of magnetized nonrotating relativistic stars, both in the Cowling approximation and in dynamical spacetimes. Finally, because of its astrophysical relevance and because it provides a severe tested for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that also in this case our results on the quasinormal mode frequencies of the excited electromagnetic fields in the Schwarzschild background agree with the perturbative studies within 0.7% and 5.6% for the real and the imaginary part of the ℓ=1 mode eigenfrequency, respectively. Finally we provide an estimate of the electromagnetic efficiency of this process.
Fragile, P Chris
2008-01-01
(Abridged) We present one of the first physically-motivated two-dimensional general relativistic magnetohydrodynamic (GRMHD) numerical simulations of a radiatively-cooled black-hole accretion disk. The fiducial simulation combines a total-energy-conserving formulation with a radiative cooling function, which includes bremsstrahlung, synchrotron, and Compton effects. By comparison with other simulations we show that in optically thin advection-dominated accretion flows, radiative cooling can significantly affect the structure, without necessarily leading to an optically thick, geometrically thin accretion disk. We further compare the results of our radiatively-cooled simulation to the predictions of a previously developed analytic model for such flows. For the very low stress parameter and accretion rate found in our simulated disk, we closely match a state called the "transition" solution between an outer advection-dominated accretion flow and what would be a magnetically-dominated accretion flow (MDAF) in th...
Energy Technology Data Exchange (ETDEWEB)
Shiokawa, Hotaka; Dolence, Joshua C.; Gammie, Charles F. [Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 West Green Street, Urbana, IL 61801 (United States); Noble, Scott C. [Center for Computational Relativity and Gravitation, School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623 (United States)
2012-01-10
Global, general relativistic magnetohydrodynamic (GRMHD) simulations of non-radiative, magnetized disks are widely used to model accreting black holes. We have performed a convergence study of GRMHD models computed with HARM3D. The models span a factor of four in linear resolution, from 96 Multiplication-Sign 96 Multiplication-Sign 64 to 384 Multiplication-Sign 384 Multiplication-Sign 256. We consider three diagnostics of convergence: (1) dimensionless shell-averaged quantities such as plasma {beta}; (2) the azimuthal correlation length of fluid variables; and (3) synthetic spectra of the source including synchrotron emission, absorption, and Compton scattering. Shell-averaged temperature is, except for the lowest resolution run, nearly independent of resolution; shell-averaged plasma {beta} decreases steadily with resolution but shows signs of convergence. The azimuthal correlation lengths of density, internal energy, and temperature decrease steadily with resolution but show signs of convergence. In contrast, the azimuthal correlation length of magnetic field decreases nearly linearly with grid size. We argue by analogy with local models, however, that convergence should be achieved with another factor of two in resolution. Synthetic spectra are, except for the lowest resolution run, nearly independent of resolution. The convergence behavior is consistent with that of higher physical resolution local model ({sup s}hearing box{sup )} calculations and with the recent non-relativistic global convergence studies of Hawley et al.
Endrizzi, A.; Ciolfi, R.; Giacomazzo, B.; Kastaun, W.; Kawamura, T.
2016-08-01
We present new results of fully general relativistic magnetohydrodynamic simulations of binary neutron star (BNS) mergers performed with the Whisky code. All the models use a piecewise polytropic approximation of the APR4 equation of state for cold matter, together with a ‘hybrid’ part to incorporate thermal effects during the evolution. We consider both equal and unequal-mass models, with total masses such that either a supramassive NS or a black hole is formed after merger. Each model is evolved with and without a magnetic field initially confined to the stellar interior. We present the different gravitational wave (GW) signals as well as a detailed description of the matter dynamics (magnetic field evolution, ejected mass, post-merger remnant/disk properties). Our simulations provide new insights into BNS mergers, the associated GW emission and the possible connection with the engine of short gamma-ray bursts (both in the ‘standard’ and in the ‘time-reversal’ scenarios) and other electromagnetic counterparts.
Endrizzi, Andrea; Giacomazzo, Bruno; Kastaun, Wolfgang; Kawamura, Takumu
2016-01-01
We present new results of fully general relativistic magnetohydrodynamic (GRMHD) simulations of binary neutron star (BNS) mergers performed with the Whisky code. All the models use a piecewise polytropic approximation of the APR4 equation of state (EOS) for cold matter, together with a "hybrid" part to incorporate thermal effects during the evolution. We consider both equal and unequal-mass models, with total masses such that either a supramassive NS or a black hole (BH) is formed after merger. Each model is evolved with and without a magnetic field initially confined to the stellar interior. We present the different gravitational wave (GW) signals as well as a detailed description of the matter dynamics (magnetic field evolution, ejected mass, post-merger remnant/disk properties). Our simulations provide new insights into BNS mergers, the associated GW emission and the possible connection with the engine of short gamma-ray bursts (both in the "standard" and in the "time-reversal" scenarios) and other electro...
Penna, Robert F; Sadowski, Aleksander
2013-01-01
Recently it has been observed that the scaling of jet power with black hole spin in galactic X-ray binaries is consistent with the predictions of the Blandford-Znajek (BZ) jet model. These observations motivate us to revisit the BZ model using general relativistic magnetohydrodynamic simulations of magnetized jets from accreting (h/r ~ 0.3), spinning (0 < a_* < 0.98) black holes. We have three main results. First, we quantify the discrepancies between the BZ jet power and our simulations: assuming maximum efficiency and uniform fields on the horizon leads to a ~10% overestimate of jet power, while ignoring the accretion disk leads to a further ~50% overestimate. Simply reducing the standard BZ jet power prediction by 60% gives a good fit to our simulation data. Our second result is to show that the membrane formulation of the BZ model correctly describes the physics underlying simulated jets: torques, dissipation, and electromagnetic fields on the horizon. This provides intuitive yet rigorous pictures f...
A General Relativistic Magnetohydrodynamics Simulation of Jet Formation with a State Transition
Nishikawa, K. I.; Richardson, G.; Koide, S.; Shibata, K.; Kudoh, T.; Hardee, P.; Fushman, G. J.
2004-01-01
We have performed the first fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation of jet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity sim 0.3c) is created as shown by previous two-dimensional axisymmetric simulations with mirror symmetry at the equator. The 3-D simulation ran over one hundred light-crossing time units which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted due in part to magnetic pressure from the twisting the initially uniform magnetic field and from gas pressure associated with shock formation. At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface of the thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outwards with a wider angle than the initial jet. The widening of the jet is consistent with the outward moving shock wave. This evolution of jet-disk coupling suggests that the low/hard state of the jet system may switch to the high/soft state with a wind, as the accretion rate diminishes.
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McKinney, Jonathan C.; Tchekhovskoy, Alexander; Blandford, Roger D.
2012-04-26
Black hole (BH) accretion flows and jets are qualitatively affected by the presence of ordered magnetic fields. We study fully three-dimensional global general relativistic magnetohydrodynamic (MHD) simulations of radially extended and thick (height H to cylindrical radius R ratio of |H/R| {approx} 0.2-1) accretion flows around BHs with various dimensionless spins (a/M, with BH mass M) and with initially toroidally-dominated ({phi}-directed) and poloidally-dominated (R-z directed) magnetic fields. Firstly, for toroidal field models and BHs with high enough |a/M|, coherent large-scale (i.e. >> H) dipolar poloidal magnetic flux patches emerge, thread the BH, and generate transient relativistic jets. Secondly, for poloidal field models, poloidal magnetic flux readily accretes through the disk from large radii and builds-up to a natural saturation point near the BH. While models with |H/R| {approx} 1 and |a/M| {le} 0.5 do not launch jets due to quenching by mass infall, for sufficiently high |a/M| or low |H/R| the polar magnetic field compresses the inflow into a geometrically thin highly non-axisymmetric 'magnetically choked accretion flow' (MCAF) within which the standard linear magneto-rotational instability is suppressed. The condition of a highly-magnetized state over most of the horizon is optimal for the Blandford-Znajek mechanism that generates persistent relativistic jets with and 100% efficiency for |a/M| {approx}> 0.9. A magnetic Rayleigh-Taylor and Kelvin-Helmholtz unstable magnetospheric interface forms between the compressed inflow and bulging jet magnetosphere, which drives a new jet-disk oscillation (JDO) type of quasi-periodic oscillation (QPO) mechanism. The high-frequency QPO has spherical harmonic |m| = 1 mode period of {tau} {approx} 70GM/c{sup 3} for a/M {approx} 0.9 with coherence quality factors Q {approx}> 10. Overall, our models are qualitatively distinct from most prior MHD simulations (typically, |H/R| << 1 and poloidal flux is
On the convexity of Relativistic Ideal Magnetohydrodynamics
Ibáñez, José-María; Aloy, Miguel-Ángel; Martí, José-María; Miralles, Juan-Antonio
2015-01-01
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity condition on the magnetic field. The result is expressed in the form of a generalized fundamental derivative written as the sum of two terms. The first one is the generalized fundamental derivative in the case of purely hydrodynamical (relativistic) flow. The second one contains the effects of the magnetic field. The analysis ...
Magnetohydrodynamics of Chiral Relativistic Fluids
Boyarsky, Alexey; Ruchayskiy, Oleg
2015-01-01
We study the dynamics of a plasma of charged relativistic fermions at very high temperature $T\\gg m$, where $m$ is the fermion mass, coupled to the electromagnetic field. In particular, we derive a magneto-hydrodynamical description of the evolution of such a plasma. We show that, as compared to conventional MHD for a plasma of non-relativistic particles, the hydrodynamical description of the relativistic plasma involves new degrees of freedom described by a pseudo-scalar field originating in a local asymmetry in the densities of left-handed and right-handed fermions. This field can be interpreted as an effective axion field. Taking into account the chiral anomaly we present dynamical equations for the evolution of this field, as well as of other fields appearing in the MHD description of the plasma. Due to its non-linear coupling to helical magnetic fields, the axion field significantly affects the dynamics of a magnetized plasma and can give rise to a novel type of inverse cascade.
Nagataki, S
2009-01-01
In order to investigate formation of relativistic jets at the center of a progenitor of a long gamma-ray burst (GRB), we develop a two-dimensional general relativistic magnetohydrodynamic (GRMHD) code. We show the code passes many, well-known test calculations, by which the reliability of the code is confirmed. Then we perform a numerical simulation of a collapsar using a realistic progenitor model. It is shown that a jet is launched from the center of the progenitor. We also find that the mass accretion rate after the launch of the jet shows rapid time variability that resembles to a typical time profile of a GRB. The structure of the jet is similar to the previous study: a poynting flux jet is surrounded by a funnel-wall jet. Even at the final stage of the simulation, bulk Lorentz factor of the jet is still low, and total energy of the jet is still as small as 10^48 erg. However, we find that the energy flux per unit rest-mass flux is as high as 10^2 at the bottom of the jet. Thus we conclude that the bulk ...
Anomalous magnetohydrodynamics in the extreme relativistic domain
Giovannini, Massimo
2016-01-01
The evolution equations of anomalous magnetohydrodynamics are derived in the extreme relativistic regime and contrasted with the treatment of hydromagnetic nonlinearities pioneered by Lichnerowicz in the absence of anomalous currents. In particular we explore the situation where the conventional vector currents are complemented by the axial-vector currents arising either from the pseudo Nambu-Goldstone bosons of a spontaneously broken symmetry or because of finite fermionic density effects. After expanding the generally covariant equations in inverse powers of the conductivity, the relativistic analog of the magnetic diffusivity equation is derived in the presence of vortical and magnetic currents. While the anomalous contributions are generally suppressed by the diffusivity, they are shown to disappear in the perfectly conducting limit. When the flow is irrotational, boost-invariant and with vanishing four-acceleration the corresponding evolution equations are explicitly integrated so that the various physic...
Takahashi, Hiroyuki R; Kawashima, Tomohisa; Sekiguchi, Yuichiro
2016-01-01
Using three-dimensional general relativistic radiation magnetohydrodynamics simulations of accretion flows around stellar mass black holes, we report that the relatively cold disk ($\\gtrsim 10^{7}$K) is truncated near the black hole. Hot and less-dense regions, of which the gas temperature is $ \\gtrsim 10^9$K and more than ten times higher than the radiation temperature (overheated regions), appear within the truncation radius. The overheated regions also appear above as well as below the disk, and sandwich the cold disk, leading to the effective Compton upscattering. The truncation radius is $\\sim 30 r_{\\rm g}$ for $\\dot{M} \\sim L_{\\rm Edd}/c^2$, where $r_{\\rm g}, \\dot M, L_\\mathrm{Edd}, c$ are the gravitational radius, mass accretion rate, Eddington luminosity, and light speed. Our results are consistent with observations of very high state, whereby the truncated disk is thought to be embedded in the hot rarefied regions. The truncation radius shifts inward to $\\sim 10 r_{\\rm g}$ with increasing mass accret...
Rarefaction wave in relativistic steady magnetohydrodynamic flows
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Sapountzis, Konstantinos, E-mail: ksapountzis@phys.uoa.gr; Vlahakis, Nektarios, E-mail: vlahakis@phys.uoa.gr [Faculty of Physics, University of Athens, 15784 Zografos, Athens (Greece)
2014-07-15
We construct and analyze a model of the relativistic steady-state magnetohydrodynamic rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity, we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow, we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.
COUNTER-ROTATION IN RELATIVISTIC MAGNETOHYDRODYNAMIC JETS
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Cayatte, V.; Sauty, C. [Laboratoire Univers et Théories, Observatoire de Paris, UMR 8102 du CNRS, Université Paris Diderot, F-92190 Meudon (France); Vlahakis, N.; Tsinganos, K. [Department of Astrophysics, Astronomy and Mechanics, Faculty of Physics, University of Athens, 15784 Zografos, Athens (Greece); Matsakos, T. [Department of Astronomy and Astrophysics, The University of Chicago, Chicago, IL 60637 (United States); Lima, J. J. G., E-mail: veronique.cayatte@obspm.fr [Centro de Astrofísica, Universidade do Porto, Rua das Estrelas, 4150-762 Porto (Portugal)
2014-06-10
Young stellar object observations suggest that some jets rotate in the opposite direction with respect to their disk. In a recent study, Sauty et al. showed that this does not contradict the magnetocentrifugal mechanism that is believed to launch such outflows. Motion signatures that are transverse to the jet axis, in two opposite directions, have recently been measured in M87. One possible interpretation of this motion is that of counter-rotating knots. Here, we extend our previous analytical derivation of counter-rotation to relativistic jets, demonstrating that counter-rotation can indeed take place under rather general conditions. We show that both the magnetic field and a non-negligible enthalpy are necessary at the origin of counter-rotating outflows, and that the effect is associated with a transfer of energy flux from the matter to the electromagnetic field. This can be realized in three cases: if a decreasing enthalpy causes an increase of the Poynting flux, if the flow decelerates, or if strong gradients of the magnetic field are present. An illustration of the involved mechanism is given by an example of a relativistic magnetohydrodynamic jet simulation.
McKinney, Jonathan C; Sadowski, Aleksander; Narayan, Ramesh
2013-01-01
Black hole (BH) accretion flows and jets are dynamic hot relativistic magnetized plasma flows whose radiative opacity can significantly affect flow structure and behavior. We describe a numerical scheme, tests, and an astrophysically relevant application using the M1 radiation closure within a new three-dimensional (3D) general relativistic (GR) radiation (R) magnetohydrodynamics (MHD) massively parallel code called HARMRAD. Our 3D GRRMHD simulation of super-Eddington accretion (about $20$ times Eddington) onto a rapidly rotating BH (dimensionless spin $j=0.9375$) shows sustained non-axisymmemtric disk turbulence, a persistent electromagnetic jet driven by the Blandford-Znajek effect, and a total radiative output consistently near the Eddington rate. The total accretion efficiency is of order $20\\%$, the large-scale electromagnetic jet efficiency is of order $10\\%$, and the total radiative efficiency that reaches large distances remains low at only order $1\\%$. However, the radiation jet and the electromagnet...
Resistive Magnetohydrodynamic Simulations of Relativistic Magnetic Reconnection
Zenitani, Seiji; Hesse, Michael; Klimas, Alex
2010-01-01
Resistive relativistic magnetohydrodynamic (RRMHD) simulations are applied to investigate the system evolution of relativistic magnetic reconnection. A time-split Harten-Lan-van Leer method is employed. Under a localized resistivity, the system exhibits a fast reconnection jet with an Alfv enic Lorentz factor inside a narrow Petschek-type exhaust. Various shock structures are resolved in and around the plasmoid such as the post-plasmoid vertical shocks and the "diamond-chain" structure due to multiple shock reflections. Under a uniform resistivity, Sweet-Parker-type reconnection slowly evolves. Under a current-dependent resistivity, plasmoids are repeatedly formed in an elongated current sheet. It is concluded that the resistivity model is of critical importance for RRMHD modeling of relativistic magnetic reconnection.
Resistive Magnetohydrodynamic Simulations of Relativistic Magnetic Reconnection
Zenitani, Seiji; Klimas, Alex
2010-01-01
Resistive relativistic magnetohydrodynamic (RRMHD) simulations are applied to investigate the system evolution of relativistic magnetic reconnection. A time-split Harten--Lan--van Leer (HLL) method is employed. Under a localized resistivity, the system exhibits a fast reconnection jet with an Alfv\\'{e}nic Lorentz factor inside a narrow Petschek-type exhaust. Various shock structures are resolved in and around the plasmoid such as the post-plasmoid vertical shocks and the "diamond--chain" structure due to multiple shock reflections. Under a uniform resistivity, Sweet--Parker-type reconnection slowly evolves. Under a current-dependent resistivity, plasmoids are repeatedly formed in an elongated current sheet. It is concluded that the resistivity model is of critical importance for RRMHD modeling of relativistic magnetic reconnection.
Relativistic Radiation Magnetohydrodynamics in Dynamical Spacetimes: Numerical Methods and Tests
2008-01-01
Many systems of current interest in relativistic astrophysics require a knowledge of radiative transfer in a magnetized gas flowing in a strongly-curved, dynamical spacetime. Such systems include coalescing compact binaries containing neutron stars or white dwarfs, disks around merging black holes, core collapse supernovae, collapsars, and gamma-ray burst sources. To model these phenomena, all of which involve general relativity, radiation (photon and/or neutrino), and magnetohydrodynamics, w...
Efficient Acceleration of Relativistic Magnetohydrodynamic Jets
Toma, Kenji
2013-01-01
Relativistic jets in active galactic nuclei, galactic microquasars, and gamma-ray bursts are widely considered to be magnetohydrodynamically driven by black hole accretion systems, although conversion mechanism from Poynting into particle kinetic energy flux is still open. Recent detailed numerical and analytical studies of global structures of steady, axisymmetric magnetohydrodynamic (MHD) flows with specific boundary conditions have not reproduced as rapid an energy conversion as required by observations. In order to find more suitable boundary conditions, we focus on the flow along a poloidal magnetic field line just inside the external boundary, without treating transfield force balance in detail. We find some examples of the poloidal field structure and corresponding external pressure profile for an efficient and rapid energy conversion as required by observations, and that the rapid acceleration requires a rapid decrease of the external pressure above the accretion disk. We also clarify the differences ...
Resistive relativistic magnetohydrodynamics from a charged multi-fluids perspective
Andersson, N
2012-01-01
We consider general relativistic magnetohydrodynamics from a charged multifluids point-of-view, taking a variational approach as our starting point. We develop the case of two charged components in detail, accounting for a phenomenological resistivity, providing specific examples for pair plasmas and proton-electron systems. We discuss both cold, low velocity, plasmas and hot systems where we account for a dynamical entropy component. The results for the cold case (which accord with recent work in the literature) provide a complete model for resistive relativistic magnetohydrodynamics, clarifying the assumptions that lead to various models that have been used in astrophysical applications. The analysis of the hot case is (as far as we are aware) novel, accounting for the relaxation times that are required to ensure causality and demonstrating the explicit coupling between fluxes of heat and charge.
A Magnetohydrodynamic Boost for Relativistic Jets
Mizuno, Yosuke; Hardee, Philip; Hartmann, Dieter H.; Nishikawa, Ken-Ichi; Zhang, Bing
2007-01-01
We performed relativistic magnetohydrodynamic simulations of the hydrodynamic boosting mechanism for relativistic jets explored by Aloy & Rezzolla (2006) using the RAISHIN code. Simulation results show that the presence of a magnetic field changes the properties of the shock interface between the tenuous, overpressured jet (V^z j) flowing tangentially to a dense external medium. We find that magnetic fields can lead to more efficient acceleration of the jet, in comparison to the pure-hydrodynamic case. A "poloidal" magnetic field (B^z), tangent to the interface and parallel to the jet flow, produces both a stronger outward moving shock and a stronger inward moving rarefaction wave. This leads to a large velocity component normal to the interface in addition to acceleration tangent to the interface, and the jet is thus accelerated to larger Lorentz factors than those obtained in the pure-hydrodynamic case. Likewise, a strong "toroidal" magnetic field (B^y), tangent to the interface but perpendicular to the jet flow, also leads to stronger acceleration tangent to the shock interface relative to the pure-hydrodynamic case. Thus. the presence and relative orientation of a magnetic field in relativistic jets can significant modify the hydrodynamic boost mechanism studied by Aloy & Rezzolla (2006).
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics
Mohseni, F; Succi, S; Herrmann, H J
2015-01-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfv\\'en waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to $\\sigma^{-\\frac{1}{2}}$, $\\sigma$ being the conductivity, w...
Generalized reduced magnetohydrodynamic equations
Energy Technology Data Exchange (ETDEWEB)
Kruger, S.E.
1999-02-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics.
Linear wave propagation in relativistic magnetohydrodynamics
Keppens, R
2008-01-01
The properties of linear Alfv\\'en, slow, and fast magnetoacoustic waves for uniform plasmas in relativistic magnetohydrodynamics (MHD) are discussed, augmenting the well-known expressions for their phase speeds with knowledge on the group speed. A 3+1 formalism is purposely adopted to make direct comparison with the Newtonian MHD limits easier and to stress the graphical representation of their anisotropic linear wave properties using the phase and group speed diagrams. By drawing these for both the fluid rest frame and for a laboratory Lorentzian frame which sees the plasma move with a three-velocity having an arbitrary orientation with respect to the magnetic field, a graphical view of the relativistic aberration effects is obtained for all three MHD wave families. Moreover, it is confirmed that the classical Huygens construction relates the phase and group speed diagram in the usual way, even for the lab frame viewpoint. Since the group speed diagrams correspond to exact solutions for initial conditions co...
Imbalanced Relativistic Force-Free Magnetohydrodynamic Turbulence
Cho, Jungyeon
2013-01-01
When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfv\\'enic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). We find that (1) spectrum of the dominant waves is steeper than that of sub-dominant waves, (2) the anisotropy of the dominant waves is weaker than that of sub-dominant waves, and (3) the dependence of the ratio of magnetic energy densities of dominant and sub-dominant waves on the ratio of energy injection rates is steeper than quadratic (i.e., \\$b_+^2/b_-^2 \\propto (\\epsilon_+/\\epsilon_-)^n \\$ with n>2). These result...
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.
Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics
Keppens, R.; Meliani, Z.; van Marle, A. J.; Delmont, P.; Vlasis, A.; van der Holst, B.
2012-01-01
Relativistic hydro and magnetohydrodynamics provide continuum fluid descriptions for gas and plasma dynamics throughout the visible universe. We present an overview of state-of-the-art modeling in special relativistic regimes, targeting strong shock-dominated flows with speeds approaching the speed
Propagation of linear waves in relativistic anisotropic magnetohydrodynamics.
Gebretsadkan, W B; Kalra, G L
2002-11-01
Gedalin [Phys. Rev. E 47, 4354 (1993)] derived a dispersion relation for linear waves in relativistic anisotropic Magnetohydrodynamics (MHD). This dispersion relation is used to point out the regions where the relativistic anisotropic MHD leads to new results that cannot be obtained using usual collisional relativistic MHD. This is highlighted by plotting a Fresnal ray surface. Conditions for the onset of firehose and mirror instabilities are also indicated. Such a study can be applied to astrophysical features such as pulsar winds, propagation of cosmic rays, etc.
Acceleration and Collimation of Relativistic Magnetohydrodynamic Disk Winds
Porth, Oliver; Fendt, Christian
2010-02-01
We perform axisymmetric relativistic magnetohydrodynamic simulations to investigate the acceleration and collimation of jets and outflows from disks around compact objects. Newtonian gravity is added to the relativistic treatment in order to establish the physical boundary condition of an underlying accretion disk in centrifugal and pressure equilibrium. The fiducial disk surface (respectively a slow disk wind) is prescribed as boundary condition for the outflow. We apply this technique for the first time in the context of relativistic jets. The strength of this approach is that it allows us to run a parameter study in order to investigate how the accretion disk conditions govern the outflow formation. Substantial effort has been made to implement a current-free, numerical outflow boundary condition in order to avoid artificial collimation present in the standard outflow conditions. Our simulations using the PLUTO code run for 500 inner disk rotations and on a physical grid size of 100 × 200 inner disk radii. The simulations evolve from an initial state in hydrostatic equilibrium and an initially force-free magnetic field configuration. Two options for the initial field geometries are applied—an hourglass-shaped potential magnetic field and a split monopole field. Most of our parameter runs evolve into a steady state solution which can be further analyzed concerning the physical mechanism at work. In general, we obtain collimated beams of mildly relativistic speed with Lorentz factors up to 6 and mass-weighted half-opening angles of 3-7 deg. The split-monopole initial setup usually results in less collimated outflows. The light surface of the outflow magnetosphere tends to align vertically—implying three relativistically distinct regimes in the flow—an inner subrelativistic domain close to the jet axis, a (rather narrow) relativistic jet and a surrounding subrelativistic outflow launched from the outer disk surface—similar to the spine-sheath structure
Generalized global symmetries and dissipative magnetohydrodynamics
Grozdanov, Sašo; Iqbal, Nabil
2016-01-01
The conserved magnetic flux of U(1) electrodynamics coupled to matter in four dimensions is associated with a generalized global symmetry. We study the realization of such a symmetry at finite temperature and develop the hydrodynamic theory describing fluctuations of a conserved 2-form current around thermal equilibrium. This can be thought of as a systematic derivation of relativistic magnetohydrodynamics, constrained only by symmetries and effective field theory. We construct the entropy current and show that at first order in derivatives, there are six dissipative transport coefficients. We present a universal definition of resistivity in a theory of dynamical electromagnetism and derive a direct Kubo formula for the resistivity in terms of correlation functions of the electric field operator. We also study fluctuations and collective modes, deriving novel expressions for the dissipative widths of magnetosonic and Alfven modes. Finally, we demonstrate that a non-trivial truncation of the theory can be perf...
Formation of relativistic jets. Magnetohydrodynamics and synchrotron radiation
Energy Technology Data Exchange (ETDEWEB)
Porth, Oliver Joachim Georg
2011-11-09
In this thesis, the formation of relativistic jets is investigated by means of special relativistic magnetohydrodynamic simulations and synchrotron radiative transfer. Our results show that the magnetohydrodynamic jet self-collimation paradigm can also be applied to the relativistic case. In the first part, jets launched from rotating hot accretion disk coronae are explored, leading to well collimated, but only mildly relativistic flows. Beyond the light-cylinder, the electric charge separation force balances the classical trans-field Lorentz force almost entirely, resulting in a decreased efficiency of acceleration and collimation in comparison to non-relativistic disk winds. In the second part, we examine Poynting dominated flows of various electric current distributions. By following the outflow for over 3000 Schwarzschild radii, highly relativistic jets of Lorentz factor Γ>or similar 8 and half-opening angles below 1 are obtained, providing dynamical models for the parsec scale jets of active galactic nuclei. Applying the magnetohydrodynamic structure of the quasi-stationary simulation models, we solve the relativistically beamed synchrotron radiation transport. This yields synthetic radiation maps and polarization patterns that can be used to confront high resolution radio and (sub-) mm observations of nearby active galactic nuclei. Relativistic motion together with the helical magnetic fields of the jet formation site imprint a clear signature on the observed polarization and Faraday rotation. In particular, asymmetries in the polarization direction across the jet can disclose the handedness of the magnetic helix and thus the spin direction of the central engine. Finally, we show first results from fully three-dimensional, high resolution adaptive mesh refinement simulations of jet formation from a rotating magnetosphere and examine the jet stability. Relativistic field-line rotation leads to an electric charge separation force that opposes the magnetic
Polko, Peter; Markoff, Sera
2012-01-01
We present a new, approximate method for modelling the acceleration and collimation of relativistic jets in the presence of gravity. This method is self-similar throughout the computational domain where gravitational effects are negligible and, where significant, self-similar within a flux tube. These solutions are applicable to jets launched from a small region (e.g., near the inner edge of an accretion disk). As implied by earlier work, the flow can converge onto the rotation axis, potentially creating a collimation shock. In this first version of the method, we derive the gravitational contribution to the relativistic equations by analogy with non-relativistic flow. This approach captures the relativistic kinetic gravitational mass of the flowing plasma, but not that due to internal thermal and magnetic energies. A more sophisticated treatment, derived from the basic general relativistic magnetohydrodynamical equations, is currently being developed. Here we present an initial exploration of parameter space...
Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2008-09-01
Full Text Available This article presents a comprehensive overview of numerical hydrodynamics and magnetohydrodynamics (MHD in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003, most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable
Kawazura, Yohei; Morrison, Philip J
2016-01-01
Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, the action principles lead to relativistic Hall MHD and well-known relativistic ideal MHD. For the first time, the Hamiltonian formulation of relativistic Hall MHD with electron thermal inertia (akin to [Comisso \\textit{et al.}, Phys. Rev. Lett. {\\bf 113}, 045001 (2014)] for the electron--positron plasma) is introduced. This thermal inertia effect allows for violation of the frozen-in magnetic flux condition in marked con...
Numerical magneto-hydrodynamics for relativistic nuclear collisions
Inghirami, Gabriele; Beraudo, Andrea; Moghaddam, Mohsen Haddadi; Becattini, Francesco; Bleicher, Marcus
2016-01-01
We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magnetohydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant $3\\!+\\!1$ formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the Quark-Gluon Plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic-flow of the final hadrons. However, s...
Numerical magneto-hydrodynamics for relativistic nuclear collisions
Inghirami, Gabriele; Del Zanna, Luca; Beraudo, Andrea; Moghaddam, Mohsen Haddadi; Becattini, Francesco; Bleicher, Marcus
2016-12-01
We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magneto-hydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant 3+1 formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the quark-gluon plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic flow of the final hadrons. However, since there are uncertainties in the description of the pre-equilibrium phase and also in the properties of the medium, a more extensive survey of the possible initial conditions as well as the inclusion of dissipative effects are indeed necessary to validate this preliminary result.
Numerical magneto-hydrodynamics for relativistic nuclear collisions
Energy Technology Data Exchange (ETDEWEB)
Inghirami, Gabriele [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Goethe-Universitaet, Institute for Theoretical Physics, Frankfurt am Main (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Forschungszentrum Juelich, John von Neumann Institute for Computing, Juelich (Germany); Del Zanna, Luca [Universita di Firenze, Dipartimento di Fisica e Astronomia, Firenze (Italy); INAF - Osservatorio Astrofisico di Arcetri, Firenze (Italy); INFN - Sezione di Firenze, Firenze (Italy); Beraudo, Andrea [INFN - Sezione di Torino, Torino (Italy); Moghaddam, Mohsen Haddadi [INFN - Sezione di Torino, Torino (Italy); Hakim Sabzevari University, Department of Physics, P. O. Box 397, Sabzevar (Iran, Islamic Republic of); Becattini, Francesco [Universita di Firenze, Dipartimento di Fisica e Astronomia, Firenze (Italy); INFN - Sezione di Firenze, Firenze (Italy); Bleicher, Marcus [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Goethe-Universitaet, Institute for Theoretical Physics, Frankfurt am Main (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Forschungszentrum Juelich, John von Neumann Institute for Computing, Juelich (Germany)
2016-12-15
We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magneto-hydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant 3 + 1 formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the quark-gluon plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic flow of the final hadrons. However, since there are uncertainties in the description of the pre-equilibrium phase and also in the properties of the medium, a more extensive survey of the possible initial conditions as well as the inclusion of dissipative effects are indeed necessary to validate this preliminary result. (orig.)
An introduction to relativistic magnetohydrodynamics I. The force-free approximation
Karas, Vladimír
2005-12-01
This lecture summarizes basic equations of relativistic magnetohydrodynamics (MHD). The aim of the lecture is to present important relations and approximations that have been often employed and found useful in the astrophysical context, namely, in situations when plasma motion is governed by magnetohydrodynamic and gravitational effects competing with each other near a black hole.
Kawazura, Yohei; Miloshevich, George; Morrison, Philip J.
2017-02-01
Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, the action principles lead to relativistic Hall MHD and well-known relativistic ideal MHD. For the first time, the Hamiltonian formulation of relativistic Hall MHD with electron thermal inertia (akin to Comisso et al., Phys. Rev. Lett. 113, 045001 (2014) for the electron-positron plasma) is introduced. This thermal inertia effect allows for violation of the frozen-in magnetic flux condition in marked contrast to nonrelativistic Hall MHD that does satisfy the frozen-in condition. We also find the violation of the frozen-in condition is accompanied by freezing-in of an alternative flux determined by a generalized vector potential. Finally, we derive a more general 3 + 1 Poisson bracket for nonrelativistic extended MHD, one that does not assume smallness of the electron ion mass ratio.
Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited
Del Zanna, L; Landi, S; Bugli, M; Bucciantini, N
2016-01-01
Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula, hence its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two dimensional numerical simulations, the linear phase and the subsequent nonlinear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics, as appropriate in situations where the Alfven velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S^-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S^-1/3 are considered, the so-called "ideal" tearing regime is retriev...
Beyond ideal magnetohydrodynamics: Resistive, reactive and relativistic plasmas
Andersson, N; Hawke, I; Comer, G L
2016-01-01
We develop a new framework for the modelling of charged fluid dynamics in general relativity. The model, which builds on a recently developed variational multi-fluid model for dissipative fluids, accounts for relevant effects like the inertia of both charge currents and heat and, for mature systems, the decoupling of superfluid components. We discuss how the model compares to standard relativistic magnetohydronamics and consider the connection between the fluid dynamics, the microphysics and the underlying equation of state. As illustrations of the formalism, we consider three distinct two-fluid models describing i) an Ohm's law for resistive charged flows, ii) a relativistic heat equation, and iii) an equation representing the momentum of a decoupled superfluid component. As a more complex example, we also formulate a three-fluid model which demonstrates the thermo-electric effect. This framework allows us to model neutron stars (and related systems) at a hierarchy of increasingly complex levels, and should ...
Anton, L; Marti, J M; Ibanez, J M; Aloy, M A; Mimica, P
2009-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numeric...
Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited
Del Zanna, L.; Papini, E.; Landi, S.; Bugli, M.; Bucciantini, N.
2016-08-01
Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula; hence, its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two-dimensional numerical simulations, the linear phase and the subsequent non-linear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics (MHD), as appropriate in situations where the Alfvén velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S-1/3 are considered, the so-called ideal tearing regime is retrieved, with modes growing independently of S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfvén velocity. In the fully non-linear stage, we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfvén speed from the X-point, and a fast reconnection rate at the predicted value {R}˜ (ln S)^{-1}.
Energy Technology Data Exchange (ETDEWEB)
Maroof, R. [Department of Physics, Abdul Wali Khan University, Mardan 23200 (Pakistan); Department of Physics, University of Peshawar, Peshawar 25000 (Pakistan); National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Ali, S. [National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Mushtaq, A. [Department of Physics, Abdul Wali Khan University, Mardan 23200 (Pakistan); National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Qamar, A. [Department of Physics, University of Peshawar, Peshawar 25000 (Pakistan)
2015-11-15
Linear properties of high and low frequency waves are studied in an electron-positron-ion (e-p-i) dense plasma with spin and relativity effects. In a low frequency regime, the magnetohydrodynamic (MHD) waves, namely, the magnetoacoustic and Alfven waves are presented in a magnetized plasma, in which the inertial ions are taken as spinless and non-degenerate, whereas the electrons and positrons are treated quantum mechanically due to their smaller mass. Quantum corrections associated with the spin magnetization and density correlations for electrons and positrons are re-considered and a generalized dispersion relation for the low frequency MHD waves is derived to account for relativistic degeneracy effects. On the basis of angles of propagation, the dispersion relations of different modes are discussed analytically in a degenerate relativistic plasma. Numerical results reveal that electron and positron relativistic degeneracy effects significantly modify the dispersive properties of MHD waves. Our present analysis should be useful for understanding the collective interactions in dense astrophysical compact objects, like, the white dwarfs and in atmosphere of neutron stars.
Magnetohydrodynamical simulations of a tidal disruption in general relativity
Sadowski, A; Gafton, E; Rosswog, S; Abarca, D
2015-01-01
We perform hydro- and magnetohydrodynamical general relativistic simulations of a tidal disruption of a $0.1\\,M_\\odot$ red dwarf approaching a $10^5\\,M_\\odot$ non-rotating massive black hole on a close (impact parameter $\\beta=10$) elliptical (eccentricity $e=0.97$) orbit. We track the debris self-interaction, circularization, and the accompanying accretion through the black hole horizon. We find that the relativistic precession leads to the formation of a self-crossing shock. The dissipated kinetic energy heats up the incoming debris and efficiently generates a quasi-spherical outflow. The self-interaction is modulated because of the feedback exerted by the flow on itself. The debris quickly forms a thick, almost marginally bound disc that remains turbulent for many orbital periods. Initially, the accretion through the black hole horizon results from the self-interaction, while in the later stages it is dominated by the debris originally ejected in the shocked region, as it gradually falls back towards the h...
Energy Technology Data Exchange (ETDEWEB)
Fuerst, Steven V.; /KIPAC, Menlo Park; Mizuno, Yosuke; /USRA, Huntsville; Nishikawa, Ken-Ichi; /USRA, Huntsville /Alabama U., Huntsville; Wu, Kinwah; /Mullard Space Sci.
2007-01-05
We calculate the emission from relativistic flows in black hole systems using a fully general relativistic radiative transfer formulation, with flow structures obtained by general relativistic magneto-hydrodynamic simulations. We consider thermal free-free emission and thermal synchrotron emission. Bright filament-like features protrude (visually) from the accretion disk surface, which are enhancements of synchrotron emission where the magnetic field roughly aligns with the line-of-sight in the co-moving frame. The features move back and forth as the accretion flow evolves, but their visibility and morphology are robust. We propose that variations and drifts of the features produce certain X-ray quasi-periodic oscillations (QPOs) observed in black-hole X-ray binaries.
Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization
Pu, Shi; Rezzolla, Luciano; Rischke, Dirk H
2016-01-01
We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work [1], we consider the fluid to have a non-zero magnetization. First, we assume a constant magnetic susceptibility $\\chi_{m}$ and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with $\\chi_{m}>0$), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with $\\chi_{m}<0$), the energy density decays faster because it feeds energy into the magnetic field. Furthermore, when the magnetic field is taken to be external and to decay in proper time $\\tau$ with a power law $\\sim\\tau^{-a}$, two distinct solutions can be found depending on the values of $a$ and $\\chi_m$. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional...
Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization
Pu, Shi; Roy, Victor; Rezzolla, Luciano; Rischke, Dirk H.
2016-04-01
We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work Roy et al., [Phys. Lett. B 750, 45 (2015)], we consider the fluid to have a nonzero magnetization. First, we assume a constant magnetic susceptibility χm and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with χm>0 ), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with χmlaw ˜τ-a, two distinct solutions can be found depending on the values of a and χm. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional Bjorken flow with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data. We find that the temperature and energy density decay more slowly because of the nonvanishing magnetization. For values of the magnetic field typical for heavy-ion collisions, this effect is, however, rather small. It is only for magnetic fields about an order of magnitude larger than expected for heavy-ion collisions that the system is substantially reheated and the lifetime of the quark phase might be extended.
Nakamura, Masanori
2014-01-01
We describe a new paradigm for understanding both relativistic motions and particle acceleration in the M87 jet: a magnetically dominated relativistic flow that naturally produces four relativistic magnetohydrodynamic (MHD) shocks (forward/reverse fast and slow modes). We apply this model to a set of optical super- and subluminal motions discovered by Biretta and coworkers with the {\\em Hubble Space Telescope} during 1994 -- 1998. The model concept consists of ejection of a {\\em single} relativistic Poynting jet, which possesses a coherent helical (poloidal + toroidal) magnetic component, at the remarkably flaring point HST-1. We are able to reproduce quantitatively proper motions of components seen in the {\\em optical} observations of HST-1 with the same model we used previously to describe similar features in radio VLBI observations in 2005 -- 2006. This indicates that the quad relativistic MHD shock model can be applied generally to recurring pairs of super/subluminal knots ejected from the upstream edge o...
Zhang, Haocheng; Li, Hui; Guo, Fan; Taylor, Greg
2017-02-01
Kink instabilities are likely to occur in the current-carrying magnetized plasma jets. Recent observations of the blazar radiation and polarization signatures suggest that the blazar emission region may be considerably magnetized. While the kink instability has been studied with first-principle magnetohydrodynamic (MHD) simulations, the corresponding time-dependent radiation and polarization signatures have not been investigated. In this paper, we perform comprehensive polarization-dependent radiation modeling of the kink instability in the blazar emission region based on relativistic MHD (RMHD) simulations. We find that the kink instability may give rise to strong flares with polarization angle (PA) swings or weak flares with polarization fluctuations, depending on the initial magnetic topology and magnetization. These findings are consistent with observations. Compared with the shock model, the kink model generates polarization signatures that are in better agreement with the general polarization observations. Therefore, we suggest that kink instabilities may widely exist in the jet environment and provide an efficient way to convert the magnetic energy and produce multiwavelength flares and polarization variations.
General relativity and relativistic astrophysics
Mukhopadhyay, Banibrata
2016-01-01
Einstein established the theory of general relativity and the corresponding field equation in 1915 and its vacuum solutions were obtained by Schwarzschild and Kerr for, respectively, static and rotating black holes, in 1916 and 1963, respectively. They are, however, still playing an indispensable role, even after 100 years of their original discovery, to explain high energy astrophysical phenomena. Application of the solutions of Einstein's equation to resolve astrophysical phenomena has formed an important branch, namely relativistic astrophysics. I devote this article to enlightening some of the current astrophysical problems based on general relativity. However, there seem to be some issues with regard to explaining certain astrophysical phenomena based on Einstein's theory alone. I show that Einstein's theory and its modified form, both are necessary to explain modern astrophysical processes, in particular, those related to compact objects.
General relativistic Boltzmann equation, I: Covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
This series of two articles aims at dissipating the rather dense haze existing in the present literature around the General Relativistic Boltzmann equation. In this first article, the general relativistic one-particle distribution function in phase space is defined as an average of delta functions.
Takamoto, Makoto
2016-01-01
In this Letter, we report compressible mode effects on relativistic magnetohydrodynamic (RMHD) turbulence in Poynting-dominated plasmas using 3-dimensional numerical simulations. We decomposed fluctuations in the turbulence into 3 MHD modes (fast, slow, and Alfv\\'en) following the procedure mode decomposition in (Cho & Lazarian 2002), and analyzed their energy spectra and structure functions separately. We also analyzed the ratio of compressible mode to Alfv\\'en mode energy with respect to its Mach number. We found the ratio of compressible mode increases not only with the Alfv\\'en Mach number but with the background magnetization, which indicates a strong coupling between the fast and Alfv\\'en modes and appearance of a new regime of RMHD turbulence in Poynting-dominated plasmas where the fast and Alfv\\'en modes strongly couples and cannot be distinguished, different from the non-relativistic MHD case. This finding will affect particle acceleration efficiency obtained by assuming Alfv\\'enic critical balan...
Conservation of Circulation in Magnetohydrodynamics
Bekenstein, J D; Bekenstein, Jacob D.; Oron, Asaf
2000-01-01
We demonstrate, both at the Newtonian and (general) relativistic levels, theexistence of a generalization of Kelvin's circulation theorem (for pure fluids)which is applicable to perfect magnetohydrodynamics. The argument is based onthe least action principle for magnetohydrodynamic flow. Examples of the newconservation law are furnished. The new theorem should be helpful inidentifying new kinds of vortex phenomena distinct from magnetic ropes or fluidvortices.
A five-wave Harten-Lax-van Leer Riemann solver for relativistic magnetohydrodynamics
Mignone, A.; Ugliano, M.; Bodo, G.
2009-03-01
We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a non-linear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten-Lax-van Leer solver or the recently proposed HLLC schemes.
Zhang, Haocheng; Li, Hui; Böttcher, Markus
2015-01-01
The optical radiation and polarization signatures in blazars are known to be highly variable during flaring activities. It is frequently argued that shocks are the main driver of the flaring events. However, the spectral variability modelings generally lack detailed considerations of the self-consistent magnetic field evolution modeling, thus so far the associated optical polarization signatures are poorly understood. We present the first simultaneous modeling of the optical radiation and polarization signatures based on 3D magnetohydrodynamic simulations of relativistic shocks in the blazar emission environment, with the simplest physical assumptions. By comparing the results with observations, we find that shocks in a weakly magnetized environment will largely lead to significant changes in the optical polarization signatures, which are seldom seen in observations. Hence an emission region with relatively strong magnetization is preferred. In such an environment, slow shocks may produce minor flares with ei...
General relativistic corrections and non-Gaussianity
Villa, Eleonora; Matarrese, Sabino
2014-01-01
General relativistic cosmology cannot be reduced to linear relativistic perturbations superposed on an isotropic and homogeneous (Friedmann-Robertson-Walker) background, even though such a simple scheme has been successfully applied to analyse a large variety of phenomena (such as Cosmic Microwave Background primary anisotropies, matter clustering on large scales, weak gravitational lensing, etc.). The general idea of going beyond this simple paradigm is what characterises most of the efforts made in recent years: the study of second and higher-order cosmological perturbations including all general relativistic contributions -- also in connection with primordial non-Gaussianities -- the idea of defining large-scale structure observables directly from a general relativistic perspective, the various attempts to go beyond the Newtonian approximation in the study of non-linear gravitational dynamics, by using e.g., Post-Newtonian treatments, are all examples of this general trend. Here we summarise some of these ...
General Relativistic Simulations of Magnetized Binary Neutron Stars
Giacomazzo, Bruno
2011-04-01
Binary neutron stars are among the most important sources of gravitational waves which are expected to be detected by the current or next generation of gravitational wave detectors, such as LIGO and Virgo, and they are also thought to be at the origin of very important astrophysical phenomena, such as short gamma-ray bursts. I will report on some recent results obtained using the fully general relativistic magnetohydrodynamic code Whisky in simulating equal-mass binary neutron star systems during the last phases of inspiral, merger and collapse to black hole surrounded by a torus. I will in particular describe how magnetic fields can affect the gravitational wave signal emitted by these sources and their possible role in powering short gamma-ray bursts.
Generalized similarity in finite range solar wind magnetohydrodynamic turbulence.
Chapman, S C; Nicol, R M
2009-12-11
Extended or generalized similarity is a ubiquitous but not well understood feature of turbulence that is realized over a finite range of scales. The ULYSSES spacecraft solar polar passes at solar minimum provide in situ observations of evolving anisotropic magnetohydrodynamic turbulence in the solar wind under ideal conditions of fast quiet flow. We find a single generalized scaling function characterizes this finite range turbulence and is insensitive to plasma conditions. The recent unusually inactive solar minimum--with turbulent fluctuations down by a factor of approximately 2 in power--provides a test of this invariance.
Equation of State in Relativistic Magnetohydrodynamics: variable versus constant adiabatic index
Mignone, A
2007-01-01
The role of the equation of state for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant $\\Gamma$-law equation of state, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic equation of state that better approximates the single-specie relativistic gas. The paper focus on three different topics. First, the influence of a more realistic equation of state on the propagation of fast magneto-sonic shocks is investigated. This calls into question the validity of the constant $\\Gamma$-law equation of state in problems where the temperature of the gas substantially changes across hydromagnetic waves. Second, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general equation of state and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of ast...
General relativistic observables of the GRAIL mission
Turyshev, Slava G; Sazhin, Mikhail V
2012-01-01
We present a realization of astronomical relativistic reference frames in the solar system and its application to the GRAIL mission. We model the necessary spacetime coordinate transformations for light-trip time computations and address some practical aspects of the implementation of the resulting model. We develop all the relevant relativistic coordinate transformations that are needed to describe the motion of the GRAIL spacecraft and to compute all observable quantities. We take into account major relativistic effects contributing to the dual one-way range observable, which is derived from one-way signal travel times between the two GRAIL spacecraft. We develop a general relativistic model for this fundamental observable of GRAIL, accurate to 1 $\\mu$m. We develop and present a relativistic model for another key observable of this experiment, the dual one-way range-rate, accurate to 1 $\\mu$m/s. The presented formulation justifies the basic assumptions behind the design of the GRAIL mission. It may also be ...
Matsumoto, Jin; Masada, Youhei; Asano, Eiji; Shibata, Kazunari
2011-06-01
The nonlinear dynamics of the outflow driven by magnetic explosion on the surface of compact object is investigated through special relativistic magnetohydrodynamic simulations. We adopt, as an initial equilibrium state, a spherical stellar object embedded in the hydrostatic plasma which has a density ρ(r) ~ r-α and is threaded by a dipole magnetic field. The injection of magnetic energy at the surface of compact star breaks the dynamical equilibrium and triggers two-component outflow. At the early evolutionary stage, the magnetic pressure increases rapidly in time around the stellar surface, initiating a magnetically driven outflow. Then it excites a strong forward shock, shock driven outflow. The expansion velocity of the magnetically driven outflow is characterized by the Alfvén velocity on the stellar surface, and follows a simple scaling relation υmag ~ υA1/2. When the initial density profile declines steeply with radius, the strong shock is accelerated self-similarly to relativistic velocity ahead of the magnetically driven component. We find that the evolution of the strong forward shock can be described by a self-similar relation Γsh ~ rsh, where Γsh is the Lorentz factor of the plasma measured at the shock surface rsh. It should be stressed that the pure hydrodynamic process is responsible for the acceleration of the shock driven outflow. Our two-component outflow model, which is the natural outcome of the magnetic explosion, would deepen the understanding of the magnetic active phenomena on various magnetized stellar objects.
Approximate Harten-Lax-van Leer Riemann solvers for relativistic magnetohydrodynamics
Mignone, Andrea; Bodo, G.; Ugliano, M.
2012-11-01
We review a particular class of approximate Riemann solvers in the context of the equations of ideal relativistic magnetohydrodynamics. Commonly prefixed as Harten-Lax-van Leer (HLL), this family of solvers approaches the solution of the Riemann problem by providing suitable guesses to the outermots characteristic speeds, without any prior knowledge of the solution. By requiring consistency with the integral form of the conservation law, a simplified set of jump conditions with a reduced number of characteristic waves may be obtained. The degree of approximation crucially depends on the wave pattern used in prepresnting the Riemann fan arising from the initial discontinuity breakup. In the original HLL scheme, the solution is approximated by collapsing the full characteristic structure into a single average state enclosed by two outermost fast mangnetosonic speeds. On the other hand, HLLC and HLLD improves the accuracy of the solution by restoring the tangential and Alfvén modes therefore leading to a representation of the Riemann fan in terms of 3 and 5 waves, respectively.
Stochastic oscillations of general relativistic disks
Harko, Tiberiu
2012-01-01
We analyze the general relativistic oscillations of thin accretion disks around compact astrophysical objects interacting with the surrounding medium through non-gravitational forces. The interaction with the external medium (a thermal bath) is modeled via a friction force, and a random force, respectively. The general equations describing the stochastically perturbed disks are derived by considering the perturbations of trajectories of the test particles in equatorial orbits, assumed to move along the geodesic lines. By taking into account the presence of a viscous dissipation and of a stochastic force we show that the dynamics of the stochastically perturbed disks can be formulated in terms of a general relativistic Langevin equation. The stochastic energy transport equation is also obtained. The vertical oscillations of the disks in the Schwarzschild and Kerr geometries are considered in detail, and they are analyzed by numerically integrating the corresponding Langevin equations. The vertical displacement...
General Relativistic Effects in Atom Interferometry
Energy Technology Data Exchange (ETDEWEB)
Dimopoulos, Savas; /Stanford U., Phys. Dept.; Graham, Peter W.; /SLAC /Stanford U., Phys. Dept.; Hogan, Jason M.; Kasevich, Mark A.; /Stanford U., Phys. Dept.
2008-03-17
Atom interferometry is now reaching sufficient precision to motivate laboratory tests of general relativity. We begin by explaining the non-relativistic calculation of the phase shift in an atom interferometer and deriving its range of validity. From this we develop a method for calculating the phase shift in general relativity. This formalism is then used to find the relativistic effects in an atom interferometer in a weak gravitational field for application to laboratory tests of general relativity. The potentially testable relativistic effects include the non-linear three-graviton coupling, the gravity of kinetic energy, and the falling of light. We propose experiments, one currently under construction, that could provide a test of the principle of equivalence to 1 part in 10{sup 15} (300 times better than the present limit), and general relativity at the 10% level, with many potential future improvements. We also consider applications to other metrics including the Lense-Thirring effect, the expansion of the universe, and preferred frame and location effects.
Newtonian view of general relativistic stars
Energy Technology Data Exchange (ETDEWEB)
Oliveira, A.M. [Instituto Federal do Espirito Santo (IFES), Grupo de Ciencias Ambientais e Recursos Naturais, Guarapari (Brazil); Velten, H.E.S.; Fabris, J.C. [Universidade Federal do Espirito Santo (UFES), Departamento de Fisica, Vitoria (Brazil); Salako, I.G. [Institut de Mathematiques et de Sciences Physiques (IMSP), Porto-Novo (Benin)
2014-11-15
Although general relativistic cosmological solutions, even in the presence of pressure, can be mimicked by using neo-Newtonian hydrodynamics, it is not clear whether there exists the same Newtonian correspondence for spherical static configurations. General relativity solutions for stars are known as the Tolman-Oppenheimer-Volkoff (TOV) equations. On the other hand, the Newtonian description does not take into account the total pressure effects and therefore cannot be used in strong field regimes. We discuss how to incorporate pressure in the stellar equilibrium equations within the neo-Newtonian framework. We compare the Newtonian, neo-Newtonian, and the full relativistic theory by solving the equilibrium equations for both three approaches and calculating the mass-radius diagrams for some simple neutron stars' equations of state. (orig.)
General relativistic neutrino transport using spectral methods
Peres, Bruno; Penner, Andrew Jason; Novak, Jérôme; Bonazzola, Silvano
2014-02-01
We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, θ, ϕ, ɛ, Θ, Φ), and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (θ, ϕ, Θ, Φ), and is fully energy-dependent. This approach is implemented in a spherical shell, using either Chebyshev polynomials or Fourier series as decomposition bases. It is here restricted to simplified collision terms (isoenergetic scattering) and to the case of a static fluid. We finish this paper by presenting test results using basic configurations, including general relativistic ones in the Schwarzschild metric, in order to demonstrate the convergence properties, the conservation of particle number and correct treatment of some general relativistic effects of our code. The use of spectral methods enables to run our test cases in a six-dimensional setting on a single processor.
Conservation of Circulation in Magnetohydrodynamics
Bekenstein, Jacob D.; Oron, Asaf
2000-01-01
We demonstrate, both at the Newtonian and (general) relativistic levels, the existence of a generalization of Kelvin's circulation theorem (for pure fluids) which is applicable to perfect magnetohydrodynamics. The argument is based on the least action principle for magnetohydrodynamic flow. Examples of the new conservation law are furnished. The new theorem should be helpful in identifying new kinds of vortex phenomena distinct from magnetic ropes or fluid vortices.
Conservation of circulation in magnetohydrodynamics
Bekenstein; Oron
2000-10-01
We demonstrate at both the Newtonian and (general) relativistic levels the existence of a generalization of Kelvin's circulation theorem (for pure fluids) that is applicable to perfect magnetohydrodynamics. The argument is based on the least action principle for magnetohydrodynamic flow. Examples of the new conservation law are furnished. The new theorem should be helpful in identifying new kinds of vortex phenomena distinct from magnetic ropes or fluid vortices.
Global regularity for generalized Hall magneto-hydrodynamics systems
Directory of Open Access Journals (Sweden)
Renhui Wan
2015-06-01
Full Text Available In this article, we consider the tridimensional generalized Hall magneto-hydrodynamics (Hall-MHD system, with $(-\\Delta^\\alpha u$ and $(-\\Delta^\\beta b$. For $\\alpha\\ge 5/4$, $\\beta\\ge 7/4$, we obtain the global regularity of classical solutions. For $0<\\alpha<5/4$ and $1/2<\\beta<7/4$, with small data, the system also possesses global classical solutions. In addition, for the standard Hall-MHD system, $\\alpha=\\beta=1$, by adding a suitable condition, we give a positive answer to the open question in [3]. At last, we study the regularity criterions of generalized Hall-MHD system. In particular, we prove the regularity criterion in terms of horizontal gradient $\
WHAM: A WENO-based general relativistic numerical scheme I: Hydrodynamics
Tchekhovskoy, Alexander; Narayan, Ramesh
2007-01-01
Active galactic nuclei, x-ray binaries, pulsars, and gamma-ray bursts are all believed to be powered by compact objects surrounded by relativistic plasma flows driving phenomena such as accretion, winds, and jets. These flows are often accurately modelled by the relativistic magnetohydrodynamics (MHD) approximation. Time-dependent numerical MHD simulations have proven to be especially insightful, but one regime that remains difficult to simulate is when the energy scales (kinetic, thermal, magnetic) within the plasma become disparate. We develop a numerical scheme that significantly improves the accuracy and robustness of the solution in this regime. We use a modified form of the WENO method to construct a finite-volume general relativistic hydrodynamics code called WHAM that converges at fifth order. We avoid (1) field-by-field decomposition by adaptively reducing down to 2-point stencils near discontinuities for a more accurate treatment of shocks, and (2) excessive reduction to low order stencils, as in th...
Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics
Shigehara, T; Mishima, T; Cheon, T; Cheon, Taksu
1999-01-01
We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\\delta$ functions. We also discuss the problem within relativistic (Dirac) framework and give the solution for a three parameter family. It gives a physical interpretation for so-called high energy substantially differ between non-relativistic and relativistic cases.
Equation of state in relativistic magnetohydrodynamics: variable versus constant adiabatic index
Mignone, A.; McKinney, Jonathan C.
2007-07-01
The role of the equation of state (EoS) for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant Γ-law EoS, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic EoS that better approximates the single-specie relativistic gas. The paper focuses on three different topics. First, the influence of a more realistic EoS on the propagation of fast magnetosonic shocks is investigated. This calls into question the validity of the constant Γ-law EoS in problems where the temperature of the gas substantially changes across hydromagnetic waves. Secondly, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general EoS and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of astrophysical relevance (including magnetized accretion flows around Kerr black holes) are compared using different equations of state. Our main conclusion is that the choice of a realistic EoS can considerably bear upon the solution when transitions from cold to hot gas (or vice versa) are present. Under these circumstances, a polytropic EoS can significantly endanger the solution.
Directory of Open Access Journals (Sweden)
Domingues M. O.
2013-12-01
Full Text Available We present a new adaptive multiresoltion method for the numerical simulation of ideal magnetohydrodynamics. The governing equations, i.e., the compressible Euler equations coupled with the Maxwell equations are discretized using a finite volume scheme on a two-dimensional Cartesian mesh. Adaptivity in space is obtained via Harten’s cell average multiresolution analysis, which allows the reliable introduction of a locally refined mesh while controlling the error. The explicit time discretization uses a compact Runge–Kutta method for local time stepping and an embedded Runge-Kutta scheme for automatic time step control. An extended generalized Lagrangian multiplier approach with the mixed hyperbolic-parabolic correction type is used to control the incompressibility of the magnetic field. Applications to a two-dimensional problem illustrate the properties of the method. Memory savings and numerical divergences of magnetic field are reported and the accuracy of the adaptive computations is assessed by comparing with the available exact solution.
Leibnizian relationalism for general relativistic physics
Vassallo, Antonio
2016-01-01
An ontology of Leibnizian relationalism, consisting in distance relations among sparse matter points and their change only, is well recognized as a serious option in the context of classical mechanics. In this paper, we investigate how this ontology fares when it comes to general relativistic physics. Using a Humean strategy, we regard the gravitational field as a means to represent the overall change in the distance relations among point particles in a way that achieves the best combination of being simple and being informative.
General relativistic simulations of magnetized binary neutron star mergers
Liu, Yuk Tung; Etienne, Zachariah B; Taniguchi, Keisuke
2008-01-01
Binary neutron stars (NSNS) are expected to be among the leading sources of gravitational waves observable by ground-based laser interferometers and may be the progenitors of short-hard gamma ray bursts. We present a series of general relativistic NSNS coalescence simulations both for unmagnetized and magnetized stars. We adopt quasiequilibrium initial data for circular, irrotational binaries constructed in the conformal thin-sandwich (CTS) framework. We adopt the BSSN formulation for evolving the metric and a high-resolution shock-capturing scheme to handle the magnetohydrodynamics. Our simulations of unmagnetized binaries confirm the results of Shibata, Taniguchi and Uryu (2003). In cases in which the mergers result in a prompt collapse to a black hole, we are able to use puncture gauge conditions to extend the evolution and determine the mass of the material that forms a disk. We find that the disk mass is less than 2% of the total mass in all cases studied. We then add a small poloidal magnetic field to t...
On general relativistic uniformly rotating white dwarfs
Boshkayev, Kuantay; Ruffini, Remo; Siutsou, Ivan
2012-01-01
Uniformly rotating white dwarfs (RWDs) are analyzed within the framework of general relativity. The Hartle's formalism is applied to construct self-consistently the internal and external solutions to the Einstein equations. The relativistic Feynman-Metropolis-Teller EoS that generalizes the Salpeter's one taking fully into account the finite size of nuclei, the Coulomb interactions as well as electroweak equilibrium in a self-consistent relativistic fashion is used to describe the WD matter. The mass, radius, angular momentum, eccentricity and quadrupole moment of RWDs are calculated as a function of the central density and rotation angular velocity. We construct the region of stability of RWDs taking into account the mass-shedding limit, inverse beta-decay instability, and the boundary established by the turning points of constant angular momentum sequences that separates stable from secularly unstable configurations. We found the minimum rotation periods 0.3, 0.5, 0.7 and 2.2 seconds and maximum masses 1.50...
General relativistic neutrino transport using spectral methods
Peres, Bruno; Novak, Jerome; Bonazzola, Silvano
2014-01-01
We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, theta, phi, epsilon, Theta, Phi)$, and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (theta, phi, Theta, Phi), and is fully energy-dependent. This approach is implemented in a spherical shell, using either Chebyshev polynomials or Fourier series as decomposition bases. It is here restricted to simplified collision terms (isoenergetic scattering) and to the case of a static fluid. We finish this paper by presenting test results using basic configurations, including general r...
Magnetic collimation of meridional-self-similar general relativistic MHD flows
Globus, Noemie; Sauty, Christophe; Cayatte, Véronique; Celnikier, Ludwik M.
2014-06-01
We present a model for the spine of relativistic Magnetohydrodynamics outflows in the Kerr geometry. Meridional self-similarity is invoked to derive semianalytical solutions close to the polar axis. The study of the energy conservation along a particular field line gives a simple criterion for the collimation of jets. Such parameter have already been derived in the classical case by Sauty et al. 1999 and also extended to the Schwarzschild metric by Meliani et al. 2006. We generalize the same study to the Kerr metric. We show that the rotation of the black hole increases the magnetic self-confinement.
General Relativistic Simulations of Magnetized Plasmas around Merging Supermassive Black Holes
Giacomazzo, Bruno; Miller, M Coleman; Reynolds, Christopher S; van Meter, James R
2012-01-01
Coalescing supermassive black hole binaries are produced by the mergers of galaxies and are the most powerful sources of gravitational waves accessible to space-based gravitational observatories. Some such mergers may occur in the presence of matter and magnetic fields and hence generate an electromagnetic counterpart. In this paper we present the first general relativistic simulations of magnetized plasma around merging supermassive black holes using the general relativistic magnetohydrodynamic code Whisky. By considering different magnetic field strengths, going from non-magnetically dominated to magnetically dominated regimes, we explore how magnetic fields affect the dynamics of the plasma and the possible emission of electromagnetic signals. In particular we observe a total amplification of the magnetic field of ~2 orders of magnitude which is driven by the accretion onto the binary and that leads to much stronger electromagnetic signals, more than a factor of 10^4 larger than comparable calculations don...
General Relativistic Simulations of Magnetized Plasmas around Merging Supermassive Black Holes
Giacomazzo, Bruno; Baker, John G.; Miller, M. Coleman; Reynolds, Christopher S.; van Meter, James R.
2012-06-01
Coalescing supermassive black hole binaries are produced by the mergers of galaxies and are the most powerful sources of gravitational waves accessible to space-based gravitational observatories. Some such mergers may occur in the presence of matter and magnetic fields and hence generate an electromagnetic counterpart. In this Letter, we present the first general relativistic simulations of magnetized plasma around merging supermassive black holes using the general relativistic magnetohydrodynamic code Whisky. By considering different magnetic field strengths, going from non-magnetically dominated to magnetically dominated regimes, we explore how magnetic fields affect the dynamics of the plasma and the possible emission of electromagnetic signals. In particular, we observe a total amplification of the magnetic field of ~2 orders of magnitude, which is driven by the accretion onto the binary and that leads to much stronger electromagnetic signals, more than a factor of 104 larger than comparable calculations done in the force-free regime where such amplifications are not possible.
Bruce, Adam L
2015-01-01
We show the traditional rocket problem, where the ejecta velocity is assumed constant, can be reduced to an integral quadrature of which the completely non-relativistic equation of Tsiolkovsky, as well as the fully relativistic equation derived by Ackeret, are limiting cases. By expanding this quadrature in series, it is shown explicitly how relativistic corrections to the mass ratio equation as the rocket transitions from the Newtonian to the relativistic regime can be represented as products of exponential functions of the rocket velocity, ejecta velocity, and the speed of light. We find that even low order correction products approximate the traditional relativistic equation to a high accuracy in flight regimes up to $0.5c$ while retaining a clear distinction between the non-relativistic base-case and relativistic corrections. We furthermore use the results developed to consider the case where the rocket is not moving relativistically but the ejecta stream is, and where the ejecta stream is massless.
General relativistic neutron stars with twisted magnetosphere
Pili, A G; Del Zanna, L
2014-01-01
Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars are extreme manifestations of the most magnetized neutron stars: magnetars. The phenomenology of their emission and spectral properties strongly support the idea that the magnetospheres of these astrophysical objects are tightly twisted in the vicinity of the star. Previous studies on equilibrium configurations have so far focused on either the internal or the external magnetic field configuration, without considering a real coupling between the two fields. Here we investigate numerical equilibrium models of magnetized neutron stars endowed with a confined twisted magnetosphere, solving the general relativistic Grad-Shafranov equation both in the interior and in the exterior of the compact object. A comprehensive study of the parameters space is provided to investigate the effects of different current distributions on the overall magnetic field structure.
Relativistic hydro and magnetohydrodynamic models for AGN jet propagation and deceleration
Keppens, R.; Meliani, Z.
2009-01-01
We present grid-adaptive computational studies of both magnetized and unmagnetized jet flows, with significantly relativistic bulk speeds, as appropriate for AGN jets. Our relativistic jet studies shed light on the observationally established classification of Fanaroff-Riley galaxies, where the appe
Slowly Rotating General Relativistic Superfluid Neutron Stars
Andersson, N
2001-01-01
We present a general formalism to treat slowly rotating general relativistic superfluid neutron stars. As a first approximation, their matter content can be described in terms of a two-fluid model, where one fluid is the neutron superfluid, which is believed to exist in the core and inner crust of mature neutron stars, and the other fluid represents a conglomerate of all other constituents (crust nuclei, protons, electrons, etc.). We obtain a system of equations, good to second-order in the rotational velocities, that determines the metric and the matter variables, irrespective of the equation of state for the two fluids. In particular, allowance is made for the so-called entrainment effect, whereby the momentum of one constituent (e.g. the neutrons) carries along part of the mass of the other constituent. As an illustration of the developed framework, we consider a simplified equation of state for which the two fluids are described by different polytropes. We determine numerically the effects of the two flui...
Balsara, Dinshaw S.; Kim, Jinho
2016-05-01
The relativistic magnetohydrodynamics (RMHD) set of equations has recently seen an increased use in astrophysical computations. Even so, RMHD codes remain fragile. The reconstruction can sometimes yield superluminal velocities in certain parts of the mesh. The current generation of RMHD codes does not have any particularly good strategy for avoiding such an unphysical situation. In this paper we present a reconstruction strategy that overcomes this problem by making a single conservative to primitive transformation per cell followed by higher order WENO reconstruction on a carefully chosen set of primitives that guarantee subluminal reconstruction of the flow variables. For temporal evolution via a predictor step we also present second, third and fourth order accurate ADER methods that keep the velocity subluminal during the predictor step. The methods presented here are very general and should apply to other PDE systems where physical realizability is most easily asserted in the primitive variables. The RMHD system also requires the magnetic field to be evolved in a divergence-free fashion. In the treatment of classical numerical MHD the analogous issue has seen much recent progress with the advent of multidimensional Riemann solvers. By developing multidimensional Riemann solvers for RMHD, we show that similar advances extend to RMHD. As a result, the face-centered magnetic fields can be evolved much more accurately using the edge-centered electric fields in the corrector step. Those edge-centered electric fields come from a multidimensional Riemann solver for RMHD which we present in this paper. The overall update results in a one-step, fully conservative scheme that is suited for AMR. In this paper we also develop several new test problems for RMHD. We show that RMHD vortices can be designed that propagate on the computational mesh as self-preserving structures. These RMHD vortex test problems provide a means to do truly multidimensional accuracy testing for
Balsara, Dinshaw S
2016-01-01
The relativistic magnetohydrodynamics (RMHD) set of equations has recently seen increased use in astrophysical computations. Even so, RMHD codes remain fragile. The reconstruction can sometimes yield superluminal velocities in certain parts of the mesh. In this paper we present a reconstruction strategy that overcomes this problem by making a single conservative to primitive transformation per cell followed by higher order WENO reconstruction on a carefully chosen set of primitives that guarantee subluminal reconstruction of the flow variables. For temporal evolution via a predictor step we also present second, third and fourth order accurate ADER methods that keep the velocity subluminal during the predictor step. The RMHD system also requires the magnetic field to be evolved in a divergence-free fashion. In the treatment of classical numerical MHD the analogous issue has seen much recent progress with the advent of multidimensional Riemann solvers. By developing multidimensional Riemann solvers for RMHD, we...
General Relativistic Simulations of the Collapsar Scenario
DeBrye, N; Aloy, M A; Font, J A
2013-01-01
We are exploring the viability of the collapsar model for long-soft gamma-ray bursts. For this we perform state-of-the-art general relativistic hydrodynamic simulations in a dynamically evolving space-time with the CoCoNuT code. We start from massive low metallicity stellar models evolved up to core gravitational instability, and then follow the subsequent evolution until the system collapses forming a compact remnant. A preliminary study of the collapse outcome is performed by varying the typical parameters of the scenario, such as the initial stellar mass, metallicity, and rotational profile of the stellar progenitor. 1D models (without rotation) have been used to test our newly developed neutrino leakage scheme. This is a fundamental piece of our approach as it allows the central remnant (in all cases considered, a metastable high-mass neutron star) to cool down, eventually collapsing to a black hole. In two dimensions, we show that sufficiently fast rotating cores lead to the formation of Kerr black holes...
Matsumoto, Jin; Masada, Youhei; Asano, Eiji; Shibata, Kazunari
2011-05-01
The nonlinear dynamics of outflows driven by magnetic explosion on the surface of a compact star is investigated through special relativistic magnetohydrodynamic simulations. We adopt, as the initial equilibrium state, a spherical stellar object embedded in hydrostatic plasma which has a density ρ(r) vprop r -α and is threaded by a dipole magnetic field. The injection of magnetic energy at the surface of a compact star breaks the equilibrium and triggers a two-component outflow. At the early evolutionary stage, the magnetic pressure increases rapidly around the stellar surface, initiating a magnetically driven outflow. A strong forward shock driven outflow is then excited. The expansion velocity of the magnetically driven outflow is characterized by the Alfvén velocity on the stellar surface and follows a simple scaling relation v mag vprop v A 1/2. When the initial density profile declines steeply with radius, the strong shock is accelerated self-similarly to relativistic velocity ahead of the magnetically driven component. We find that it evolves according to a self-similar relation Γsh vprop r sh, where Γsh is the Lorentz factor of the plasma measured at the shock surface r sh. A purely hydrodynamic process would be responsible for the acceleration mechanism of the shock driven outflow. Our two-component outflow model, which is the natural outcome of the magnetic explosion, can provide a better understanding of the magnetic active phenomena on various magnetized compact stars.
General relativistic observables for the ACES experiment
Turyshev, Slava G; Toth, Viktor T
2015-01-01
We develop a high-precision model for relativistic observables of the Atomic Clock Ensemble in Space (ACES) experiment on the International Space Station (ISS). We develop all relativistic coordinate transformations that are needed to describe the motion of ACES in Earth orbit and to compute observable quantities. We analyze the accuracy of the required model as it applies to the proper-to-coordinate time transformations, light time equation, and spacecraft equations of motion. We consider various sources of nongravitational noise and their effects on ACES. We estimate the accuracy of orbit reconstruction that is needed to satisfy the ACES science objectives. Based on our analysis, we derive models for the relativistic observables of ACES, which also account for the contribution of atmospheric drag on the clock rate. We include the Earth's oblateness coefficient $J_2$ and the effects of major nongravitational forces on the orbit of the ISS. We demonstrate that the ACES reference frame is pseudo-inertial at th...
General relativistic tidal heating for Moller pseudotensor
So, Lau Loi
2015-01-01
Thorne elucidated that the relativistic tidal heating is the same as the Newtonian theory. Moreover, Thorne also claimed that the tidal heating is independent of how one localizes gravitational energy and is unambiguously given by a certain formula. Purdue and Favata calculated the tidal heating for different classical pseudotensors including Moller and obtained the results all matched with the Newtonian perspective. After re-examined this Moller pseudotensor, we find that there does not exist any tidal heating value. Thus we claim that the relativistic tidal heating is pseudotensor independent under the condition that if the peusdotensor is a Freud typed superpotential.
Polko, P.; Meier, D.L.; Markoff, S.
2013-01-01
We present a new, approximate method for modelling the acceleration and collimation of relativistic jets in the presence of gravity. This method is self-similar throughout the computational domain where gravitational effects are negligible and, where significant, self-similar within a flux tube.
General relativistic aspects of ferromagneto-fluid
Energy Technology Data Exchange (ETDEWEB)
Asgekar, G.G.; Patwardhan, C.G.
1988-03-01
The implications of Bianchi identities pertaining to the spacetime of relativistic ferrofluid with infinite conductivity and variable magnetic permeability are investigated. Some kinematical and dynamical corollaries emerging out of a preferred geometrical symmetry called an isometry with respect to the flow vector and the magnetic field vector are developed.
General relativistic aspects of ferromagneto-fluid.
Asgekar, G. G.; Patwardhan, C. G.
1988-03-01
The implications of Bianchi identities pertaining to the spacetime of relativistic ferrofluid with infinite conductivity and variable magnetic permeability are investigated. Some kinematical and dynamical corollaries emerging out of a preferred geometrical symmetry called an isometry with respect to the flow vector and the magnetic field vector are developed.
General relativistic spectra of accretion disks around rotating neutron stars
Bhattacharya, S; Thampan, A V
2000-01-01
General relativistic spectra from accretion disks around rotating neutron stars in the appropriate space-time geometry for several different equation of state, spin rates and mass of the compact object have been computed. The analysis involves the computation of the relativistically corrected radial temperature profiles and the effect of Doppler and gravitational red-shifts on the spectra. Light bending effects have been omitted for simplicity. The relativistic spectrum is compared with the Newtonian one and it is shown that the difference between the two is primarily due to the different radial temperature profile for the relativistic and Newtonian disk solutions. To facilitate direct comparison with observations, a simple empirical function has been presented which describes the numerically computed relativistic spectra well. This empirical function (which has three parameters including normalization) also describes the Newtonian spectrum adequately. Thus the function can in principle be used to distinguish...
A Two-dimensional Magnetohydrodynamics Scheme for General Unstructured Grids
Livne, Eli; Dessart, Luc; Burrows, Adam; Meakin, Casey A.
2007-05-01
We report a new finite-difference scheme for two-dimensional magnetohydrodynamics (MHD) simulations, with and without rotation, in unstructured grids with quadrilateral cells. The new scheme is implemented within the code VULCAN/2D, which already includes radiation hydrodynamics in various approximations and can be used with arbitrarily moving meshes (ALEs). The MHD scheme, which consists of cell-centered magnetic field variables, preserves the nodal finite difference representation of divB by construction, and therefore any initially divergence-free field remains divergence-free through the simulation. In this paper, we describe the new scheme in detail and present comparisons of VULCAN/2D results with those of the code ZEUS/2D for several one-dimensional and two-dimensional test problems. The code now enables two-dimensional simulations of the collapse and explosion of the rotating, magnetic cores of massive stars. Moreover, it can be used to simulate the very wide variety of astrophysical problems for which multidimensional radiation magnetohydrodynamics (RMHD) is relevant.
Cosmological Measurements with General Relativistic Galaxy Correlations
Raccanelli, Alvise; Bertacca, Daniele; Doré, Olivier; Durrer, Ruth
2015-01-01
We investigate the cosmological dependence and the constraining power of large-scale galaxy correlations, including all redshift-distortions, wide-angle, lensing and gravitational potential effects on linear scales. We analyze the cosmological information present in the lensing convergence and in the gravitational potential terms describing the so-called "relativistic effects," and we find that, while smaller than the information contained in intrinsic galaxy clustering, it is not negligible. We investigate how neglecting them does bias cosmological measurements performed by future spectroscopic and photometric large-scale surveys such as SKA and Euclid. We perform a Fisher analysis using the CLASS code, modified to include scale-dependent galaxy bias and redshift-dependent magnification and evolution bias. Our results show that neglecting relativistic terms introduces an error in the forecasted precision in measuring cosmological parameters of the order of a few tens of percent, in particular when measuring ...
Newtonian and General Relativistic Models of Spherical Shells
Vogt, D
2009-01-01
A family of spherical shells with varying thickness is derived by using a simple Newtonian potential-density pair. Then, a particular isotropic form of a metric in spherical coordinates is used to construct a General Relativistic version of the Newtonian family of shells. The matter of these relativistic shells presents equal azimuthal and polar pressures, while the radial pressure is a constant times the tangential pressure. We also make a first study of stability of both the Newtonian and relativistic families of shells.
Ultra-Relativistic Magneto-Hydro-Dynamic Jets in the context of Gamma Ray Bursts
Fendt, C; Fendt, Christian; Ouyed, Rachid
2004-01-01
We present a detailed numerical study of the dynamics and evolution of ultrarelativistic magnetohydrodynamic jets in the black hole-disk system under extreme magnetization conditions. We find that Lorentz factors of up to 3000 are achieved and derived a modifiedMichel scaling (Gamma ~ sigma) which allows for a wide variation in the flow Lorentz factor. Pending contamination induced by mass-entrainment, the linear Michel scaling links modulations in the ultrarelativistic wind to variations in mass accretion in the disk for a given magnetization. The jet is asymptotically dominated by the toroidal magnetic field allowing for efficient collimation. We discuss our solutions (jets) in the context of Gamma ray bursts and describe the relevant features such as the high variability in the Lorentz factor and how high collimation angles (~ 0-5 degrees), or cylindrical jets, can be achieved. We isolate a jet instability mechanism we refer to as the "bottle-neck" instability which essentially relies on a high magnetizati...
A new three-dimensional general-relativistic hydrodynamics code
Baiotti, L.; Hawke, I.; Montero, P. J.; Rezzolla, L.
We present a new three-dimensional general relativistic hydrodynamics code, the Whisky code. This code incorporates the expertise developed over the past years in the numerical solution of Einstein equations and of the hydrodynamics equations in a curved spacetime, and is the result of a collaboration of several European Institutes. We here discuss the ability of the code to carry out long-term accurate evolutions of the linear and nonlinear dynamics of isolated relativistic stars.
A new three-dimensional general-relativistic hydrodynamics code
Baiotti, Luca; Montero, Pedro J; Rezzolla, Luciano
2010-01-01
We present a new three-dimensional general relativistic hydrodynamics code, the Whisky code. This code incorporates the expertise developed over the past years in the numerical solution of Einstein equations and of the hydrodynamics equations in a curved spacetime, and is the result of a collaboration of several European Institutes. We here discuss the ability of the code to carry out long-term accurate evolutions of the linear and nonlinear dynamics of isolated relativistic stars.
General Relativistic Mean Field Theory for rotating nuclei
Energy Technology Data Exchange (ETDEWEB)
Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki
1998-03-01
The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)
HERO - A 3D general relativistic radiative post-processor for accretion discs around black holes
Zhu, Yucong; Narayan, Ramesh; Sadowski, Aleksander; Psaltis, Dimitrios
2015-08-01
HERO (Hybrid Evaluator for Radiative Objects) is a 3D general relativistic radiative transfer code which has been tailored to the problem of analysing radiation from simulations of relativistic accretion discs around black holes. HERO is designed to be used as a post-processor. Given some fixed fluid structure for the disc (i.e. density and velocity as a function of position from a hydrodynamic or magnetohydrodynamic simulation), the code obtains a self-consistent solution for the radiation field and for the gas temperatures using the condition of radiative equilibrium. The novel aspect of HERO is that it combines two techniques: (1) a short-characteristics (SC) solver that quickly converges to a self-consistent disc temperature and radiation field, with (2) a long-characteristics (LC) solver that provides a more accurate solution for the radiation near the photosphere and in the optically thin regions. By combining these two techniques, we gain both the computational speed of SC and the high accuracy of LC. We present tests of HERO on a range of 1D, 2D, and 3D problems in flat space and show that the results agree well with both analytical and benchmark solutions. We also test the ability of the code to handle relativistic problems in curved space. Finally, we discuss the important topic of ray defects, a major limitation of the SC method, and describe our strategy for minimizing the induced error.
Bai, Xue-Ning; Sironi, Lorenzo; Spitkovsky, Anatoly
2014-01-01
We formulate a magnetohydrodynamic-particle-in-cell (MHD-PIC) method for describing the interaction between collisionless cosmic ray (CR) particles and a thermal plasma. The thermal plasma is treated as a fluid, obeying equations of ideal MHD, while CRs are treated as relativistic Lagrangian particles subject to the Lorentz force. Backreaction from CRs to the gas is included in the form of momentum and energy feedback. In addition, we include the electromagnetic feedback due to CR-induced Hall effect that becomes important when the electron-ion drift velocity of the background plasma induced by CRs approaches the Alfv\\'en velocity. Our method is applicable on scales much larger than the ion inertial length, bypassing the microscopic scales that must be resolved in conventional PIC methods, while retaining the full kinetic nature of the CRs. We have implemented and tested this method in the Athena MHD code, where the overall scheme is second-order accurate and fully conservative. As a first application, we des...
A general relativistic signature in the galaxy bispectrum
Umeh, Obinna; Maartens, Roy; Clarkson, Chris
2016-01-01
Next-generation galaxy surveys will increasingly rely on the galaxy bispectrum to improve cosmological constraints, especially on primordial non-Gaussianity. A key theoretical requirement that remains to be developed is the analysis of general relativistic effects on the bispectrum, which arise from observing galaxies on the past lightcone. Here we compute for the first time all the local relativistic corrections to the bispectrum, from Doppler, gravitational potential and higher-order effects. For the galaxy bispectrum, the problem is much more complex than for the power spectrum, since we need the lightcone corrections at second order. Mode-coupling contributions at second order mean that relativistic corrections can be non-negligible at smaller scales than in the case of the power spectrum. In a primordial Gaussian universe, we show that the relativistic bispectrum for a moderately squeezed shape can differ from the Newtonian prediction by $\\sim 30\\%$ when the short modes are at the equality scale. For the...
Broderick, Avery E
2010-01-01
For the first time it has become possible to compare global 3D general relativistic magnetohydrodynamic (GRMHD) jet formation simulations directly to very-long baseline interferometric multi-frequency polarization observations of the pc-scale structure of active galactic nucleus (AGN) jets. Unlike the jet emission, which requires post hoc modeling of the non-thermal electrons, the Faraday rotation measures (RMs) depend primarily upon simulated quantities and thus provide a robust way in which to confront simulations with observations. We compute RM distributions of 3D global GRMHD jet formation simulations, with which we explore the dependence upon model and observational parameters, emphasizing the signatures of structures generic to the theory of MHD jets. With typical parameters, we find that it is possible to reproduce the observed magnitudes and many of the structures found in AGN jet RMs, including the presence of transverse RM gradients. In our simulations the RMs are generated within a smooth extensio...
Mizuno, Y.; Nishikawa, K.I.; Zhang, B.; Giacomazzo, B.; Hardee, P.E.; Nagataki, S.; Hartmann, D.H.
2008-01-01
We solve the Riemann problem for the deceleration of arbitrarily magnetized relativistic ejecta injected into a static unmagnetized medium. We find that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization s (the Poynting-to-kinetic energy flux ratio), and the shock becomes a rarefaction wave when s exceeds a critical value, sc, defined by the balance between the magnetic pressure in the ejecta and the thermal pressure in the forward shock. In the rarefaction wave regime, we find that the rarefied region is accelerated to a Lorentz factor that is significantly larger than the initial value. This acceleration mechanism is due to the strong magnetic pressure in the ejecta.
Generalized Relativistic Chapman-Enskog Solution of the Boltzmann Equation
García-Perciante, A L; García-Colin, L S
2007-01-01
The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to the thermodynamic force in its first order solution. Both existence and uniqueness of such a solution are proved based on the standard theory of integral equations. The mathematical implications of the generalization here introduced are briefly explored.
LOGARITHMICALLY IMPROVED REGULARITY CRITERION FOR THE 3D GENERALIZED MAGNETO-HYDRODYNAMIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
赵继红; 刘桥
2014-01-01
This article proves the logarithmically improved Serrin’s criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10] (Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365: 806-808) and [18] (Zhang Z J. Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011, 375: 799-802).
A generally-relativistic gauge classification of the Dirac fields
Fabbri, Luca
2016-01-01
We consider generally-relativistic gauge transformations for the spinorial fields finding two mutually exclusive but together exhaustive classes in which fermions are placed adding supplementary information to the results obtained by Lounesto, and identifying quantities analogous to the momentum vector and the Pauli-Lubanski axial vector we discuss how our results are similar to those obtained by Wigner; by taking into account the most general Dirac equations we will investigate the consequences for the dynamics: and in particular we shall address the problem of getting the non-relativistic approximation in a consistent way. We are going to comment on extensions.
Mizuno, Yosuke; Lyubarsky, Yuri; ishikawa, Ken-Ichi; Hardee, Philip E.
2010-01-01
We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the non-linear regime the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depends moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and the non-linear regime is reached at a later time than for constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the non-linear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the non-linear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the non-linear regime nearly ceases for increasing magnetic pitch.
Narayan, Ramesh; Zhu, Yucong; Psaltis, Dimitrios; Saḑowski, Aleksander
2016-03-01
We describe Hybrid Evaluator for Radiative Objects Including Comptonization (HEROIC), an upgraded version of the relativistic radiative post-processor code HERO described in a previous paper, but which now Includes Comptonization. HEROIC models Comptonization via the Kompaneets equation, using a quadratic approximation for the source function in a short characteristics radiation solver. It employs a simple form of accelerated lambda iteration to handle regions of high scattering opacity. In addition to solving for the radiation field, HEROIC also solves for the gas temperature by applying the condition of radiative equilibrium. We present benchmarks and tests of the Comptonization module in HEROIC with simple 1D and 3D scattering problems. We also test the ability of the code to handle various relativistic effects using model atmospheres and accretion flows in a black hole space-time. We present two applications of HEROIC to general relativistic magnetohydrodynamics simulations of accretion discs. One application is to a thin accretion disc around a black hole. We find that the gas below the photosphere in the multidimensional HEROIC solution is nearly isothermal, quite different from previous solutions based on 1D plane parallel atmospheres. The second application is to a geometrically thick radiation-dominated accretion disc accreting at 11 times the Eddington rate. Here, the multidimensional HEROIC solution shows that, for observers who are on axis and look down the polar funnel, the isotropic equivalent luminosity could be more than 10 times the Eddington limit, even though the spectrum might still look thermal and show no signs of relativistic beaming.
GENERAL RELATIVISTIC SIMULATIONS OF MAGNETIZED PLASMAS AROUND MERGING SUPERMASSIVE BLACK HOLES
Energy Technology Data Exchange (ETDEWEB)
Giacomazzo, Bruno [JILA, University of Colorado and National Institute of Standards and Technology, 440 UCB, Boulder, CO 80309 (United States); Baker, John G.; Van Meter, James R. [Gravitational Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 21114 (United States); Coleman Miller, M.; Reynolds, Christopher S. [Department of Astronomy, University of Maryland, College Park, MD 20742 (United States)
2012-06-10
Coalescing supermassive black hole binaries are produced by the mergers of galaxies and are the most powerful sources of gravitational waves accessible to space-based gravitational observatories. Some such mergers may occur in the presence of matter and magnetic fields and hence generate an electromagnetic counterpart. In this Letter, we present the first general relativistic simulations of magnetized plasma around merging supermassive black holes using the general relativistic magnetohydrodynamic code Whisky. By considering different magnetic field strengths, going from non-magnetically dominated to magnetically dominated regimes, we explore how magnetic fields affect the dynamics of the plasma and the possible emission of electromagnetic signals. In particular, we observe a total amplification of the magnetic field of {approx}2 orders of magnitude, which is driven by the accretion onto the binary and that leads to much stronger electromagnetic signals, more than a factor of 10{sup 4} larger than comparable calculations done in the force-free regime where such amplifications are not possible.
General relativistic Boltzmann equation, II: Manifestly covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann equati
General relativistic Boltzmann equation, II: Manifestly covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann
Cherenkov loss factor of short relativistic bunches:general approach
Baturin, S S
2013-01-01
The interaction of short relativistic charged particle bunches with waveguides and other accelerator system components is a critical issue for the development of X-ray FELs (free electron lasers) and linear collider projects. Wakefield Cherenkov losses of short bunches have been studied previously for resistive wall, disk-loaded, corrugated and dielectric loaded waveguides. It was noted in various publications [1] that if the slowdown layer is thin, the Cherenkov loss factor of a short bunch does not depend on the guiding system material and is a constant for any given transverse cross section dimensions of the waveguides. In this paper, we consider a new approach to the analysis of loss factors for relativistic short bunches and formulate a general integral relation that allows calculation of the loss factor for a short relativistic bunch passing an arbitrary waveguide system. The loss factors calculated by this new method for various types of waveguides with arbitrary thickness slowdown layers, including in...
HERO: A 3D General Relativistic Radiative Postprocessor for Accretion Discs around Black Holes
Zhu, Yucong; Sadowski, Aleksander; Psaltis, Dimitrios
2015-01-01
HERO (Hybrid Evaluator for Radiative Objects) is a 3D general relativistic radiative transfer code which has been tailored to the problem of analyzing radiation from simulations of relativistic accretion discs around black holes. HERO is designed to be used as a postprocessor. Given some fixed fluid structure for the disc (i.e. density and velocity as a function of position from a hydrodynamics or magnetohydrodynamics simulation), the code obtains a self-consistent solution for the radiation field and for the gas temperatures using the condition of radiative equilibrium. The novel aspect of HERO is that it combines two techniques: 1) a short characteristics (SC) solver that quickly converges to a self consistent disc temperature and radiation field, with 2) a long characteristics (LC) solver that provides a more accurate solution for the radiation near the photosphere and in the optically thin regions. By combining these two techniques, we gain both the computational speed of SC and the high accuracy of LC. W...
Causal Stability Conditions for General Relativistic Spacetimes
Howard, E M
2016-01-01
A brief overview of some open questions in general relativity with important consequences for causality theory is presented, aiming to a better understanding of the causal structure of the spacetime. Special attention is accorded to the problem of fundamental causal stability conditions. Several questions are raised and some of the potential consequences of recent results regarding the causality problem in general relativity are presented. A key question is whether causality violating regions are locally allowed. The new concept of almost stable causality is introduced; meanwhile, related conditions and criteria for the stability and almost stability of the causal structure are discussed.
TOPICAL REVIEW: General relativistic boson stars
Schunck, Franz E
2008-01-01
There is accumulating evidence that (fundamental) scalar fields may exist in Nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. Similarly as for white dwarfs and neutron stars, there exists a limiting mass, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and the spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation, however, modifications of general relativity, as in the case of Jordan-Brans-Dicke theory as a low energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to constituent mass, an effective radius, and a ...
TOPICAL REVIEW: General relativistic boson stars
Schunck, Franz E.; Mielke, Eckehard W.
2003-10-01
There is accumulating evidence that (fundamental) scalar fields may exist in nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. As with white dwarfs and neutron stars, a limiting mass exists similarly, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation; however, modifications of general relativity, as in the case of Jordan Brans Dicke theory as a low-energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to the constituent mass, an effective radius and a large particle number. Due to the Heisenberg principle, a completely stable branch exists, and as a coherent state, it allows for rotating solutions with quantized angular momentum. In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.
General Relativistic White Dwarfs and Their Astrophysical Implications
Boshkayev, Kuantay; Ruffini, Remo; Siutsou, Ivan
2014-01-01
We consider applications of general relativistic uniformly-rotating white dwarfs to several astrophysical phenomena related to the spin-up and the spin-down epochs and to delayed type Ia supernova explosions of super-Chandrasekhar white dwarfs, where we estimate the "spinning down" lifetime due to magnetic-dipole braking. In addition, we describe the physical properties of Soft Gamma Repeaters and Anomalous X-Ray Pulsars as massive rapidly-rotating highly-magnetized white dwarfs. Particularly we consider one of the so-called low-magnetic-field magnetars SGR 0418+5729 as a massive rapidly-rotating highly-magnetized white dwarf and give bounds for the mass, radius, moment of inertia, and magnetic field by requiring the general relativistic uniformly-rotating configurations to be stable.
General relativistic white dwarfs and their astrophysical implications
Energy Technology Data Exchange (ETDEWEB)
Boshkayev, Kuantay [Al-Farabi Kazakh National University, Almaty (Kazakhstan); Rueda, Jorge A.; Ruffini, Remo [Sapienza University of Rome, Rome (Italy); Siutsou, Ivan [ICRANet, Square of Republic, Pescara (Italy)
2014-09-15
We consider applications of general relativistic uniformly-rotating white dwarfs to several astrophysical phenomena related to the spin-up and the spin-down epochs and to delayed type Ia supernova explosions of super-Chandrasekhar white dwarfs, where we estimate the 'spinning down' lifetime due to magnetic-dipole braking. In addition, we describe the physical properties of Soft Gamma Repeaters and Anomalous X-Ray Pulsars as massive rapidly-rotating highly-magnetized white dwarfs. Particularly we consider one of the so-called low-magnetic-field magnetars SGR 0418+5729 as a massive rapidly-rotating highly- magnetized white dwarf and give bounds for the mass, radius, moment of inertia, and magnetic field by requiring the general relativistic uniformly rotating configurations to be stable.
General Relativistic Transfer Equation on a Kerr Black Hole
Zannias, T.
1998-12-01
The general relativistic transfer equation describing the interaction of a massless gas with a hot plasma is analyzed on the background of a Kerr black hole. On physical grounds we single out two natural orthonormal frames relative to which the radiative transfer equation takes its simplest form. First the field of the local rest frame defined by the plasma and secondly the local rest frame associated with Bardeens-ZAMOS observers. Applications of the formalism to accretion problems will also briefly discussed.
A new spherically symmetric general relativistic hydrodynamical code
Romero, J V; Martí, J M; Miralles, J A; Romero, Jose V; Ibanez, Jose M; Marti, Jose M; Miralles, Juan A
1995-01-01
In this paper we present a full general relativistic one-dimensional hydro-code which incorporates a modern high-resolution shock-capturing algorithm, with an approximate Riemann solver, for the correct modelling of formation and propagation of strong shocks. The efficiency of this code in treating strong shocks is demonstrated by some numerical experiments. The interest of this technique in several astrophysical scenarios is discussed.
General factorization scheme with application to relativistic Hermite polynomials
Rosu, H C; Obregón, O; Reyes, Marco A; Obregon, Octavio
1995-01-01
We present a sufficiently general factorization scheme of second-order linear differential equations having discrete (polynomial) indeces both in the coefficient of the first-derivative term and of the derivative-free one. We apply it to the relativistic Hermite equation in order to perform the factorization with respect to the polynomial degree confirming the factorization of Aldaya, Bisquert and Navarro-Salas, but also obtaining another slightly modified factorization, and to the Gegenbauer equation for the factorization with respect to the order. Moreover, by making use of Nagel's relation between Gegenbauer and relativistic Hermite polynomials we write down ladder-like operations with respect to the order for the latter ones, which are another interesting result of the paper.
General Relativistic Smoothed Particle Hydrodynamics code developments: A progress report
Faber, Joshua; Silberman, Zachary; Rizzo, Monica
2017-01-01
We report on our progress in developing a new general relativistic Smoothed Particle Hydrodynamics (SPH) code, which will be appropriate for studying the properties of accretion disks around black holes as well as compact object binary mergers and their ejecta. We will discuss in turn the relativistic formalisms being used to handle the evolution, our techniques for dealing with conservative and primitive variables, as well as those used to ensure proper conservation of various physical quantities. Code tests and performance metrics will be discussed, as will the prospects for including smoothed particle hydrodynamics codes within other numerical relativity codebases, particularly the publicly available Einstein Toolkit. We acknowledge support from NSF award ACI-1550436 and an internal RIT D-RIG grant.
Equation of State in a Generalized Relativistic Density Functional Approach
Typel, Stefan
2015-01-01
The basic concepts of a generalized relativistic density functional approach to the equation of state of dense matter are presented. The model is an extension of relativistic mean-field models with density-dependent couplings. It includes explicit cluster degrees of freedom. The formation and dissolution of nuclei is described with the help of mass shifts. The model can be adapted to the description of finite nuclei in order to study the effect of $\\alpha$-particle correlations at the nuclear surface on the neutron skin thickness of heavy nuclei. Further extensions of the model to include quark degrees of freedom or an energy dependence of the nucleon self-energies are outlined.
Observability of the General Relativistic Precession of Periastra in Exoplanets
Jordan, Andres
2008-01-01
The general relativistic precession rate of periastra in close-in exoplanets can be orders of magnitude larger than the magnitude of the same effect for Mercury. The realization that some of the close-in exoplanets have significant eccentricities raises the possibility that this precession might be detectable. We explore in this work the observability of the periastra precession using radial velocity and transit light curve observations. Our analysis is independent of the source of precession, which can also have significant contributions due to additional planets and tidal deformations. We find that precession of the periastra of the magnitude expected from general relativity can be detectable in timescales of <~ 10 years with current observational capabilities by measuring the change in the primary transit duration or in the time difference between primary and secondary transits. Radial velocity curves alone would be able to detect this precession for super-massive, close-in exoplanets orbiting inactive ...
Energy Technology Data Exchange (ETDEWEB)
Zhao, Guangpu [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China); Jian, Yongjun, E-mail: jianyj@imu.edu.cn [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China); Chang, Long [School of Mathematics and Statistics, Inner Mongolia University of Finance and Economics, Hohhot, Inner Mongolia 010051 (China); Buren, Mandula [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China)
2015-08-01
By using the method of separation of variables, an analytical solution for the magnetohydrodynamic (MHD) flow of the generalized Maxwell fluids under AC electric field through a two-dimensional rectangular micropump is reduced. By the numerical computation, the variations of velocity profiles with the electrical oscillating Reynolds number Re, the Hartmann number Ha, the dimensionless relaxation time De are studied graphically. Further, the comparison with available experimental data and relevant researches is presented. - Highlights: • MHD flow of the generalized Maxwell fluids under AC electric field is analyzed. • The MHD flow is confined to a two-dimensional rectangular micropump. • Analytical solution is obtained by using the method of separation of variables. • The influences of related parameters on the MHD velocity are discussed.
Modelling general relativistic perfect fluids in field theoretic language
Mitskievich, N V
1999-01-01
Skew-symmetric massless fields, their potentials being $r$-forms, are close analogues of Maxwell's field (though the non-linear cases also should be considered). We observe that only two of them ($r=$2 and 3) automatically yield stress-energy tensors characteristic to normal perfect fluids. It is shown that they naturally describe both non-rotating ($r=2$) and rotating (then a combination of $r=2$ and $r=3$ fields is indispensable) general relativistic perfect fluids possessing every type of equations of state. Meanwile, a free $r=3$ field is completely equivalent to appearance of the cosmological term in Einstein's equations. Sound waves represent perturbations propagating on the background of the $r=2$ field. Some exotic properties of these two fields are outlined.
General Relativistic Simulations of Binary Neutron Star Mergers
Giacomazzo, Bruno; Rezzolla, Luciano; Baiotti, Luca; Link, David; Font, José A.
2011-08-01
Binary neutron star mergers are one of the possible candidates for the central engine of short gamma-ray bursts (GRBs) and they are also powerful sources of gravitational waves. We have used our fully general relativistic hydrodynamical code Whisky to investigate the merger of binary neutron star systems and we have in particular studied the properties of the tori that can be formed by these systems, their possible connection with the engine of short GRBs and the gravitational wave signals that detectors such as advanced LIGO will be able to detect. We have also shown how the mass of the torus varies as a function of the total mass of the neutron stars composing the binary and of their mass ratio and we have found that tori sufficiently massive to power short GRBs can indeed be formed.
General Relativistic Effects in the Core Collapse Supernova Mechanism
Bruenn, S W; Mezzacappa, A
2001-01-01
We apply our recently developed code for spherically symmetric, fully general relativistic (GR) Lagrangian hydrodynamics and multigroup flux-limited diffusion neutrino transport to examine the effects of GR on the hydrodynamics and transport during collapse, bounce, and the critical shock reheating phase of core collapse supernovae. Comparisons of models computed with GR versus Newtonian hydrodynamics show that collapse to bounce takes slightly less time in the GR limit, and that the shock propagates slightly farther out in radius before receding. After a secondary quasistatic rise in the shock radius, the shock radius declines considerably more rapidly in the GR simulations than in the corresponding Newtonian simulations. During the shock reheating phase, core collapse computed with GR hydrodynamics results in a substantially more compact structure from the center out to the stagnated shock. The inflow speed of material behind the shock is also increased. Comparisons also show that the luminosity and rms ene...
Donmez, O
2004-01-01
In this paper, the general procedure to solve the General Relativistic Hydrodynamical(GRH) equations with Adaptive-Mesh Refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of general relativistic hydrodynamic equations are done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second order convergence of the code in 1D, 2D and 3D. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the general relativistic hydrodynamical equa...
Gallo, Emanuel
2016-01-01
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. By construction, the model incorporates the back reaction due to gravitational radiation generated by the motion of the particle. Our approach differs from other constructions tackling the same kind of problem.
Lou, Yu-Qing; Xia, Yu-Kai
2017-05-01
We study magnetohydrodynamic (MHD) self-similar collapses and void evolution, with or without shocks, of a general polytropic quasi-spherical magnetofluid permeated by random transverse magnetic fields under the Paczynski-Wiita gravity that captures essential general relativistic effects of a Schwarzschild black hole (BH) with a growing mass. Based on the derived set of non-linear MHD ordinary differential equations, we obtain various asymptotic MHD solutions, the geometric and analytical properties of the magnetosonic critical curve (MSCC) and MHD shock jump conditions. Novel asymptotic MHD solution behaviours near the rim of central expanding voids are derived analytically. By exploring numerical global MHD solutions, we identify allowable boundary conditions at large radii that accommodate a smooth solution and show that a reasonable amount of magnetization significantly increases the mass accretion rate in the expansion-wave-collapse solution scenario. We also construct the counterparts of envelope-expansion-core-collapse solutions that cross the MSCC twice, which are found to be closely paired with a sequence of global smooth solutions satisfying a novel type of central MHD behaviours. MHD shocks with static outer and various inner flow profiles are also examined. Astrophysical applications include dynamic core collapses of magnetized massive stars and compact objects as well as formation of supermassive, hypermassive, dark matter and mixed matter BHs in the Universe, including the early Universe. Such gigantic BHs can be detected in X-ray/gamma-ray sources, quasars, ultraluminous infrared galaxies or extremely luminous infrared galaxies and dark matter overwhelmingly dominated elliptical galaxies as well as massive dark matter halos, etc. Gravitational waves and electromagnetic wave emissions in broad band (including e.g., gamma-ray bursts and fast radio bursts) can result from this type of dynamic collapses of forming BHs involving magnetized media.
Leung, Chun Sing; Harko, Tiberiu
2013-01-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation-dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution of the luminosity it is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.
Generalized Langevin Equation Description of Stochastic Oscillations of General Relativistic Disks
Indian Academy of Sciences (India)
Chun Sing Leung; Gabriela Mocanu; Tiberiu Harko
2014-09-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation–dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and Kerr cases. The power spectral distribution of the luminosity is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.
Relativistic Configuration Interaction Treatment of Generalized Oscillator Strength for Krypton
Institute of Scientific and Technical Information of China (English)
WANG Huang-Chun; QU Yi-Zhi; LIU Chun-Hua
2007-01-01
A fully relativistic configuration interaction method is developed to investigate the transition energies and general oscillator strengths of the lower lying states of krypton, for both optically allowed and optically forbidden transitions. The calculated results are in agreement with the recent experimental measurements. The calculated transition energies for the 5s and 5s' transitions are 9.970 and 10.717eV, which agree with the experimental data of 10.033 and 10.643 eV. The calculated oscillator strengths are 0.211 and 0.170, comparable with the experimental results 0.214(±0.012) and 0.194 (±0.012), respectively. The momentum transfer positions ( K2 in a.u.) of the minimum and maximum GOSs in the 4s24p6 → 4s24p5 (5s + 5s') transitions are 1.105 and 2.225, comparable with the measurements results 1.24 and 2.97 [Phys. Rev. A 67 (2003) 062708].
Matsas, G E A
2003-01-01
We investigate and solve in the context of General Relativity the apparent paradox which appears when bodies floating in a background fluid are set in relativistic motion. Suppose some macroscopic body, say, a submarine designed to lie just in equilibrium when it rests (totally) immersed in a certain background fluid. The puzzle arises when different observers are asked to describe what is expected to happen when the submarine is given some high velocity parallel to the direction of the fluid surface. On the one hand, according to observers at rest with the fluid, the submarine would contract and, thus, sink as a consequence of the density increase. On the other hand, mariners at rest with the submarine using an analogous reasoning for the fluid elements would reach the opposite conclusion. The general relativistic extension of the Arquimedes law for moving bodies shows that the submarine sinks.
Zanotti, Olindo; Dumbser, Michael
2015-01-01
We present a new numerical tool for solving the special relativistic ideal MHD equations that is based on the combination of the following three key features: (i) a one-step ADER discontinuous Galerkin (DG) scheme that allows for an arbitrary order of accuracy in both space and time, (ii) an a posteriori subcell finite volume limiter that is activated to avoid spurious oscillations at discontinuities without destroying the natural subcell resolution capabilities of the DG finite element framework and finally (iii) a space-time adaptive mesh refinement (AMR) framework with time-accurate local time-stepping. The divergence-free character of the magnetic field is instead taken into account through the so-called 'divergence-cleaning' approach. The convergence of the new scheme is verified up to 5th order in space and time and the results for a sample of significant numerical tests including shock tube problems, the RMHD rotor problem and the Orszag-Tang vortex system are shown. We also consider a simple case of t...
Chu, M. S.; Guo, Wenfeng
2016-06-01
The frequency spectrum and mode structure of axisymmetric electrostatic oscillations [the zonal flow (ZF), sound waves (SW), geodesic acoustic modes (GAM), and electrostatic mean flows (EMF)] in tokamaks with general cross-sections and toroidal flows are studied analytically using the electrostatic approximation for magnetohydrodynamic modes. These modes constitute the "electrostatic continua." Starting from the energy principle for a tokamak plasma with toroidal rotation, we showed that these modes are completely stable. The ZF, the SW, and the EMF could all be viewed as special cases of the general GAM. The Euler equations for the general GAM are obtained and are solved analytically for both the low and high range of Mach numbers. The solution consists of the usual countable infinite set of eigen-modes with discrete eigen-frequencies, and two modes with lower frequencies. The countable infinite set is identified with the regular GAM. The lower frequency mode, which is also divergence free as the plasma rotation tends to zero, is identified as the ZF. The other lower (zero) frequency mode is a pure geodesic E×B flow and not divergence free is identified as the EMF. The frequency of the EMF is shown to be exactly 0 independent of plasma cross-section or its flow Mach number. We also show that in general, sound waves with no geodesic components are (almost) completely lost in tokamaks with a general cross-sectional shape. The exception is the special case of strict up-down symmetry. In this case, half of the GAMs would have no geodesic displacements. They are identified as the SW. Present day tokamaks, although not strictly up-down symmetric, usually are only slightly up-down asymmetric. They are expected to share the property with the up-down symmetric tokamak in that half of the GAMs would be more sound wave-like, i.e., have much weaker coupling to the geodesic components than the other half of non-sound-wave-like modes with stronger coupling to the geodesic
General relativistic polytropes with a repulsive cosmological constant
Stuchlík, Zdeněk; Hledík, Stanislav; Novotný, Jan
2016-11-01
Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters—the polytropic index n , the ratio of central pressure and central energy density of matter σ , and the ratio of energy density of vacuum and central density of matter λ . The static equilibrium configurations are determined by two coupled first-order nonlinear differential equations that are solved by numerical methods with the exception of polytropes with n =0 corresponding to the configurations with a uniform distribution of energy density, when the solution is given in terms of elementary functions. The geometry of the polytropes is conveniently represented by embedding diagrams of both the ordinary space geometry and the optical reference geometry reflecting some dynamical properties of the geodesic motion. The polytropes are represented by radial profiles of energy density, pressure, mass, and metric coefficients. For all tested values of n >0 , the static equilibrium configurations with fixed parameters n , σ , are allowed only up to a critical value of the cosmological parameter λc=λc(n ,σ ). In the case of n >3 , the critical value λc tends to zero for special values of σ . The gravitational potential energy and the binding energy of the polytropes are determined and studied by numerical methods. We discuss in detail the polytropes with an extension comparable to those of the dark matter halos related to galaxies, i.e., with extension ℓ>100 kpc and mass M >1 012 M⊙ . For such largely extended polytropes, the cosmological parameter relating the vacuum energy to the central density has to be larger than λ =ρvac/ρc˜10-9. We demonstrate that the extension of the static general relativistic polytropic configurations cannot exceed the so-called static radius related to their external spacetime, supporting the idea
Waves in General Relativistic Two-fluid Plasma around a Schwarzschild Black Hole
Rahman, M Atiqur
2010-01-01
Waves propagating in the relativistic electron-positron or ions plasma are investigated in a frame of two-fluid equations using the 3+1 formalism of general relativity developed by Thorne, Price and Macdonald (TPM). The plasma is assumed to be freefalling in the radial direction toward the event horizon due to the strong gravitational field of a Schwarzschild black hole. The local dispersion relations for transverse and longitudinal waves have been derived, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon using WKB approximation
Generalized quantum similarity in atomic systems: A quantifier of relativistic effects
Martín, A. L.; Angulo, J. C.; Antolín, J.; López-Rosa, S.
2017-02-01
Quantum similarity between Hartree-Fock and Dirac-Fock electron densities reveals the depth of relativistic effects on the core and valence regions in atomic systems. The results emphasize the relevance of differences in the outermost subshells, as pointed out in recent studies by means of Shannon-like functionals. In this work, a generalized similarity functional allows us to go far beyond the Shannon-based analyses. The numerical results for systems throughout the Periodic Table show that discrepancies between the relativistic and non-relativistic descriptions are patently governed by shell-filling patterns.
Choreographic solution to the general-relativistic three-body problem.
Imai, Tatsunori; Chiba, Takamasa; Asada, Hideki
2007-05-18
We reexamine the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particle moves periodically in a single closed orbit. One is a stable figure-eight orbit for a three-body system, which was found first by Moore (1993) and rediscovered with its existence proof by Chenciner and Montgomery (2000). In general relativity, however, the periastron shift prohibits a binary system from orbiting in a single closed curve. Therefore, it is unclear whether general-relativistic effects admit choreography such as the figure eight. We examine general-relativistic corrections to initial conditions so that an orbit for a three-body system can be choreographic and a figure eight. This illustration suggests that the general-relativistic N-body problem also may admit a certain class of choreographic solutions.
Horak, Jiri
2013-01-01
We study the dynamics of spiral waves and oscillation modes in relativistic rotating discs around black holes. Generalizing the Newtonian theory, we show that wave absorption can take place at the corotation resonance, where the pattern frequency of the wave matches the background disc rotation rate. We derive the general relativistic expression for the disc vortensity (vorticity divided by surface density), which governs the behaviour of density perturbation near corotation. Depending on the gradient of the generalized disc vortensity, corotational wave absorption can lead to the amplification or damping of the spiral wave. We apply our general theory of relativistic wave dynamics to calculate the non-axisymmetric inertial-acoustic modes (also called p-modes) trapped in the inner-most region of a black hole accretion disc. Because general relativity changes the profiles of the radial epicyclic frequency and disc vortensity near the inner disc edge close to the black hole, these p-modes can become overstable ...
Generalized Relativistic Wave Equations with Intrinsic Maximum Momentum
Ching, Chee Leong
2013-01-01
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential are stronger than vector potential. The energy spectrum of the systems studied are bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
Generalized relativistic wave equations with intrinsic maximum momentum
Ching, Chee Leong; Ng, Wei Khim
2014-05-01
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
Relativistic corrections to the central force problem in a generalized potential approach
Singh, Ashmeet
2014-01-01
We present a novel technique to obtain the relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy. Throughout the paper, we focus on the attractive inverse square law central force. The generalised potential can be made a part of the regular classical lagrangian which can reproduce the relativistic force equation upto second order in $|\\vec{v}|/c$. We then go on to derive the relativistically corrected Hamiltonian from the Lagrangian and estimate the corrections to the total energy of the system. We employ our methodology to calculate the relativistic correction to the circular orbit in attractive gravitational force. We also estimate to the first order energy correction in the ground state of the hydrogen atom in the semi-classical approach. Our predictions in both problems give the reasonable agreement with the known results. Thus we feel that this work has pedagogical value and can be used by undergraduate students to better understand the ...
De Rijcke, Sven; Boelens, Thomas
2014-01-01
We show that the general relativistic theory of the dynamics of isotropic stellar clusters can be developed essentially along the same lines as the Newtonian theory. We prove that the distribution function can be derived from any isotropic momentum moment and that every higher-order moment of the distribution can be written as an integral over a zeroth-order moment. We propose a mathematically simple expression for the distribution function of a family of isotropic general relativistic cluster models and investigate their dynamical properties. In the Newtonian limit, these models obtain a distribution function of the form F(E) ~ (E-E_0)^alpha, with E binding energy and E_0 a constant that determines the model's outer radius. The slope alpha sets the steepness of the distribution function and the corresponding radial density and pressure profiles. We show that the field equations only yield solutions with finite mass for alpha3.5, only Newtonian models exist. In other words: within the context of this family o...
Generalized shock conditions and the contact discontinuity in the Hall-magnetohydrodynamics model
Energy Technology Data Exchange (ETDEWEB)
Hameiri, Eliezer [Courant Institute of Mathematical Sciences, New York University, New York 10012 (United States)
2013-02-15
It is shown that shocks and contact discontinuities in the Hall-magnetohydrodynamics (HMHD) model must satisfy solvability conditions that replace some of the familiar Rankine-Hugoniot jump conditions when the latter do not apply due to singular behavior of fluxes of conserved quantities. Some of these conditions depend on the larger topology of the plasma and magnetic field and are not merely 'local.' The contact discontinuity which separates two adjoining plasma regions or plasma and vacuum regions is the simplest case where the new jump conditions are applicable and is discussed for a toroidal plasma with sheared magnetic field such as the tokamak, but with no initial mass flow. It is proven that a static discontinuous tokamak-like equilibrium is linearly stable in the HMHD model if it is linearly stable within the ideal magnetohydrodynamics model, provided that the electron pressure depends only on the density, and some other restrictions on the ratio of pressure to density gradients also apply. When the electron pressure does depend on two thermodynamic variables, a sufficient condition for Hall-MHD plasma stability is derived as well.
General relativistic simulations of compact binary mergers as engines of short gamma-ray bursts
Paschalidis, Vasileios
2016-01-01
Black hole - neutron star (BHNS) and neutron star - neutron star (NSNS) binaries are among the favored candidates for the progenitors of the black hole - disk systems that may be the engines powering short-hard gamma ray bursts. After almost two decades of simulations of binary NSNSs and BHNSs in full general relativity we are now beginning to understand the ingredients that may be necessary for these systems to launch incipient jets. Here, we review our current understanding, and summarize the surprises and lessons learned from state-of-the-art (magnetohydrodynamic) simulations in full general relativity of BHNS and NSNS mergers as jet engines for short-hard gamma-ray bursts.
Institute of Scientific and Technical Information of China (English)
WANG Yu-Sheng; ZHANG Xiao-Ni; YUAN Bao-He; FANG Jian-Hui; YANG Guo-Hong; LIN Peng; PANG Ting
2008-01-01
Based on the concept of higher-order adiabatic invariants of mechanical system with action of a small perturbation, the perturbation to Lie symmetry and generalized Hojman adiabatic invariants for the relativistic Hamilton system are studied. Perturbation to Lie symmetry is discussed under general infinitesimal transformation of groups in which time is variable. The form and the criterion of generalized Hojman adiabatic invariants for this system are obtained. Finally, an example is given to illustrate the results.
Post-relativistic gravity a hidden variable theory for general relativity
Schmelzer, I
1996-01-01
Post-relativistic gravity is a hidden variable theory for general relativity. It introduces the pre-relativistic notions absolute space, absolute time, and ether as hidden variables into general relativity. Evolution is defined by the equations of general relativity and the harmonic coordinate condition interpreted as a physical equation. There are minor differences in predictions compared with general relativity (i.e. trivial topology of the universe is predicted). The unobservable absolute time is designed to solve the problem of time in quantization of general relativity. Background space and time define a Newtonian frame for the quantization of the gravitational field. By the way, a lot of other conceptual problems of quantization will be solved (i.e. no constraints, no topological foam, no black hole and bib bang singularities, natural vacuum definition for quantum fields on classical background).
Whistler-Mode Waves Growth by a Generalized Relativistic Kappa-Type Distribution
Institute of Scientific and Technical Information of China (English)
ZHOU Qing-Hua; JIANG Bin; SHI Xiang-Hua; LI Jun-Qiu
2009-01-01
The instability of field-aligned Whistler-mode waves in space plasmas is studied by using a recently developed generalized relativistic kappa-type (KT) distribution. Numerical calculations are performed for a direct compar-ison between the new KT distribution and the current kappa distribution. We show that the wave growth for the KT distribution tends to occur in the lower wave frequency (e.g., ω 0.1Ωe) due to a larger fractional num-ber of the resonant electrons ηrel (which controls the wave growth), while primarily locating in the higher wave frequency for the kappa distribution. Moreover, the relativistic anisotropy Arel by the KT distribution is found to be smaller than that by the kappa distribution, leading to a smaller peak of wave growth. The results present a further understanding of plasma wave instability particularly in those plasmas where relativistic electrons are present.
Narayan, Ramesh; Psaltis, Dimitrios; Sadowski, Aleksander
2015-01-01
We describe HEROIC, an upgraded version of the relativistic radiative post-processor code HERO described in a previous paper, but which now Includes Comptonization. HEROIC models Comptonization via the Kompaneets equation, using a quadratic approximation for the source function in the short characteristics radiation solver. It employs a simple form of accelerated lambda iteration to handle regions of high scattering opacity. In addition to solving for the radiation field, HEROIC also solves for the gas temperature by applying the condition of radiative equilibrium. We present benchmarks and tests of the Comptonization module in HEROIC with simple 1D and 3D scattering problems. We also test the ability of the code to handle various relativistic effects using model atmospheres and accretion flows in a black hole space-time. We present two applications of HEROIC to general relativistic MHD simulations of accretion discs. One application is to a thin accretion disc around a black hole. We find that the gas below ...
Donmez, Orhan
We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.
The generalized Coulomb interactions for relativistic scalar bosons
Zarrinkamar, S.; Panahi, H.; Rezaei, M.
2016-07-01
Approximate analytical solutions of Duffin-Kemmer-Petiau (DKP) equation are obtained for the truncated Coulomb, generalized Cornell, Richardson and Song-Lin potentials via the quasi-exact analytical ansatz approach.
General relativistic effects in quantum interference of "clocks"
Zych, Magdalena; Costa, Fabio; Brukner, Časlav
2016-01-01
Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and is also not fully understood by theory. This contribution reviews recent ideas for a new type of experiments: quantum interference of "clocks", which aim to test novel quantum effects that arise from time dilation. "Clock" interference experiments could be realised with atoms or photons in near future laboratory experiments.
A Two-Dimensional MagnetoHydrodynamics Scheme for General Unstructured Grids
Livne, E; Burrows, A; Meakin, C A; Livne, Eli; Dessart, Luc; Burrows, Adam; Meakin, Casey A.
2007-01-01
We report a new finite-difference scheme for two-dimensional magnetohydrodynamics (MHD) simulations, with and without rotation, in unstructured grids with quadrilateral cells. The new scheme is implemented within the code VULCAN/2D, which already includes radiation-hydrodynamics in various approximations and can be used with arbitrarily moving meshes (ALE). The MHD scheme, which consists of cell-centered magnetic field variables, preserves the nodal finite difference representation of $div(\\bB)$ by construction, and therefore any initially divergence-free field remains divergence-free through the simulation. In this paper, we describe the new scheme in detail and present comparisons of VULCAN/2D results with those of the code ZEUS/2D for several one-dimensional and two-dimensional test problems. The code now enables two-dimensional simulations of the collapse and explosion of the rotating, magnetic cores of massive stars. Moreover, it can be used to simulate the very wide variety of astrophysical problems for...
General relativistic effects in quantum interference of “clocks”
Zych, M.; Pikovski, I.; Costa, F.; Brukner, Č.
2016-06-01
Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and is also not fully understood by theory. This contribution reviews recent ideas for a new type of experiments: quantum interference of “clocks”, which aim to test novel quantum effects that arise from time dilation. “Clock” interference experiments could be realised with atoms or photons in near future laboratory experiments.
A choreographic solution to the general relativistic three-body problem
Imai, T; Chiba, T; Asada, Hideki; Chiba, Takamasa; Imai, Tatsunori
2007-01-01
We revisit the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particles move periodically in a single closed orbit. One is a stable figure-eight orbit of a three-body system, which was found first by Moore (1993) and re-discovered with its existence proof by Chenciner and Montgomery (2000), In general relativity, however, the periastron shift prohibits a binary system from orbiting in a closed curve. Therefore, it is unclear whether general relativistic effects admit a choreographic solution such as the figure-eight. We carefully examine general relativistic corrections to initial conditions so that an orbit to a three-body system can be closed in a figure-eight. This solution is still choreographic without causing periastron shift. This illustration suggests that the general relativistic N-body problem also may admit a certain class of choreographic solutions.
Dönmez, Orhan
2004-09-01
In this paper, the general procedure to solve the general relativistic hydrodynamical (GRH) equations with adaptive-mesh refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of GRH equations are obtained by high resolution shock Capturing schemes (HRSC), specifically designed to solve nonlinear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second-order convergence of the code in one, two and three dimensions. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the GRH equations are tested using two different test problems which are Geodesic flow and Circular motion of particle In order to do this, the flux part of GRH equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time.
General Relativistic Non-radial Oscillations of Compact Stars
Hall, Zack, II; Jaikumar, Prashanth
2017-01-01
Currently, we lack a means of identifying the type of matter at the core of compact stars, but in the future, we may be able to use gravitational wave signals produced by fluid oscillations inside compact stars to discover new phases of dense matter. To this end, we study the fluid perturbations inside compact stars such as Neutron Stars and Strange Quark Stars, focusing on modes that couple to gravitational waves. Using a modern equation of state for quark matter that incorporates interactions at moderately high densities, we implement an efficient computational scheme to solve the oscillation equations in the framework of General Relativity, and determine the complex eigenfrequencies that describe the oscillation and damping of the non-radial fluid modes. We discuss the significance of our results for future detection of these modes through gravitational waves. This work is supported in part by the CSULB Graduate Research Fellowship and by the National Science Foundation NSF PHY-1608959.
Masson, J.; Chabrier, G.; Hennebelle, P.; Vaytet, N.; Commerçon, B.
2016-03-01
Angular momentum transport and the formation of rotationally supported structures are major issues in our understanding of protostellar core formation. Whereas purely hydrodynamical simulations lead to large Keplerian disks, ideal magnetohydrodynamics (MHD) models yield the opposite result, with essentially no disk formation. This stems from the flux-freezing condition in ideal MHD, which leads to strong magnetic braking. In this paper, we provide a more accurate description of the evolution of the magnetic flux redistribution by including resistive terms in the MHD equations. We focus more particularly on the effect of ambipolar diffusion on the properties of the first Larson core and its surrounding structure, exploring various initial magnetisations and magnetic field versus rotation axis orientations of a 1 M⊙ collapsing prestellar dense core. We used the non-ideal magnetohydrodynamics version of the adaptive mesh refinement code RAMSES to carry out these calculations. The resistivities required to calculate the ambipolar diffusion terms were computed using a reduced chemical network of charged, neutral, and grain species. Including ambipolar diffusion leads to the formation of a magnetic diffusion barrier (also known as the decoupling stage) in the vicinity of the core, which prevents accumulation of magnetic flux in and around the core and amplification of the field above 0.1 G. The mass and radius of the first Larson core, however, remain similar between ideal and non-ideal MHD models. This diffusion plateau, preventing further amplification of the field and reorganising the field topology, has crucial consequences for magnetic braking processes, allowing the formation of disk structures. Magnetically supported outflows launched in ideal MHD models are weakened or even disappear when using non-ideal MHD. In contrast to ideal MHD calculations, misalignment between the initial rotation axis and the magnetic field direction does not significantly affect the
Quantum interferometric visibility as a witness of general relativistic proper time.
Zych, Magdalena; Costa, Fabio; Pikovski, Igor; Brukner, Časlav
2011-10-18
Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter-wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov-Bohm effect, where a particle in a flat space-time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'-a particle with evolving internal degrees of freedom-that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space-time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics.
Critical rotation of general-relativistic polytropic models revisited
Geroyannis, V.; Karageorgopoulos, V.
2013-09-01
We develop a perturbation method for computing the critical rotational parameter as a function of the equatorial radius of a rigidly rotating polytropic model in the "post-Newtonia approximation" (PNA). We treat our models as "initial value problems" (IVP) of ordinary differential equations in the complex plane. The computations are carried out by the code dcrkf54.f95 (Geroyannis and Valvi 2012 [P1]; modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane). Such a complex-plane treatment removes the syndromes appearing in this particular family of IVPs (see e.g. P1, Sec. 3) and allows continuation of the numerical integrations beyond the surface of the star. Thus all the required values of the Lane-Emden function(s) in the post-Newtonian approximation are calculated by interpolation (so avoiding any extrapolation). An interesting point is that, in our computations, we take into account the complete correction due to the gravitational term, and this issue is a remarkable difference compared to the classical PNA. We solve the generalized density as a function of the equatorial radius and find the critical rotational parameter. Our computations are extended to certain other physical characteristics (like mass, angular momentum, rotational kinetic energy, etc). We find that our method yields results comparable with those of other reliable methods. REFERENCE: V.S. Geroyannis and F.N. Valvi 2012, International Journal of Modern Physics C, 23, No 5, 1250038:1-15.
Cosmology and stellar equilibrium using Newtonian hydrodynamics with general relativistic pressure
Baqui, P O; Piattella, O F
2015-01-01
We revisit the analysis made by Hwang and Noh [JCAP 1310 (2013)] aiming the construction of a Newtonian set of equations incorporating pressure effects typical of General Relativity theory. We perform in an explicit way the deduction of the Hwang-Noh equations, comparing it with similar computations found in the literature. Later, we investigate stellar equilibrium and cosmology, at background and perturbative levels, using the new set of equations. It is shown that, in this context, the predictions for the background evolution of the universe are deeply changed with respect to the full relativistic theory: the acceleration of the universe is achieved with positive pressure. The properties of neutron stars are reproduced qualitatively, but the upper mass is at least one order of magnitude higher than that obtained in General Relativity. However, the perturbed cosmological equations at small scales reproduce those found in the relativistic context. We argue that this last result may open new possibilities for ...
General Relativistic Precession in Small Solar System Bodies
Sekhar, Aswin; Werner, Stephanie; Hoffmann, Volker; Asher, David; Vaubaillon, Jeremie; Hajdukova, Maria; Li, Gongjie
2016-10-01
Introduction: One of the greatest successes of the Einstein's General Theory of Relativity (GR) was the correct prediction of the precession of perihelion of Mercury. The closed form expression to compute this precession tells us that substantial GR precession would occur only if the bodies have a combination of both moderately small perihelion distance and semi-major axis. Minimum Orbit Intersection Distance (MOID) is a quantity which helps us to understand the closest proximity of two orbits in space. Hence evaluating MOID is crucial to understand close encounters and collision scenarios better. In this work, we look at the possible scenarios where a small GR precession in argument of pericentre (ω) can create substantial changes in MOID for small bodies ranging from meteoroids to comets and asteroids.Analytical Approach and Numerical Integrations: Previous works have looked into neat analytical techniques to understand different collision scenarios and we use those standard expressions to compute MOID analytically. We find the nature of this mathematical function is such that a relatively small GR precession can lead to drastic changes in MOID values depending on the initial value of ω. Numerical integrations were done with package MERCURY incorporating the GR code to test the same effects. Numerical approach showed the same interesting relationship (as shown by analytical theory) between values of ω and the peaks/dips in MOID values. Previous works have shown that GR precession suppresses Kozai oscillations and this aspect was verified using our integrations. There is an overall agreement between both analytical and numerical methods.Summary and Discussion: We find that GR precession could play an important role in the calculations pertaining to MOID and close encounter scenarios in the case of certain small solar system bodies (depending on their initial orbital elements). Previous works have looked into impact probabilities and collision scenarios on
Institute of Scientific and Technical Information of China (English)
Luo Shao-Kai
2007-01-01
For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of the theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables t, qs and (q)s. An example is given to illustrate the application of the results.
A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion
Energy Technology Data Exchange (ETDEWEB)
Ojeda-Guillén, D., E-mail: dojedag@ipn.mx [Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, Delegación Gustavo A. Madero, C.P. 07738 Ciudad de México (Mexico); Mota, R. D. [Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacán, C.P. 04430 Ciudad de México (Mexico); Granados, V. D. [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, Delegación Gustavo A. Madero, C.P. 07738 Ciudad de México (Mexico)
2016-06-15
We introduce a generalization of the Jaynes-Cummings model and study some of its properties. We obtain the energy spectrum and eigenfunctions of this model by using the tilting transformation and the squeezed number states of the one-dimensional harmonic oscillator. As physical applications, we connect this new model to two important and novelty problems: the relativistic parametric amplifier and the quantum simulation of a single trapped ion.
General Relativistic Radiative Transfer Code in Rotating Black Hole Spacetime: {ARTIST}
Takahashi, Rohta; Umemura, Masayuki
2016-10-01
We present a general relativistic radiative transfer code, {ARTIST} (Authentic Radiative Transfer In Space-Time), which is a perfectly causal scheme to pursue the propagation of radiation with absorption and scattering around a Kerr black hole. The code explicitly solves the invariant radiation intensity along null geodesics in the Kerr-Schild coordinates, and therefore properly includes light bending, Doppler boosting, frame dragging, and gravitational redshifts. The notable aspect of {ARTIST} is that it conserves the radiative energy with high accuracy, and is not subject to the numerical diffusion, since the transfer is solved on long characteristics along null geodesics. We first solve the wavefront propagation around a Kerr black hole, which was originally explored by Hanni (1977). This demonstrates repeated wavefront collisions, light bending, and causal propagation of radiation with the speed of light. We show that the decay rate of the total energy of wavefronts near a black hole is determined solely by the black hole spin in late phases, in agreement with analytic expectations. As a result, the {ARTIST} turns out to correctly solve the general relativistic radiation fields until late phases as t ˜ 90M. We also explore the effects of absorption and scattering, and apply this code for a photon wall problem and an orbiting hot spot problem. All the simulations in the present study are performed in the equatorial plane around a Kerr black hole. The {ARTIST} is the first step to realize the general relativistic radiation hydrodynamics.
General relativistic radiative transfer code in rotating black hole space-time: ARTIST
Takahashi, Rohta; Umemura, Masayuki
2017-02-01
We present a general relativistic radiative transfer code, ARTIST (Authentic Radiative Transfer In Space-Time), that is a perfectly causal scheme to pursue the propagation of radiation with absorption and scattering around a Kerr black hole. The code explicitly solves the invariant radiation intensity along null geodesics in the Kerr-Schild coordinates, and therefore properly includes light bending, Doppler boosting, frame dragging, and gravitational redshifts. The notable aspect of ARTIST is that it conserves the radiative energy with high accuracy, and is not subject to the numerical diffusion, since the transfer is solved on long characteristics along null geodesics. We first solve the wavefront propagation around a Kerr black hole that was originally explored by Hanni. This demonstrates repeated wavefront collisions, light bending, and causal propagation of radiation with the speed of light. We show that the decay rate of the total energy of wavefronts near a black hole is determined solely by the black hole spin in late phases, in agreement with analytic expectations. As a result, the ARTIST turns out to correctly solve the general relativistic radiation fields until late phases as t ˜ 90 M. We also explore the effects of absorption and scattering, and apply this code for a photon wall problem and an orbiting hotspot problem. All the simulations in this study are performed in the equatorial plane around a Kerr black hole. The ARTIST is the first step to realize the general relativistic radiation hydrodynamics.
General relativistic simulations of compact binary mergers as engines for short gamma-ray bursts
Paschalidis, Vasileios
2017-04-01
Black hole—neutron star (BHNS) and neutron star—neutron star (NSNS) binaries are among the favored candidates for the progenitors of the black hole—disk systems that may be the engines powering short-hard gamma ray bursts. After almost two decades of simulations of binary NSNSs and BHNSs in full general relativity we are now beginning to understand the ingredients that may be necessary for these systems to launch incipient jets. Here, we review our current understanding, and summarize the surprises and lessons learned from state-of-the-art (magnetohydrodynamic) simulations in full general relativity of BHNS and NSNS mergers as jet engines for short-hard gamma-ray bursts. We also propose a new approach to probing the nuclear equation of state by virtue of multimessenger observations.
A New Formulation for General Relativistic Force-Free Electrodynamics and Its Applications
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We formulate the general relativistic force-free electrodynamics in a new 3+1 language. In this formulation, when we have properly defined electric and magnetic fields, the covariant Maxwell equations could be cast in the traditional form with new vacuum con stitutive constraint equations. The fundamental equation governing a stationary, axisymmet ric force-free black hole magnetosphere is derived using this formulation which recasts the Grad-Shafranov equation in a simpler way. Compared to the classic 3+1 system of Thorne and MacDonald, the new system of 3+1 equations is more suitable for numerical use for it keeps the hyperbolic structure of the electrodynamics and avoids the singularity at the event horizon. This formulation could be readily extended to non-relativistic limit and find applications in flat spacetime. We investigate its application to disk wind, black hole magnetosphere and solar physics in both flat and curved spacetime.
Analytical Solution of Relativistic Few-Body Bound Systems with a Generalized Yukawa Potential
Aslanzadeh, M.; Rajabi, A. A.
2016-03-01
We have investigated in this paper the few-body bound systems in a simple semi-relativistic scheme. For this aim, we introduced a spin independent relativistic description for a few-identical body system by presenting the analytical solution of few-particle Klein-Gordon equation. Performing calculations in D-dimensional configuration on the basis of the hypercentral approach, we reduced the few-body Klein-Gordon equation to a Schrödinger-like form. This equation is solved by using the Nikiforov-Uvarov method, through which the energy equations and eigenfunctions for a few-body bound system are obtained. We used the spin- and isospin-independent generalized Yukawa potential in our calculations, and the dependence of the few-body binding energies on the potential parameters has been investigated.
On the General Solution to Einstein's Vacuum Field and Its Implications for Relativistic Degeneracy
Directory of Open Access Journals (Sweden)
Crothers S. J.
2005-04-01
Full Text Available The general solution to Einstein’s vacuum field equations for the point-mass in all its configurations must be determined in such a way as to provide a means by which an infinite sequence of particular solutions can be readily constructed. It is from such a solution that the underlying geometry of Einstein’s universe can be rightly explored. I report here on the determination of the general solution and its consequences for the theoretical basis of relativistic degeneracy, i.e. gravitational collapse and the black hole.
Indian Academy of Sciences (India)
Wang Zhi-Yun; Chen Pei-Jie
2016-06-01
A generalized Langevin equation driven by fractional Brownian motion is used to describe the vertical oscillations of general relativistic disks. By means of numerical calculation method, the displacements, velocities and luminosities of oscillating disks are explicitly obtained for different Hurst exponent $H$. The results show that as $H$ increases, the energies and luminosities of oscillating disk are enhanced, and the spectral slope at high frequencies of the power spectrum density of disk luminosity is also increased. This could explain the observational features related to the Intra Day Variability of the BL Lac objects.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
The 2D surfaces that generate Newtonian and general relativistic orbits with small eccentricities
Middleton, Chad A
2015-01-01
Embedding diagrams prove to be quite useful when learning general relativity as they offer a way of visualizing spacetime curvature through warped two dimensional (2D) surfaces. In this manuscript we present a different 2D construct that also serves as a useful conceptual tool for gaining insight into gravitation, in particular, orbital dynamics - namely the cylindrically symmetric surfaces that generate Newtonian and general relativistic orbits with small eccentricities. Although we first show that no such surface exists that can exactly reproduce the arbitrary bound orbits of Newtonian gravitation or of general relativity (or, more generally, of any spherically symmetric potential), surfaces do exist that closely approximate the resulting orbital motion for small eccentricities; exactly the regime that describes the motion of the solar system planets. These surfaces help to illustrate the similarities, as well as the differences, between the two theories of gravitation (i.e. stationary elliptical orbits in ...
Magnetic collimation of meridional-self-similar general relativistic MHD flows
Globus, Noemie; Cayatte, Véronique; Celnikier, Ludwik M
2014-01-01
We present a model for the spine of relativistic MHD outflows in the Kerr geometry. Meridional self-similarity is invoked to derive semi-analytical solutions close to the polar axis. The study of the energy conservation along a particular field line gives a simple criterion for the collimation of jets. Such parameter have already been derived in the classical case by Sauty et al. 1999 and also extended to the Schwarzschild metric by Meliani et al. 2006. We generalize the same study to the Kerr metric. We show that the rotation of the black hole increases the magnetic self-confinement.
The role of currents distribution in general relativistic equilibria of magnetized neutron stars
Bucciantini, N; Del Zanna, L
2014-01-01
Magnetic fields play a critical role in the phenomenology of neutron stars. There is virtually no observable aspect which is not governed by them. Despite this, only recently efforts have been done to model magnetic fields in the correct general relativistic regime, characteristic of these compact objects. In this work we present, for the first time a comprehensive and detailed parameter study, in general relativity, of the role that the current distribution, and the related magnetic field structure, have in determining the precise structure of neutron stars. In particular, we show how the presence of localized currents can modify the field strength at the stellar surface, and we look for general trends, both in terms of energetic properties, and magnetic field configurations. Here we verify that, among other things, for a large class of different current distributions the resulting magnetic configurations are always dominated by the poloidal component of the current.
Newtonian analogue of static general relativistic spacetimes: An extension to naked singularities
Ghosh, Shubhrangshu; Bhadra, Arunava
2015-01-01
We formulate a generic Newtonian like analogous potential for static spherically symmetric general relativistic (GR) spacetime, and subsequently derived proper Newtonian like analogous potential corresponding to Janis-Newman-Winicour (JNW) and Reissner-Nordstr\\"{o}m (RN) spacetimes, both exhibiting naked singularities. The derived potentials found to reproduce the entire GR features including the orbital dynamics of the test particle motion and the orbital trajectories, with precise accuracy. The nature of the particle orbital dynamics including their trajectory profiles in JNW and RN geometries show altogether different behavior with distinctive traits as compared to the nature of particle dynamics in Schwarzschild geometry. Exploiting the Newtonian like analogous potentials, we found that the radiative efficiency of a geometrically thin and optically thick Keplerian accretion disk around naked singularities corresponding to both JNW and RN geometries, in general, is always higher than that for Schwarzschild...
Energy Technology Data Exchange (ETDEWEB)
Haas, Fernando; Pascoal, Kellen Alves [Instituto de Física, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, 91501-970 Porto Alegre, RS (Brazil); Mendonça, José Tito [IPFN, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal and Instituto de Física, Universidade de São Paulo, 05508-090 São Paulo, SP (Brazil)
2016-01-15
A new neutrino magnetohydrodynamics (NMHD) model is formulated, where the effects of the charged weak current on the electron-ion magnetohydrodynamic fluid are taken into account. The model incorporates in a systematic way the role of the Fermi neutrino weak force in magnetized plasmas. A fast neutrino-driven short wavelengths instability associated with the magnetosonic wave is derived. Such an instability should play a central role in strongly magnetized plasma as occurs in supernovae, where dense neutrino beams also exist. In addition, in the case of nonlinear or high frequency waves, the neutrino coupling is shown to be responsible for breaking the frozen-in magnetic field lines condition even in infinite conductivity plasmas. Simplified and ideal NMHD assumptions were adopted and analyzed in detail.
Energy Technology Data Exchange (ETDEWEB)
Gorlin, S.M.; Ljubimov, G.A.; Bitjurin, V.A.; Kovbasjuk, V.I.; Maximenko, V.I.; Medin, S.A.; Barshak, A.E.
1979-12-25
A magnetohydrodynamic device having a duct for a conducting gas to flow at an angle with the direction of the magnetic field induction vector is described. The duct is situated in the magnetic system and is provided with a plurality of electrodes adapted to interact electrically with the gas, whereas the cross-sectional shape of the duct working space is bounded by a closed contour formed by a curve inscribed into a rectangle. 1 claim.
Mueller, B; Marek, A
2012-01-01
We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the CoCoNuT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the spacetime metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 solar mass progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared to Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated ele...
Fully General Relativistic Simulations of Black Hole-Neutron Star Mergers
Etienne, Zachariah B; Liu, Yuk Tung; Shapiro, Stuart L; Taniguchi, Keisuke; Baumgarte, Thomas W
2007-01-01
Black hole-neutron star (BHNS) binaries are expected to be among the leading sources of gravitational waves observable by ground-based detectors, and may be the progenitors of short-hard gamma ray bursts (SGRBs) as well. Here, we discuss our new fully general relativistic calculations of merging BHNS binaries, which use high-accuracy, low-eccentricity, conformal thin-sandwich configurations as initial data. Our evolutions are performed using the moving puncture method and include a fully relativistic, high-resolution shock-capturing hydrodynamics treatment. Focusing on systems in which the neutron star is irrotational and the black hole is nonspinning with a 3:1 mass ratio, we investigate the inspiral, merger, and disk formation in the system. We find that the vast majority of material is promptly accreted and no more than 3% of the neutron star's rest mass is ejected into a tenuous, gravitationally bound disk. We find similar results for mass ratios of 2:1 and 1:1, even when we reduce the NS compaction in th...
General relativistic models for rotating magnetized neutron stars in conformally flat space-time
Pili, A. G.; Bucciantini, N.; Del Zanna, L.
2017-09-01
The extraordinary energetic activity of magnetars is usually explained in terms of dissipation of a huge internal magnetic field of the order of 1015-16 G. How such a strong magnetic field can originate during the formation of a neutron star (NS) is still subject of active research. An important role can be played by fast rotation: if magnetars are born as millisecond rotators dynamo mechanisms may efficiently amplify the magnetic field inherited from the progenitor star during the collapse. In this case, the combination of rapid rotation and strong magnetic field determine the right physical condition not only for the development of a powerful jet-driven explosion, manifesting as a gamma-ray burst, but also for a copious gravitational waves emission. Strong magnetic fields are indeed able to induce substantial quadrupolar deformations in the star. In this paper, we analyse the joint effect of rotation and magnetization on the structure of a polytropic and axisymmetric NS, within the ideal magneto-hydrodynamic regime. We will consider either purely toroidal or purely poloidal magnetic field geometries. Through the sampling of a large parameter space, we generalize previous results in literature, inferring new quantitative relations that allow for a parametrization of the induced deformation, that takes into account also the effects due to the stellar compactness and the current distribution. Finally, in the case of purely poloidal field, we also discuss how different prescription on the surface charge distribution (a gauge freedom) modify the properties of the surrounding electrosphere and its physical implications.
Pétri, J
2014-01-01
The close vicinity of neutron stars remains poorly constrained by observations. Although plenty of data are available for the peculiar class of pulsars we are still unable to deduce the underlying plasma distribution in their magnetosphere. In the present paper, we try to unravel the magnetospheric structure starting from basic physics principles and reasonable assumptions about the magnetosphere. Beginning with the monopole force-free case, we compute accurate general-relativistic solutions for the electromagnetic field around a slowly rotating magnetized neutron star. Moreover, here we address this problem by including the important effect of plasma screening. This is achieved by solving the time-dependent Maxwell equations in a curved space-time following the 3+1~formalism. We improved our previous numerical code based on pseudo-spectral methods in order to allow for possible discontinuities in the solution. Our algorithm based on a multi-domain decomposition of the simulation box belongs to the discontinu...
General relativistic radiative transfer in hot astrophysical plasmas a characteristic approach
Zane, S; Nobili, L; Erna, M; Zane, Silvia; Turolla, Roberto; Nobili, Luciano; Erna, Myris
1996-01-01
In this paper we present a characteristic method for solving the transfer equation in differentially moving media in a curved spacetime. The method is completely general, but its capabilities are exploited at best in presence of symmetries, when the existence of conserved quantities allows to derive analytical expressions for the photon trajectories in phase space. In spherically--symmetric, stationary configurations the solution of the transfer problem is reduced to the integration of a single ordinary differential equation along the bi--parametric family of characteristic rays. Accurate expressions for the radiative processes relevant to continuum transfer in a hot astrophysical plasma have been used in evaluating the source term, including relativistic e--p, e--e bremsstrahlung and Compton scattering. A numerical code for the solution of the transfer problem in moving media in a Schwarzschild spacetime has been developed and tested. Some applications, concerning ``hot'' and ``cold'' accretion onto non--rot...
Sdowski, Aleksander; Tchekhovskoy, Alexander; Zhu, Yucong
2012-01-01
A numerical scheme is described for including radiation in multi-dimensional general-relativistic conservative fluid dynamics codes. In this method, a covariant form of the M1 closure scheme is used to close the radiation moments, and the radiative source terms are treated semi-implicitly in order to handle both optically thin and optically thick regimes. The scheme has been implemented in a conservative general relativistic radiation hydrodynamics code KORAL. The robustness of the code is demonstrated on a number of test problems, including radiative relativistic shock tubes, static radiation pressure supported atmosphere, shadows, beams of light in curved spacetime, and radiative Bondi accretion. The advantages of M1 closure relative to other approaches such as Eddington closure and flux-limited diffusion are discussed, and its limitations are also highlighted.
Herrera, L; Ibañez, J; Ospino, J
2014-01-01
We carry out a general study on the collapse of axially (and reflection) symmetric sources in the context of general relativity. All basic equations and concepts required to perform such a general study are deployed. These equations are written down for a general anisotropic dissipative fluid. The proposed approach allows for analytical studies as well as for numerical applications. A causal transport equation derived from the Israel-Stewart theory is applied, to discuss some thermodynamic aspects of the problem. A set of scalar functions (the structure scalars) derived from the orthogonal splitting of the Riemann tensor are calculated and their role in the dynamics of the source is clearly exhibited. The characterization of the gravitational radiation emitted by the source is discussed.
Relativistic MHD with adaptive mesh refinement
Energy Technology Data Exchange (ETDEWEB)
Anderson, Matthew [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States); Hirschmann, Eric W [Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602 (United States); Liebling, Steven L [Department of Physics, Long Island University-C W Post Campus, Brookville, NY 11548 (United States); Neilsen, David [Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602 (United States)
2006-11-22
This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference convex ENO method (CENO) in 3 + 1 dimensions, and the AMR is Berger-Oliger. Hyperbolic divergence cleaning is used to control the {nabla} . B = 0 constraint. We present results from three flat space tests, and examine the accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel solution. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. Finally, we discuss strong scaling results for parallel unigrid and AMR runs.
Boquist, Carl W.; Marchant, David D.
1978-01-01
A ceramic-metal composite suitable for use in a high-temperature environment consists of a refractory ceramic matrix containing 10 to 50 volume percent of a continuous high-temperature metal reinforcement. In a specific application of the composite, as an electrode in a magnetohydrodynamic generator, the one surface of the electrode which contacts the MHD fluid may have a layer of varying thickness of nonreinforced refractory ceramic for electrode temperature control. The side walls of the electrode may be coated with a refractory ceramic insulator. Also described is an electrode-insulator system for a MHD channel.
Energy Technology Data Exchange (ETDEWEB)
Vacaru, Olivia [National College of Iasi (Romania); Vacaru, Sergiu I. [Quantum Gravity Research, Topanga, CA (United States); University ' ' Al.I. Cuza' ' Iasi, Project IDEI, Iasi (Romania); Werner-Heisenberg-Institute, Max-Planck-Institute for Physics, Munich (Germany); Leibniz University of Hannover, Institute for Theoretical Physics (Germany); Ruchin, Vyacheslav
2017-03-15
Using double 2 + 2 and 3 + 1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in general relativity (GR). Such F- and W-functionals were introduced in the Ricci flow theory of three dimensional (3-d) Riemannian metrics by Perelman (the entropy formula for the Ricci flow and its geometric applications. arXiv:math.DG/0211159). Non-relativistic 3-d Ricci flows are characterized by associated statistical thermodynamical values determined by W-entropy. Generalizations for geometric flows of 4-d pseudo-Riemannian metrics are considered for models with local thermodynamical equilibrium and separation of dissipative and non-dissipative processes in relativistic hydrodynamics. The approach is elaborated in the framework of classical field theories (relativistic continuum and hydrodynamic models) without an underlying kinetic description, which will be elaborated in other work. The 3 + 1 splitting allows us to provide a general relativistic definition of gravitational entropy in the Lyapunov-Perelman sense. It increases monotonically as structure forms in the Universe. We can formulate a thermodynamic description of exact solutions in GR depending, in general, on all spacetime coordinates. A corresponding 2 + 2 splitting with nonholonomic deformation of linear connection and frame structures is necessary for generating in very general form various classes of exact solutions of the Einstein and general relativistic geometric flow equations. Finally, we speculate on physical macrostates and microstate interpretations of the W-entropy in GR, geometric flow theories and possible connections to string theory (a second unsolved problem also contained in Perelman's work) in Polyakov's approach. (orig.)
Kopeikin, S M; Kopeikin, Sergei; Fomalont, Ed
2002-01-01
A relativistic sub-picosecond model of gravitational time delay in radio astronomical observations is worked out and a new experimental test of general relativity is discussed in which the effect of retardation of gravity associated with its finite speed can be observed. As a consequence, the speed of gravity can be measured by differential VLBI observations. Retardation in propagation of gravity is a central part of the Einstein theory of general relativity which has not been tested directly so far. The idea of the proposed gravitational experiment is based on the fact that gravity in general relativity propagates with finite speed so that the deflection of light caused by the body must be sensitive to the ratio of the body's velocity to the speed of gravity. The interferometric experiment can be performed, for example, during the very close angular passage of a quasar by Jupiter. Due to the finite speed of gravity and orbital motion of Jupiter, the variation in its gravitational field reaches observer on Ea...
Geroyannis, Vassilis S
2014-01-01
We develop a "hybrid approximative scheme" in the framework of the post-Newtonian approximation for computing general-relativistic polytropic models simulating neutron stars in critical rigid rotation. We treat the differential equations governing such a model as a "complex initial value problem", and we solve it by using the so-called "complex-plane strategy". We incorporate into the computations the complete solution for the relativistic effects, this issue representing a significant improvement with regard to the classical post-Newtonian approximation, as verified by extended comparisons of the numerical results.
Energy Extraction from Spinning Black Holes via Relativistic Jets
Narayan, Ramesh; Tchekhovskoy, Alexander
2013-01-01
It has for long been an article of faith among astrophysicists that black hole spin energy is responsible for powering the relativistic jets seen in accreting black holes. Two recent advances have strengthened the case. First, numerical general relativistic magnetohydrodynamic simulations of accreting spinning black holes show that relativistic jets form spontaneously. In at least some cases, there is unambiguous evidence that much of the jet energy comes from the black hole, not the disk. Second, spin parameters of a number of accreting stellar-mass black holes have been measured. For ballistic jets from these systems, it is found that the radio luminosity of the jet correlates with the spin of the black hole. This suggests a causal relationship between black hole spin and jet power, presumably due to a generalized Penrose process.
Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation
Frønsdal, Christian
Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity, including matter, is here viewed as a problem of coupling Einstein’s theory of pure gravity to an independently chosen and well-defined field theory of matter. It is well known that this is accomplished in a most natural way when both theories are formulated as relativistic, Lagrangian field theories, as is the case with Einstein-Maxwell theory. Special matter models of this type have been available; here a more general thermodynamical model that allows for vortex flows is presented. In a wider context, the problem of subjecting hydrodynamics and thermodynamics to an action principle is one that has been pursued for at least 150 years. A solution to this problem has been known for some time, but only under the strong restriction to potential flows. A variational principle for general flows has become available. It represents a development of the Navier-Stokes-Fourier approach to fluid dynamics. The principal innovation is the recognition that two kinds of flow velocity fields are needed, one the gradient of a scalar field and the other the time derivative of a vector field, the latter closely associated with vorticity. In the relativistic theory that is presented here, the latter is the Hodge dual of an exact 3-form, well known as the notoph field of Ogievetskij and Palubarinov, the B-field of Kalb and Ramond and the vorticity field of Lund and Regge. The total number of degrees of freedom of a unary system, including the density and the two velocity fields is 4, as expected — as in classical hydrodynamics. In this paper, we do not reduce Einstein’s dynamical equation for the metric to phenomenology, which would have denied the relevance of any intrinsic dynamics for the matter sector, nor do we abandon the equation of continuity - the very soul of hydrodynamics.
Troxel, M A; Ishak, Mustapha
2013-01-01
We study the effects and implications of anisotropies at the scale of galaxy clusters by building an exact general relativistic model of a cluster using the inhomogeneous and anisotropic Szekeres metric. The model is built from a modified Navarro-Frenk-White (NFW) density profile. We compare this to a corresponding spherically symmetric structure in the Lemaitre-Tolman (LT) model and quantify the impact of introducing varying levels of anisotropy. We examine two physical measures of gravitational infall -- the growth rate of density and the velocity of the source dust in the model. We introduce a generalization of the LT dust velocity profile for the Szekeres metric and demonstrate its consistency with the growth rate of density. We find that the growth rate of density in one substructure increases by 0.5%, 1.5%, and 3.75% for 5%, 10%, and 15% levels of introduced anisotropy, which is measured as the fractional displaced mass relative to the spherically symmetric case. The infall velocity of the dust is found...
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
Tessarotto, Massimo; Cremaschini, Claudio
2016-08-01
In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm " pilot-wave" interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton-Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.
Energy Technology Data Exchange (ETDEWEB)
Mueller, Bernhard; Janka, Hans-Thomas; Marek, Andreas, E-mail: bjmuellr@mpa-garching.mpg.de, E-mail: thj@mpa-garching.mpg.de [Max-Planck-Institut fuer Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching (Germany)
2012-09-01
We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the COCONUT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the space-time metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 M{sub Sun} progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared with Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models, the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50%-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.
Arzeliès, Henri
1972-01-01
Relativistic Point Dynamics focuses on the principles of relativistic dynamics. The book first discusses fundamental equations. The impulse postulate and its consequences and the kinetic energy theorem are then explained. The text also touches on the transformation of main quantities and relativistic decomposition of force, and then discusses fields of force derivable from scalar potentials; fields of force derivable from a scalar potential and a vector potential; and equations of motion. Other concerns include equations for fields; transfer of the equations obtained by variational methods int
Pétri, J
2014-01-01
Pulsars are believed to loose their rotational kinetic energy primarily by a large amplitude low frequency electromagnetic wave which is eventually converted into particle creation, acceleration and followed by a broad band radiation spectrum. To date, there exist no detailed calculation of the exact spin-down luminosity with respect to the neutron star magnetic moment and spin frequency, including general-relativistic effects. Estimates are usually given according to the flat spacetime magnetodipole formula. The present paper pursue our effort to look for accurate solutions of the general-relativistic electromagnetic field around a slowly rotating magnetized neutron star. In a previous work, we already found approximate stationary solutions to this problem. Here we address again this problem but using a more general approach. We indeed solve the full set of time-dependent Maxwell equations in a curved vacuum space-time following the 3+1 formalism. The numerical code is based on our pseudo-spectral method exp...
Roedig, Constanze; Alic, Daniela
2012-01-01
We present the implementation of an implicit-explicit (IMEX) Runge-Kutta numerical scheme for general relativistic hydrodynamics coupled to an optically thick radiation field in two existing GR-hydrodynamics codes. We argue that the necessity of such an improvement arises naturally in astrophysically relevant regimes where the optical thickness is high as the equations become stiff. By performing several 1D tests we verify the codes' new ability to deal with this stiffness and show consistency. Then, still in 1D, we compute a luminosity versus accretion rate diagram for the setup of spherical accretion onto a Schwarzschild black hole and find good agreement with previous work. Lastly, we revisit the supersonic Bondi Hoyle Lyttleton (BHL) accretion in 2D where we can now present simulations of realistic temperatures, down to T~10^6 K. Here we find that radiation pressure plays an important role, but also that these highly dynamical set-ups push our approximate treatment towards the limit of physical applicabil...
High-Order Fully General-Relativistic Hydrodynamics: new Approaches and Tests
Radice, David; Galeazzi, Filippo
2013-01-01
We present a new approach for achieving high-order convergence in fully general-relativistic hydrodynamic simulations. The approach is implemented in WhiskyTHC, a new code that makes use of state-of-the-art numerical schemes and was key in achieving, for the first time, higher than second-order convergence in the calculation of the gravitational radiation from inspiraling binary neutron stars Radice et al. (2013). Here, we give a detailed description of the algorithms employed and present results obtained for a series of classical tests involving isolated neutron stars. In addition, using the gravitational-wave emission from the late inspiral and merger of binary neutron stars, we make a detailed comparison between the results obtained with the new code and those obtained when using standard second-order schemes commonly employed for matter simulations in numerical relativity. We find that even at moderate resolutions and for binaries with large compactness, the phase accuracy is improved by a factor 50 or mo...
The general relativistic instability supernova of a supermassive population III star
Energy Technology Data Exchange (ETDEWEB)
Chen, Ke-Jung; Woosley, Stan [Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064 (United States); Heger, Alexander [Monash Centre for Astrophysics, Monash University, Victoria 3800 (Australia); Almgren, Ann [Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Whalen, Daniel J. [T-2, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Johnson, Jarrett L., E-mail: kchen@ucolick.org [XTD-PRI, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)
2014-08-01
The formation of supermassive Population III stars with masses ≳10,000 M{sub ☉} in primeval galaxies in strong ultraviolet backgrounds at z ∼ 15 may be the most viable pathway to the formation of supermassive black holes by z ∼ 7. Most of these stars are expected to live for short times and then directly collapse to black holes, with little or no mass loss over their lives. However, we have now discovered that non-rotating primordial stars with masses close to 55,000 M{sub ☉} can instead die as highly energetic thermonuclear supernovae powered by explosive helium burning, releasing up to 10{sup 55} erg, or about 10,000 times the energy of a Type Ia supernova. The explosion is triggered by the general relativistic contribution of thermal photons to gravity in the core of the star, which causes the core to contract and explosively burn. The energy release completely unbinds the star, leaving no compact remnant, and about half of the mass of the star is ejected into the early cosmos in the form of heavy elements. The explosion would be visible in the near infrared at z ≲ 20 to Euclid and the Wide-Field Infrared Survey Telescope, perhaps signaling the birth of supermassive black hole seeds and the first quasars.
Odyssey: A Public GPU-Based Code for General-Relativistic Radiative Transfer in Kerr Spacetime
Pu, Hung-Yi; Younsi, Ziri; Yoon, Suk-Jin
2016-01-01
General-relativistic radiative transfer (GRRT) calculations coupled with the calculation of geodesics in the Kerr spacetime are an essential tool for determining the images, spectra and light curves from matter in the vicinity of black holes. Such studies are especially important for ongoing and upcoming millimeter/submillimeter (mm/sub-mm) Very Long Baseline Interferometry (VLBI) observations of the supermassive black holes at the centres of Sgr A^{*} and M87. To this end we introduce Odyssey, a Graphics Processing Unit(GPU)-based code for ray tracing and radiative transfer in the Kerr spacetime. On a single GPU, the performance of Odyssey can exceed 1 nanosecond per photon, per Runge-Kutta integration step. Odyssey is publicly available, fast, accurate, and flexible enough to be modified to suit the specific needs of new users. Along with a Graphical User Interface (GUI) powered by a video-accelerated display architecture, we also present an educational software tool, Odyssey_Edu, for showing in real time h...
Odyssey: A Public GPU-based Code for General Relativistic Radiative Transfer in Kerr Spacetime
Pu, Hung-Yi; Yun, Kiyun; Younsi, Ziri; Yoon, Suk-Jin
2016-04-01
General relativistic radiative transfer calculations coupled with the calculation of geodesics in the Kerr spacetime are an essential tool for determining the images, spectra, and light curves from matter in the vicinity of black holes. Such studies are especially important for ongoing and upcoming millimeter/submillimeter very long baseline interferometry observations of the supermassive black holes at the centers of Sgr A* and M87. To this end we introduce Odyssey, a graphics processing unit (GPU) based code for ray tracing and radiative transfer in the Kerr spacetime. On a single GPU, the performance of Odyssey can exceed 1 ns per photon, per Runge-Kutta integration step. Odyssey is publicly available, fast, accurate, and flexible enough to be modified to suit the specific needs of new users. Along with a Graphical User Interface powered by a video-accelerated display architecture, we also present an educational software tool, Odyssey_Edu, for showing in real time how null geodesics around a Kerr black hole vary as a function of black hole spin and angle of incidence onto the black hole.
General-Relativistic Simulations of Three-Dimensional Core-Collapse Supernovae
Ott, C D; Moesta, P; Haas, R; Drasco, S; O'Connor, E; Reisswig, C; Meakin, C; Schnetter, E
2012-01-01
We study the three-dimensional (3D) hydrodynamics of the post-core-bounce phase of the collapse of a 27 solar-mass star and pay special attention to the development of the standing accretion shock instability (SASI) and neutrino-driven convection. To this end, we perform 3D general-relativistic simulations with a 3-species neutrino leakage scheme with neutrino heating. Unlike "light-bulb" heating/cooling schemes, the leakage scheme captures the essential aspects of neutrino cooling, heating, and lepton number exchange as predicted by radiation-hydrodynamics simulations. The 27 solar-mass progenitor was studied in 2D by B. Mueller et al. (2012; arXiv:1205.7078), who observed strong growth of the SASI while neutrino-driven convection was suppressed. In our 3D simulations, neutrino-driven convection grows from numerical perturbations imposed by our Cartesian grid. It becomes the dominant instability and leads to large-scale non-oscillatory deformations of the shock front. These will result in strongly aspherical...
General relativistic modelling of the negative reverberation X-ray time delays in AGN
Emmanoulopoulos, D; Dovciak, M; McHardy, I M
2014-01-01
We present the first systematic physical modelling of the time-lag spectra between the soft (0.3-1 keV) and the hard (1.5-4 keV) X-ray energy bands, as a function of Fourier frequency, in a sample of 12 active galactic nuclei which have been observed by XMM-Newton. We concentrate particularly on the negative X-ray time-lags (typically seen above $10^{-4}$ Hz) i.e. soft band variations lag the hard band variations, and we assume that they are produced by reprocessing and reflection by the accretion disc within a lamp-post X-ray source geometry. We also assume that the response of the accretion disc, in the soft X-ray bands, is adequately described by the response in the neutral iron line (Fe k$\\alpha$) at 6.4 keV for which we use fully general relativistic ray-tracing simulations to determine its time evolution. These response functions, and thus the corresponding time-lag spectra, yield much more realistic results than the commonly-used, but erroneous, top-hat models. Additionally we parametrize the positive ...
Pinpointing the base of the AGN jets through general relativistic X-ray reverberation studies
Emmanoulopoulos, D
2014-01-01
Many theoretical models of Active Galactic Nuclei (AGN) predict that the X-ray corona, lying above the black hole, constitutes the base of the X-ray jet. Thus, by studying the exact geometry of the close black hole environment, we can pinpoint the launching site of the jet. Detection of negative X-ray reverberation time delays (i.e. soft band X-ray variations lagging behind the corresponding hard band X-ray variations) can yield significant information about the geometrical properties of the AGN, such as the location of the X-ray source, as well as the physical properties of the the black hole, such as its mass and spin. In the frame-work of the lamp-post geometry, I present the first systematic X-ray time-lag modelling results of an ensemble of 12 AGN, using a fully general relativistic (GR) ray tracing approach for the estimation of the systems' response functions. By combing these state-of-the art GR response models with statistically innovative fitting routines, I derive the geometrical layout of the clos...
Cattaneo, Carlo
2011-01-01
This title includes: Pham Mau Quam: Problemes mathematiques en hydrodynamique relativiste; A. Lichnerowicz: Ondes de choc, ondes infinitesimales et rayons en hydrodynamique et magnetohydrodynamique relativistes; A.H. Taub: Variational principles in general relativity; J. Ehlers: General relativistic kinetic theory of gases; K. Marathe: Abstract Minkowski spaces as fibre bundles; and, G. Boillat: Sur la propagation de la chaleur en relativite.
Directory of Open Access Journals (Sweden)
O. Ye. Hentosh
2016-01-01
Full Text Available The possibility of applying the method of reducing upon finite-dimensional invariant subspaces, generated by the eigenvalues of the associated spectral problem, to some two-dimensional generalization of the relativistic Toda lattice with the triple matrix Lax type linearization is investigated. The Hamiltonian property and Lax-Liouville integrability of the vector fields, given by this system, on the invariant subspace related with the Bargmann type reduction are found out.
Beneke, M.; Hellmann, C.; Ruiz-Femenia, P.
2012-01-01
We compute analytically the tree-level annihilation rates of a collection of non-relativistic neutralino and chargino two-particle states in the general MSSM, including the previously unknown off-diagonal rates. The results are prerequisites to the calculation of the Sommerfeld enhancement in the MSSM, which will be presented in subsequent work. They can also be used to obtain concise analytic expressions for MSSM dark matter pair annihilation in the present Universe for a large number of exc...
Harko, T
2016-01-01
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equa...
Roedig, C.; Zanotti, O.; Alic, D.
2012-10-01
We present the implementation of an implicit-explicit (IMEX) Runge-Kutta numerical scheme for general relativistic (GR) hydrodynamics coupled to an optically thick radiation field in two existing GR-(magneto)hydrodynamics codes. We argue that the necessity of such an improvement arises naturally in most astrophysically relevant regimes where the optical thickness is high as the equations become stiff. By performing several simple 1D tests, we verify the codes' new ability to deal with this stiffness and show consistency. Then, still in one spatial dimension, we compute a luminosity versus accretion rate diagram for the set-up of spherical accretion on to a Schwarzschild black hole and find good agreement with previous work which included more radiation processes than we currently have available. Lastly, we revisit the supersonic Bondi-Hoyle-Lyttleton (BHL) accretion in two dimensions where we can now present simulations of realistic temperatures, down to T ˜ 106 K or less. Here we find that radiation pressure plays an important role, but also that these highly dynamical set-ups push our approximate treatment towards the limit of physical applicability. The main features of radiation hydrodynamics BHL flows manifest as (i) an effective adiabatic index approaching γeff ˜ 4/3; (ii) accretion rates two orders of magnitude lower than without radiation pressure, but still super-Eddington; (iii) luminosity estimates around the Eddington limit, hence with an overall radiative efficiency as small as ηBHL˜10-2; (iv) strong departures from thermal equilibrium in shocked regions; (v) no appearance of the flip-flop instability. We conclude that the current optically thick approximation to the radiation transfer does give physically substantial improvements over the pure hydro also in set-ups departing from equilibrium, and, once accompanied by an optically thin treatment, is likely to provide a fundamental tool for investigating accretion flows in a large variety of
General relativistic modelling of the negative reverberation X-ray time delays in AGN
Emmanoulopoulos, D.; Papadakis, I. E.; Dovčiak, M.; McHardy, I. M.
2014-04-01
We present the first systematic physical modelling of the time-lag spectra between the soft (0.3-1 keV) and the hard (1.5-4 keV) X-ray energy bands, as a function of Fourier frequency, in a sample of 12 active galactic nuclei which have been observed by XMM-Newton. We concentrate particularly on the negative X-ray time-lags (typically seen above 10-4 Hz), i.e. soft-band variations lag the hard-band variations, and we assume that they are produced by reprocessing and reflection by the accretion disc within a lamp-post X-ray source geometry. We also assume that the response of the accretion disc, in the soft X-ray bands, is adequately described by the response in the neutral Fe Kα line at 6.4 keV for which we use fully general relativistic ray-tracing simulations to determine its time evolution. These response functions, and thus the corresponding time-lag spectra, yield much more realistic results than the commonly used, but erroneous, top-hat models. Additionally, we parametrize the positive part of the time-lag spectra (typically seen below 10-4 Hz) by a power law. We find that the best-fitting black hole (BH) masses, M, agree quite well with those derived by other methods, thus providing us with a new tool for BH mass determination. We find no evidence for any correlation between M and the BH spin parameter, α, the viewing angle, θ, or the height of the X-ray source above the disc, h. Also on average, the X-ray source lies only around 3.7 gravitational radii above the accretion disc and θ is distributed uniformly between 20° and 60°. Finally, there is a tentative indication that the distribution of α may be bimodal above and below 0.62.
Dynamical Relativistic Systems and the Generalized Gauge Fields of Manifestly Covariant Theories
Horwitz, L P
1998-01-01
The problem of the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on phase space. The original work of Zaslovskii et al showed that the resulting evolution contains a stochastic flow in phase space to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistically charged particle in interaction with the electromagnetic field. We review the standard derivation of the covariant Lorentz force, and review the structure of the relativistic equations used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field. We show how this agreement is achieved, and criticize some of the fundamental assumptions underlying these derivations. We argue that a more complete theory, involving ``off-shell'' electromagnetic fields should be utilized. We then discuss the formulation of the off-shell electromagne...
Troxel, M A; Peel, Austin
2013-01-01
The study of relativistic, higher order and nonlinear effects has become necessary in recent years in the pursuit of precision cosmology. We develop and apply here a framework to study gravitational lensing in exact models in general relativity that are not restricted to homogeneity and isotropy, and where full nonlinearity and relativistic effects are included. We apply the framework to a specific, anisotropic galaxy cluster model which is based on a modified NFW halo density profile and described by the Szekeres metric. We examine the effects of increasing levels of anisotropy in the galaxy cluster on lensing observables like the convergence and shear for various lensing geometries, finding a strong nonlinear response in both the convergence and shear for rays passing through anisotropic regions of the cluster. Deviation from the expected values in a spherically symmetric structure are asymmetric with respect to path direction and thus will persist as a statistical effect when averaged over some ensemble of...
Sekhar, Aswin; Asher, David; Morbidelli, Alessandro; Werner, Stephanie; Vaubaillon, Jeremie; Li, Gongjie
2017-06-01
Two well known phenomena in orbital dynamics associated with low perihelion distance bodies are general relativistic (GR) precession and Lidov-Kozai (LK) oscillations.In this work, we are interested to identify bodies evolving in the near future (i.e. thousands of years in this case) into rapid sungrazing and sun colliding phases and undergoing inclination flips, due to LK like oscillations and being GR active at the same time. We find that LK mechanism leads to secular lowering of perihelion distance which in turn leads to a huge increase in GR precession of the argument of pericentre depending on the initial orbital elements. This in turn gives feedback to the LK mechanism as the eccentricity, inclination and argument of pericentre in Kozai cycles are closely correlated. In this work, we find real examples of solar system bodies which show rapid enhancement in GR precession rates due to LK like oscillations and there are cases where GR precession rate peaks to about 60 times that of the GR precession of Mercury thus showing the strength and complementary nature between these two dynamical phenomena.An analytical treatment is done on few bodies to understand the difference in their orbital evolution in the context of LK mechanism with and without GR precession term by incorporating suitable Hamiltonian dynamics. This result is subsequently matched using numerical integrations to find direct correlations. Real solar system bodies showing both GR precession and LK like oscillations are identified using compiled observational records from IAU-Minor Planet Center, Cometary Catalogue, IAU-Meteor Data Center and performing analytical plus numerical tests on them. This intermediate state (where GR and LK effects are comparable and co-exist) brings up the interesting possibility of drastic changes in GR precession rates during orbital evolution due to sungrazing and sun colliding phases induced by the LK like mechanism, thus combining both these important effects in a
GPU-based four-dimensional general-relativistic ray tracing
Kuchelmeister, Daniel; Müller, Thomas; Ament, Marco; Wunner, Günter; Weiskopf, Daniel
2012-10-01
This paper presents a new general-relativistic ray tracer that enables image synthesis on an interactive basis by exploiting the performance of graphics processing units (GPUs). The application is capable of visualizing the distortion of the stellar background as well as trajectories of moving astronomical objects orbiting a compact mass. Its source code includes metric definitions for the Schwarzschild and Kerr spacetimes that can be easily extended to other metric definitions, relying on its object-oriented design. The basic functionality features a scene description interface based on the scripting language Lua, real-time image output, and the ability to edit almost every parameter at runtime. The ray tracing code itself is implemented for parallel execution on the GPU using NVidia's Compute Unified Device Architecture (CUDA), which leads to performance improvement of an order of magnitude compared to a single CPU and makes the application competitive with small CPU cluster architectures. Program summary Program title: GpuRay4D Catalog identifier: AEMV_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMV_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 73649 No. of bytes in distributed program, including test data, etc.: 1334251 Distribution format: tar.gz Programming language: C++, CUDA. Computer: Linux platforms with a NVidia CUDA enabled GPU (Compute Capability 1.3 or higher), C++ compiler, NVCC (The CUDA Compiler Driver). Operating system: Linux. RAM: 2 GB Classification: 1.5. External routines: OpenGL Utility Toolkit development files, NVidia CUDA Toolkit 3.2, Lua5.2 Nature of problem: Ray tracing in four-dimensional Lorentzian spacetimes. Solution method: Numerical integration of light rays, GPU-based parallel programming using CUDA, 3D
Change in General Relativistic precession rates due to Lidov-Kozai oscillations in the Solar System
Sekhar, Aswin; Asher, David J.; Werner, Stephanie C.; Vaubaillon, Jeremie; Li, Gongjie
2017-04-01
Introduction: Two well known phenomena associated with low perihelion distance bodies in orbital dynamics are general relativistic (GR) precession and Lidov-Kozai (LK) oscillations. The accurate prediction of the perihelion shift of Mercury in accord with real observations is one of the significant triumphs of the general theory of relativity developed by Einstein. The Lidov-Kozai mechanism was first proposed and derived by Kozai and independently by Lidov explaining the periodic exchange between eccentricities e and inclinations i thereby increasing or decreasing the perihelion distance q secularly in the orbiting body. Co-existence of GR Precession and LK Oscillations: In this work, we were interested to identify bodies evolving in the near future (i.e. thousands of years in this case) into rapid sungrazing and sun colliding phases and undergoing inclination flips, due to LK oscillations and being GR active at the same time. Of all the bodies we checked from the IAU-Minor Planet Center, and Marsden plus Kracht families from the comet catalogue, 96P/Machholz 1 stands out because it shows all these trends in the near future. LK leads to secular lowering of q which in turn leads to a huge increase in GR precession of argument of pericentre. This in turn gives feedback to the LK mechanism as the e,i and argument of pericentre in Kozai cycles are closely correlated. In this work, we find real examples of solar system bodies which show the continuum nature between GR precession domi-nant and LK mechanism dominant regimes. Results and Discussion: We have shown that there are bodies in the solar system in which both GR precession and LK mechanism can co-exist at the same time and for which these effects can be measured and identified using analytical and numerical techniques. Thus there is a continuum of bodies encompassing, firstly GR precession dominant, secondly GR precession plus LK mechanism co-existing and finally LK mechanism dominant states which are all
Relativistic Hydrodynamics in Heavy-Ion Collisions: General Aspects and Recent Developments
Directory of Open Access Journals (Sweden)
Amaresh Jaiswal
2016-01-01
Full Text Available Relativistic hydrodynamics has been quite successful in explaining the collective behaviour of the QCD matter produced in high energy heavy-ion collisions at RHIC and LHC. We briefly review the latest developments in the hydrodynamical modeling of relativistic heavy-ion collisions. Essential ingredients of the model such as the hydrodynamic evolution equations, dissipation, initial conditions, equation of state, and freeze-out process are reviewed. We discuss observable quantities such as particle spectra and anisotropic flow and effect of viscosity on these observables. Recent developments such as event-by-event fluctuations, flow in small systems (proton-proton and proton-nucleus collisions, flow in ultracentral collisions, longitudinal fluctuations, and correlations and flow in intense magnetic field are also discussed.
A General Relativistic Model for Magnetic Monopole-Infused Compact Objects
Pazameta, Zoran
2012-01-01
Emergent concepts from astroparticle physics are incorporated into a classical solution of the Einstein-Maxwell equations for a binary magnetohydrodynamic fluid, in order to describe the final equilibrium state of compact objects infused with magnetic monopoles produced by proton-proton collisions within the intense dipolar magnetic fields generated by these objects during their collapse. It is found that the effective mass of such an object's acquired monopolar magnetic field is three times greater than the mass of its native fluid and monopoles combined, necessitating that the interior matter undergo a transition to a state of negative pressure in order to attain equilibrium. Assuming full symmetry between the electric and magnetic Maxwell equations yields expressions for the monopole charge density and magnetic field by direct analogy with their electrostatic equivalents; inserting these into the Einstein equations then leads to an interior metric which is well-behaved from the origin to the surface, where...
Müller, Bernhard; Janka, Hans-Thomas
2014-06-01
Considering six general relativistic, two-dimensional (2D) supernova (SN) explosion models of progenitor stars between 8.1 and 27 M ⊙, we systematically analyze the properties of the neutrino emission from core collapse and bounce to the post-explosion phase. The models were computed with the VERTEX-COCONUT code, using three-flavor, energy-dependent neutrino transport in the ray-by-ray-plus approximation. Our results confirm the close similarity of the mean energies, langErang, of \\bar{\
Novak, Jerome; Dimmelmeier, Harrald; Font-Roda, Jose A.
2004-12-01
We present a new three-dimensional general relativistic hydrodynamics code which can be applied to study stellar core collapses and the resulting gravitational radiation. This code uses two different numerical techniques to solve partial differential equations arising in the model: high-resolution shock capturing (HRSC) schemes for the evolution of hydrodynamic quantities and spectral methods for the solution of Einstein equations. The equations are written and solved using spherical polar coordinates, best suited to stellar topology. Einstein equations are formulated within the 3+1 formalism and conformal flat condition (CFC) for the 3-metric and gravitational radiation is extracted using Newtonian quadrupole formulation.
Kinetic approach to Kaluza's magnetohydrodynamics
Sandoval-Villalbazo, A.; Garcia-Colin, L. S.
2011-11-01
Ten years ago we presented a formalism by means of which the basic tenets of relativistic magnetohydrodynamics were derived using Kaluza's ideas about unifying fields in terms of the corresponding space time curvature for a given metric. In this work we present an attempt to obtain the thermodynamic properties of a charged fluid using using Boltzmann's equation for a dilute system adapted to kaluza's formalism. The main results that we obtain are analytical expressions for the main currents and corresponding forces, within the formalism of linear irreversible thermodynamics. We also indicate how transport coefficients can be calculated. Other relevant results are also mentioned. A. Sandoval-Villalbazo and L.S. Garcia-Colin; Phys. of Plasmas 7, 4823 (2000).
Hayata, Tomoya; Hongo, Masaru; Noumi, Toshifumi
2015-01-01
We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time-evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without choice of frame such as the Landau-Lifshitz or Eckart frame.
Numerical solutions of general-relativistic field equations for rapidly rotating neutron stars
Institute of Scientific and Technical Information of China (English)
吴雪君; 须重明
1997-01-01
Stationary axial symmetric equilibrium configurations rapidly rotating with uniform angular velocity in the framework of genera! relativity are considered. Sequences of models are numerically computed by means of a computer code that solves the full Einstein equations exactly. This code employs Neugebauer’s minimal surface formalism, where the field equations are equivalent to two-dimensional minimal surface equations for 4 metric potentials. The calculations are based upon 10 different equations of state. Results of various structures of neutron stars and the rotational effects on stellar structures and properties are reported. Finally some limits to equations of state of neutron stars and the stability for rapidly rotating relativistic neutron stars are discussed.
Magnetogenesis through Relativistic Velocity Shear
Miller, Evan
Magnetic fields at all scales are prevalent in our universe. However, current cosmological models predict that initially the universe was bereft of large-scale fields. Standard magnetohydrodynamics (MHD) does not permit magnetogenesis; in the MHD Faraday's law, the change in magnetic field B depends on B itself. Thus if B is initially zero, it will remain zero for all time. A more accurate physical model is needed to explain the origins of the galactic-scale magnetic fields observed today. In this thesis, I explore two velocity-driven mechanisms for magnetogenesis in 2-fluid plasma. The first is a novel kinematic 'battery' arising from convection of vorticity. A coupling between thermal and plasma oscillations, this non-relativistic mechanism can operate in flows that are incompressible, quasi-neutral and barotropic. The second mechanism results from inclusion of thermal effects in relativistic shear flow instabilities. In such flows, parallel perturbations are ubiquitously unstable at small scales, with growth rates of order with the plasma frequency over a defined range of parameter-space. Of these two processes, instabilities seem far more likely to account for galactic magnetic fields. Stable kinematic effects will, at best, be comparable to an ideal Biermann battery, which is suspected to be orders of magnitude too weak to produce the observed galactic fields. On the other hand, instabilities grow until saturation is reached, a topic that has yet to be explored in detail on cosmological scales. In addition to investigating these magnetogenesis sources, I derive a general dispersion relation for three dimensional, warm, two species plasma with discontinuous shear flow. The mathematics of relativistic plasma, sheared-flow instability and the Biermann battery are also discussed.
Magnetohydrodynamic Shearing Waves
Johnson, B M
2006-01-01
I consider the nonaxisymmetric linear theory of an isothermal magnetohydrodynamic (MHD) shear flow. The analysis is performed in the shearing box, a local model appropriate for a thin disk geometry. Linear perturbations in this model can be decomposed in terms of shearing waves (shwaves), which appear spatially as plane waves in a frame comoving with the shear. The time dependence of these waves cannot in general be expressed in terms of a frequency eigenvalue as in a normal mode decomposition, and numerical integration of a set of first-order amplitude equations is required for a complete characterization of their behavior. Their generic time dependence, however, is oscillatory with slowly-varying frequency and amplitude, and one can construct accurate analytic solutions by applying the Wentzel-Kramers-Brillouin method to the full set of amplitude equations. For the bulk of wavenumber space, therefore, the shwaves are well-approximated as modes with time-dependent frequencies and amplitudes. The incompressiv...
Bagayoko, Diola
In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127104 (2014)]. This understanding included necessary steps ab initio electronic structure calculations have to take if their results are to possess the full physical content of DFT. These steps guarantee the fulfillment of conditions of validity of DFT; not surprisingly, they have led to accurate descriptions of several dozens of semiconductors, from first principle, without invoking derivative discontinuity or self-interaction correction. This presentation shows the mathematically and physically rigorous understanding of the relativistic extension of DFT by Rajagopal and Callaway {Phys. Rev. B 7, 1912 (1973)]. As in the non-relativistic case, the attainment of the absolute minima of the occupied energies is a necessary condition for the corresponding current density to be that of the ground state of the system and for computational results to agree with corresponding, experimental ones. Acknowledgments:This work was funded in part by the US National Science Foundation [NSF, Award Nos. EPS-1003897, NSF (2010-2015)-RII-SUBR, and HRD-1002541], the US Department of Energy, National Nuclear Security Administration (NNSA, Award No. DE-NA0002630), LaSPACE, and LONI-SUBR.
General Relativistic Radiant Shock Waves in the Post-Quasistatic Approximation
Energy Technology Data Exchange (ETDEWEB)
H, Jorge A Rueda [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Escuela de Fisica, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); Nunez, L A [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Centro Nacional de Calculo Cientifico, Universidad de Los Andes, CeCalCULA, Corporacion Parque Tecnologico de Merida, Merida 5101, Venezuela (Venezuela)
2007-05-15
An evolution of radiant shock wave front is considered in the framework of a recently presented method to study self-gravitating relativistic spheres, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post-quasistatic approximation. The spherical matter configuration is divided into two regions by the shock and each side of the interface having a different equation of state and anisotropic phase. In order to simulate dissipation effects due to the transfer of photons and/or neutrinos within the matter configuration, we introduce the flux factor, the variable Eddington factor and a closure relation between them. As we expected the strong of the shock increases the speed of the fluid to relativistic ones and for some critical values is larger than light speed. In addition, we find that energy conditions are very sensible to the anisotropy, specially the strong energy condition. As a special feature of the model, we find that the contribution of the matter and radiation to the radial pressure are the same order of magnitude as in the mant as in the core, moreover, in the core radiation pressure is larger than matter pressure.
General Relativistic Hydrodynamic Simulation of Accretion Flow from a Stellar Tidal Disruption
Shiokawa, Hotaka; Cheng, Roseanne M; Piran, Tsvi; Noble, Scott C
2015-01-01
We study how the matter dispersed when a supermassive black hole tidally disrupts a star joins an accretion flow. Combining a relativistic hydrodynamic simulation of the stellar disruption with a relativistic hydrodynamics simulation of the tidal debris motion, we track such a system until ~80% of the stellar mass bound to the black hole has settled into an accretion flow. Shocks near the stellar pericenter and also near the apocenter of the most tightly-bound debris dissipate orbital energy, but only enough to make the characteristic radius comparable to the semi-major axis of the most-bound material, not the tidal radius as previously thought. The outer shocks are caused by post-Newtonian effects, both on the stellar orbit during its disruption and on the tidal forces. Accumulation of mass into the accretion flow is non-monotonic and slow, requiring ~3--10x the orbital period of the most tightly-bound tidal streams, while the inflow time for most of the mass may be comparable to or longer than the mass accu...
Directory of Open Access Journals (Sweden)
J Ghanbari
2009-12-01
Full Text Available Dynamics of stationary axisymmetric configuration of the viscous accreting fluids surrounding a non-rotating compact object in final stages of accretion flow is presented here. For the special case of thin disk approximation, the relativistic fluid equations ignoring self-gravity of the disk are derived in Schwarzschild geometry. For two different state equations, two sets of self-consistent analytical solutions of fully relativistic fluid equations are obtained separately. The effect of bulk viscosity coefficient on the physical functions are investigated for each state equation, as well as the bounds that exert on the free parameters due to the condition of accretion flow in the last stages. The solutions found show that the radial and azimuthal velocities, density and pressure of the fluid increase inwards for both state equations. Also, viscosity has no effect on the velocities and density distributions in both state equations. Two state equations show different types of behavior with respect to the bulk viscosity coefficient. For p=K state equation, if there is no bulk viscosity, the pressure remains constant throughout the disk, whereas with increasing bulk viscosity the pressure falls off in the inner regions but soon stabilizes at an almost constant value. However, for p=ρc2 state equation, the pressure is never constant, even in the absence of bulk viscosity. The larger the value of ηb, the higher the value of pressure in the inner regions.
Nobili, Anna M.
2016-12-01
The universality of free fall and the weak equivalence principle, which are at the basis of general relativity, have been confirmed to 1 part in 1 013. Space experiments with macroscopic test masses of different composition orbiting Earth inside a low altitude satellite aim to improve this precision by 2 orders of magnitude (with the Microscope satellite launched on April 25, 2016) and up to 4 orders of magnitude (with the Galileo Galilei satellite). At such a high precision, many tiny effects must be taken into account in order to be ruled out as the source of a spurious violation signal. In this work, we investigate the general relativistic effects, including those which involve the rotation of both Earth and the test masses, and show that they are by far too small to be considered even in the most challenging experiment.
Nobili, Anna M
2016-01-01
The Universality of Free Fall and the Weak Equivalence Principle, which are at the basis of General Relativity, have been confirmed to 1 part in 10^13. Space experiments with macroscopic test masses of different composition orbiting the Earth inside a low altitude satellite aim at improving this precision by two orders of magnitude (with the Microscope satellite, launched on 25 April 2016) and up to four orders of magnitude (with the 'Galileo Galilei' - GG satellite). At such a high precision many tiny effects must be taken into account in order to be ruled out as the source of a spurious violation signal. In this work we investigate the general relativistic effects, including those which involve the rotation of both the source body and the test masses, and show that they are by far too small to be considered even in the most challenging experiment.
On Magnetic Self-Collimation of Relativistic Jets
Globus, N.; Cayatte, V.; Sauty, C.
We present a semi-analytical model using the equations of general relativistic magnetohydrodynamics (GRMHD) for jets emitted by a rotating black hole. We assume steady axisymmetric outflows of a relativistic ideal fluid in Kerr metrics. We express the conservation equations in the frame of the FIDucial Observer (FIDO or ZAMO) using a 3+1 space-time splitting. Calculating the total energy variation between a non-polar field line and the polar axis, we extend to the Kerr metric the simple criterion for the magnetic collimation of jets obtained for a nonrotating black hole by Meliani et al.10 We show that the black role rotation induced a more efficient magnetic collimation of the jet.
Dynamic multiscaling in magnetohydrodynamic turbulence
Ray, Samriddhi Sankar; Pandit, Rahul
2016-01-01
We present the first study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.
Dynamic multiscaling in magnetohydrodynamic turbulence.
Ray, Samriddhi Sankar; Sahoo, Ganapati; Pandit, Rahul
2016-11-01
We present a study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.
Numerical modeling of a Global Navigation Satellite System in a general relativistic framework
Delva, P; Cadez, A
2010-01-01
In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space-time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are obtained analytically, describing respectively trajectories of satellites and electromagnetic signals. We implement an algorithm to calculate Schwarzschild coordinates of a GNSS user who receives proper times sent by four satellites, knowing their orbital parameters; the inverse procedure is implemented to check for consistency. The constellation of satellites therefore realizes a geocentric inertial reference system with no \\emph{a priori} realization of a terrestrial reference frame. We show that the calculation is very fast and could be implemented in a real GNSS, as an alternative to usual post-Newtonian corrections. Effects of non-gravitational perturbations on positioning errors are assessed, and methods to reduce them are sketched. In particular, inter-links between satelli...
A general relativistic approach to the Navarro-Frenk-White (NFW) galactic halos
Matos, T; Sussman, R A; Matos, Tonatiuh; Nunez, Dario; Sussman, Roberto A
2004-01-01
In order to study their interplay with large scale cosmic evolution and with relativistic effects, such as gravitational lenses, quintessence sources or gravitational waves, we construct a post-Newtonian fluid framework for the "Navarro-Frenk-White'' (NFW) models of galactic halos that follow from N-body numerical simulations. Since these simulations are unable to resolve regions very near the halo center, the extrapolation of the fitting formula leads to a spherically averaged "universal'' density profile that diverges at the origin. We remove this inconvenient feature by replacing a small central region of the NFW halo with an interior Schwarzschild solution with constant density, continuously matched to the remaining NFW spacetime. A model of a single halo, as an isolated object with finite mass, follows by smoothly matching the NFW spacetime to a Schwarzschild vacuum exterior along the virial radius, the physical "cut-off'' customarily imposed, as the mass associated with NFW profiles diverges asymptotica...
A general relativistic approach to the Navarro Frenk White galactic halos
Matos, Tonatiuh; Núñez, Darío; Sussman, Roberto A.
2004-11-01
Although galactic dark matter halos are basically Newtonian structures, the study of their interplay with large-scale cosmic evolution and with relativistic effects, such as gravitational lenses, quintessence sources or gravitational waves, makes it necessary to obtain adequate relativistic descriptions for these self-gravitating systems. With this purpose in mind, we construct a post-Newtonian fluid framework for the 'Navarro Frenk White' (NFW) models of galactic halos that follow from N-body numerical simulations. Since these simulations are unable to resolve regions very near the halo centre, the extrapolation of the fitting formula leads to a spherically averaged 'universal' density profile that diverges at the origin. We remove this inconvenient feature by replacing a small central region of the NFW halo with an interior Schwarzschild solution with constant density, continuously matched to the remaining NFW spacetime. A model of a single halo, as an isolated object with finite mass, follows by smoothly matching the NFW spacetime to a Schwarzschild vacuum exterior along the virial radius, the physical 'cut-off' customarily imposed, as the mass associated with NFW profiles diverges asymptotically. Numerical simulations assume weakly interacting collisionless particles, hence we suggest that NFW halos approximately satisfy an 'ideal gas' type of equation of state, where mass-density is the dominant rest-mass contribution to matter-energy, with the internal energy contribution associated with an anisotropic kinetic pressure. We show that, outside the central core, this pressure and the mass density roughly satisfy a polytropic relation. Since stellar polytropes are the equilibrium configurations in Tsallis' non-extensive formalism of statistical mechanics, we argue that NFW halos might provide a rough empirical estimate of the free parameter q of Tsallis' formalism.
Wu, Kailiang; Tang, Huazhong
2017-01-01
The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics (RHD). This paper develops high-order accurate, physical-constraints-preserving (PCP), central, discontinuous Galerkin (DG) methods for the one- and two-dimensional special RHD equations with a general EOS. It is built on our theoretical analysis of the admissible states for RHD and the PCP limiting procedure that enforce the admissibility of central DG solutions. The convexity, scaling invariance, orthogonal invariance, and Lax–Friedrichs splitting property of the admissible state set are first proved with the aid of its equivalent form. Then, the high-order central DG methods with the PCP limiting procedure and strong stability-preserving time discretization are proved, to preserve the positivity of the density, pressure, specific internal energy, and the bound of the fluid velocity, maintain high-order accuracy, and be L1-stable. The accuracy, robustness, and effectiveness of the proposed methods are demonstrated by several 1D and 2D numerical examples involving large Lorentz factor, strong discontinuities, or low density/pressure, etc.
Relativistic MHD simulations of core-collapse GRB jets: 3D instabilities and magnetic dissipation
Bromberg, Omer
2015-01-01
Relativistic jets naturally occur in astrophysical systems that involve accretion onto compact objects, such as core collapse of massive stars in gamma-ray bursts (GRBs) and accretion onto supermassive black holes in active galactic nuclei (AGN). It is generally accepted that these jets are powered electromagnetically, by the magnetised rotation of a central compact object. However, how they produce the observed emission and survive the propagation for many orders of magnitude in distance without being disrupted by current-driven non-axisymmetric instabilities is the subject of active debate. We carry out time-dependent 3D relativistic magnetohydrodynamic simulations of relativistic, Poynting flux dominated jets. The jets are launched self-consistently by the rotation of a strongly magnetised central compact object. This determines the natural degree of azimuthal magnetic field winding, a crucial factor that controls jet stability. We find that the jets are susceptible to two types of instability: (i) a globa...
Reisswig, C; Ott, C D; Abdikamalov, E; Moesta, P; Pollney, D; Schnetter, E
2013-01-01
We present a new three-dimensional general-relativistic hydrodynamic evolution scheme coupled to dynamical spacetime evolutions which is capable of efficiently simulating stellar collapse, isolated neutron stars, black hole formation, and binary neutron star coalescence. We make use of a set of adapted curvi-linear grids (multipatches) coupled with flux-conservative cell-centered adaptive mesh refinement. This allows us to significantly enlarge our computational domains while still maintaining high resolution in the gravitational-wave extraction zone, the exterior layers of a star, or the region of mass ejection in merging neutron stars. The fluid is evolved with a high-resolution shock capturing finite volume scheme, while the spacetime geometry is evolved using fourth-order finite differences. We employ a multi-rate Runge-Kutta time integration scheme for efficiency, evolving the fluid with second-order and the spacetime geometry with fourth-order integration, respectively. We validate our code by a number ...
Fokas, Athanassios S; Grigoriou, D
2015-01-01
Let $r(\\varphi)$ denote the orbit of Mercury and other planets. We compare the formula of General Relativity (GR) for $r(\\varphi)$, as well as the formula for the corresponding perihelion precession angle $\\Delta \\varphi$, with the formulae obtained via the relativistic gravitational law, $F=GMm\\gamma^3/r^2$. The latter law can be derived from Newton's gravitational law by employing the gravitational rather than the rest mass of the rotating body and using special relativity (SR) together with the equivalence principle to compute the inertial and hence the gravitational, mass. Remarkably, it is found that the two expressions for $r(\\varphi)$ differ only by a factor of 2 and by an additive constant. This constant does not affect the formula for the $\\Delta \\varphi$, thus the two expressions for $\\Delta\\varphi$ differ only by a factor of 2.
Teraki, Yuto
2014-01-01
We examine the radiation spectra from relativistic electrons moving in a Langmuir turbulence expected to exist in high energy astrophysical objects by using numerical method. The spectral shape is characterized by the spatial scale {\\lambda}, field strength {\\sigma}, and frequency of the Langmuir waves, and in term of frequency they are represented by {\\omega}_0 = 2{\\pi}c/{\\lambda}, {\\omega}_st = e{\\sigma}/mc, and {\\omega}_p, respectively. We normalize {\\omega}_st and {\\omega}_p by {\\omega}_0 as \\a \\equiv {\\omega}_st/{\\omega}_0 and \\b \\equiv{\\omega}_p/{\\omega}_0, and examine the spectral shape in the a-b plane. An earlier study based on Diffusive Radiation in Langmuir turbulence (DRL) theory by Fleishman and Toptygin showed that the typical frequency is {\\gamma}^2{\\omega}_p and that the low frequency spectrum behaves as F_{\\omega} pronto {\\omega}^1 for b > 1 irrespective of a. Here, we adopt the first principle numerical approach to obtain the radiation spectra in more detail. We generate Langmuir turbulence ...
Murad, Mohammad Hassan; Pant, Neeraj
2014-03-01
In this paper we have studied a particular class of exact solutions of Einstein's gravitational field equations for spherically symmetric and static perfect fluid distribution in isotropic coordinates. The Schwarzschild compactness parameter, GM/ c 2 R, can attain the maximum value 0.1956 up to which the solution satisfies the elementary tests of physical relevance. The solution also found to have monotonic decreasing adiabatic sound speed from the centre to the boundary of the fluid sphere. A wide range of fluid spheres of different mass and radius for a given compactness is possible. The maximum mass of the fluid distribution is calculated by using stellar surface density as parameter. The values of different physical variables obtained for some potential strange star candidates like Her X-1, 4U 1538-52, LMC X-4, SAX J1808.4-3658 given by our analytical model demonstrate the astrophysical significance of our class of relativistic stellar models in the study of internal structure of compact star such as self-bound strange quark star.
General relativistic considerations of the field shedding model of fast radio bursts
Punsly, Brian; Bini, Donato
2016-06-01
Popular models of fast radio bursts (FRBs) involve the gravitational collapse of neutron star progenitors to black holes. It has been proposed that the shedding of the strong neutron star magnetic field (B) during the collapse is the power source for the radio emission. Previously, these models have utilized the simplicity of the Schwarzschild metric which has the restriction that the magnetic flux is magnetic `hair' that must be shed before final collapse. But neutron stars have angular momentum and charge and a fully relativistic Kerr-Newman solution exists in which B has its source inside of the event horizon. In this Letter, we consider the magnetic flux to be shed as a consequence of the electric discharge of a metastable collapsed state of a Kerr-Newman black hole. It has also been argued that the shedding model will not operate due to pair creation. By considering the pulsar death line, we find that for a neutron star with B = 1011-1013 G and a long rotation period, >1s this is not a concern. We also discuss the observational evidence supporting the plausibility of magnetic flux shedding models of FRBs that are spawned from rapidly rotating progenitors.
General Relativistic Considerations of the Field Shedding Model of Fast Radio Bursts
Punsly, Brian
2016-01-01
Popular models of fast radio bursts (FRBs) involve the gravitational collapse of neutron star progenitors to black holes. It has been proposed that the shedding of the strong neutron star magnetic field ($B$) during the collapse is the power source for the radio emission. Previously, these models have utilized the simplicity of the Schwarzschild metric which has the restriction that the magnetic flux is magnetic "hair" that must be shed before final collapse. But, neutron stars have angular momentum and charge and a fully relativistic Kerr Newman solution exists in which $B$ has its source inside of the event horizon. In this letter, we consider the magnetic flux to be shed as a consequence of the electric discharge of a metastable collapsed state of a Kerr Newman black hole. It has also been argued that the shedding model will not operate due to pair creation. By considering the pulsar death line, we find that for a neutron star with $B = 10^{11} - 10^{13}$ G and a long rotation period, $>1$ s this is not a ...
Harko, T.; Mak, M. K.
2016-09-01
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index n. The explicit form of the solution is presented for the polytropic index n=1, and for the indexes n=1/2 and n=1/5, respectively. The case of n=3 is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.
Heller, René
2017-09-01
As new concepts of sending interstellar spacecraft to the nearest stars are now being investigated by various research teams, crucial questions about the timing of such a vast financial and labour investment arise. If humanity could build high-speed interstellar lightsails and reach α Centauri 20 yr after launch, would it be better to wait a few years, then take advantage of further technology improvements and arrive earlier despite waiting? The risk of being overtaken by a future, faster probe has been described earlier as the incentive trap. Based on 211 yr of historical data, we find that the speed growth of artificial vehicles, from steam-driven locomotives to Voyager 1, is much faster than previously believed, about 4.72 per cent annually or a doubling every 15 yr. We derive the mathematical framework to calculate the minimum of the wait time to launch t plus travel time τ(t) and extend it into the relativistic regime. We show that the t + τ(t) minimum disappears for nearby targets. There is no use of waiting once we can reach an object within about 20 yr of travel, irrespective of the actual speed. In terms of speed, the t + τ(t) minimum for a travel to α Centauri occurs at 19.6 per cent the speed of light (c), in agreement with the 20 per cent c proposed by the Breakthrough Starshot initiative. If interstellar travel at 20 per cent c could be achieved within 45 yr from today and the kinetic energy be increased at a rate consistent with the historical record, then humans can reach the 10 most nearby stars within 100 yr from today.
Experiments in Magnetohydrodynamics
Rayner, J. P.
1970-01-01
Describes three student experiments in magnetohydrodynamics (MHD). In these experiments, it was found that the electrical conductivity of the local water supply was sufficient to demonstrate effectively some of the features of MHD flowmeters, generators, and pumps. (LC)
Magnetohydrodynamic fluidic system
Lee, Abraham P.; Bachman, Mark G.
2004-08-24
A magnetohydrodynamic fluidic system includes a reagent source containing a reagent fluid and a sample source containing a sample fluid that includes a constituent. A reactor is operatively connected to the supply reagent source and the sample source. MHD pumps utilize a magnetohydrodynamic drive to move the reagent fluid and the sample fluid in a flow such that the reagent fluid and the sample fluid form an interface causing the constituent to be separated from the sample fluid.
Magnetic Dissipation in Relativistic Jets
Directory of Open Access Journals (Sweden)
Yosuke Mizuno
2016-10-01
Full Text Available The most promising mechanisms for producing and accelerating relativistic jets, and maintaining collimated structure of relativistic jets involve magnetohydrodynamical (MHD processes. We have investigated the magnetic dissipation mechanism in relativistic jets via relativistic MHD simulations. We found that the relativistic jets involving a helical magnetic field are unstable for the current-driven kink instability, which leads to helically distorted structure in relativistic jets. We identified the regions of high current density in filamentary current sheets, indicative of magnetic reconnection, which are associated to the kink unstable regions and correlated to the converted regions of magnetic to kinetic energies of the jets. We also found that an over-pressured relativistic jet leads to the generation of a series of stationary recollimation shocks and rarefaction structures by the nonlinear interaction of shocks and rarefaction waves. The differences in the recollimation shock structure due to the difference of the magnetic field topologies and strengths may be observable through mm-VLBI observations and space-VLBI mission.
Multifluid magnetohydrodynamic turbulent decay
Downes, Turlough P
2011-01-01
It is generally believed that turbulence has a significant impact on the dynamics and evolution of molecular clouds and the star formation which occurs within them. Non-ideal magnetohydrodynamic effects are known to influence the nature of this turbulence. We present the results of a suite of 512-cubed resolution simulations of the decay of initially super-Alfvenic and supersonic fully multifluid MHD turbulence. We find that ambipolar diffusion increases the rate of decay of the turbulence while the Hall effect has virtually no impact. The decay of the kinetic energy can be fitted as a power-law in time and the exponent is found to be -1.34 for fully multifluid MHD turbulence. The power spectra of density, velocity and magnetic field are all steepened significantly by the inclusion of non-ideal terms. The dominant reason for this steepening is ambipolar diffusion with the Hall effect again playing a minimal role except at short length scales where it creates extra structure in the magnetic field. Interestingl...
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
Sadowski, A; Narayan, R; Abarca, D; McKinney, J C
2016-01-01
We present a numerical method which evolves a two-temperature, magnetized, radiative, accretion flow around a black hole, within the framework of general relativistic radiation magnetohydrodynamics. As implemented in the code KORAL, the gas consists of two sub-components -- ions and electrons -- which share the same dynamics but experience independent, relativistically consistent, thermodynamical evolution. The electrons and ions are heated independently according to a standard prescription from the literature for magnetohydrodynamical turbulent dissipation. Energy exchange between the particle species via Coulomb collisions is included. In addition, electrons gain and lose energy and momentum by absorbing and emitting synchrotron and bremsstrahlung radiation, and through Compton scattering. All evolution equations are handled within a fully covariant framework in the relativistic fixed-metric spacetime of the black hole. Numerical results are presented for five models of low luminosity black hole accretion. ...
Relativistic MHD with Adaptive Mesh Refinement
Anderson, M; Liebling, S L; Neilsen, D; Anderson, Matthew; Hirschmann, Eric; Liebling, Steven L.; Neilsen, David
2006-01-01
We solve the relativistic magnetohydrodynamics (MHD) equations using a finite difference Convex ENO method (CENO) in 3+1 dimensions within a distributed parallel adaptive mesh refinement (AMR) infrastructure. In flat space we examine a Balsara blast wave problem along with a spherical blast wave and a relativistic rotor test both with unigrid and AMR simulations. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. We also investigate the impact of hyperbolic divergence cleaning for the spherical blast wave and relativistic rotor. We include unigrid and mesh refinement parallel performance measurements for the spherical blast wave.
Energy Technology Data Exchange (ETDEWEB)
Rowland, D R [Student Support Services, University of Queensland, Brisbane QLD 4072 (Australia)
2006-01-01
Introductory courses covering modern physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics.
General Relativistic Energy Conditions The Hubble expansion in the epoch of galaxy formation
Visser, M
1997-01-01
The energy conditions of Einstein gravity (classical general relativity) are designed to extract as much information as possible from classical general relativity without enforcing a particular equation of state for the stress-energy. This systematic avoidance of the need to specify a particular equation of state is particularly useful in a cosmological setting --- since the equation of state for the cosmological fluid in a Friedmann-Robertson-Walker type universe is extremely uncertain. I shall show that the energy conditions provide simple and robust bounds on the behaviour of both the density and look-back time as a function of red-shift. I shall show that current observations suggest that the so-called strong energy condition (SEC) is violated sometime between the epoch of galaxy formation and the present. This implies that no possible combination of ``normal'' matter is capable of fitting the observational data.
Handbook of relativistic quantum chemistry
Energy Technology Data Exchange (ETDEWEB)
Liu, Wenjian (ed.) [Peking Univ., Beijing (China). Center for Computational Science and Engineering
2017-03-01
This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.
Three-fluid plasmas in star formation I. Magneto-hydrodynamic equations
Pinto, Cecilia; Bacciotti, Francesca
2008-01-01
Interstellar magnetic fields influence all stages of the process of star formation, from the collapse of molecular cloud cores to the formation of protostellar jets. This requires us to have a full understanding of the physical properties of magnetized plasmas of different degrees of ionization for a wide range of densities and temperatures. We derive general equations governing the magneto-hydrodynamic evolution of a three-fluid medium of arbitrary ionization, also including the possibility of charged dust grains as the main charge carriers. In a companion paper (Pinto & Galli 2007), we complement this analysis computing accurate expressions of the collisional coupling coefficients. Over spatial and temporal scales larger than the so-called large-scale plasma limit and the collision-dominated plasma limit, and for non-relativistic fluid speeds, we obtain an advection-diffusion for the magnetic field. We derive the general expressions for the resistivities, the diffusion time scales and the heating rates ...
Yoo, Jaiyul; Seljak, Uros; Zaldarriaga, Matias
2012-01-01
Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing ...
Mueller, B
2014-01-01
Considering general relativistic, two-dimensional (2D) supernova (SN) explosion models of progenitor stars between 8.1 and 27 solar masses, we systematically analyze the properties of the neutrino emission from core collapse and bounce to the post-explosion phase. The models were computed with the Vertex-CoCoNuT code, using three-flavor, energy-dependent neutrino transport in the ray-by-ray-plus approximation. Our results confirm the close similarity of the mean energies of electron antineutrinos and heavy-lepton neutrinos and even their crossing during the accretion phase for stars with M>10 M_sun as observed in previous 1D and 2D simulations with state-of-the-art neutrino transport. We establish a roughly linear scaling of the electron antineutrino mean energy with the proto-neutron star (PNS) mass, which holds in time as well as for different progenitors. Convection inside the PNS affects the neutrino emission on the 10-20% level, and accretion continuing beyond the onset of the explosion prevents the abru...
Generalized magnetofluid connections in pair plasmas
Energy Technology Data Exchange (ETDEWEB)
Asenjo, Felipe A., E-mail: felipe.asenjo@uai.cl [Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago 7941169 (Chile); Comisso, Luca, E-mail: lcomisso@princeton.edu [Department of Astrophysical Sciences and Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08544 (United States); Dipartimento Energia, Politecnico di Torino, Torino 10129, Italy and Istituto dei Sistemi Complessi-CNR, Roma 00185 (Italy); Mahajan, Swadesh M., E-mail: mahajan@mail.utexas.edu [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)
2015-12-15
We extend the magnetic connection theorem of ideal magnetohydrodynamics to nonideal relativistic pair plasmas. Adopting a generalized Ohm's law, we prove the existence of generalized magnetofluid connections that are preserved by the plasma dynamics. We show that these connections are related to a general antisymmetric tensor that unifies the electromagnetic and fluid fields. The generalized magnetofluid connections set important constraints on the plasma dynamics by forbidding transitions between configurations with different magnetofluid connectivity. An approximated solution is explicitly shown where the corrections due to current inertial effects are found.
Relativistic Self-similar Dynamic Collapses of Black Holes in General Polytropic Spherical Clouds
Lian, Biao
2013-01-01
We study the hydrodynamic self-similar mass collapses of general polytropic (GP) spherical clouds to central Schwarzschild black holes and void evolution with or without shocks. In order to grossly capture characteristic effects of general relativity (GR) outside yet close to the event horizon of a Schwarzschild black hole and to avoid mathematical complexity, we adopt the approximation of the Paczynski-Wiita gravity to replace the simple Newtonian gravity in our model formulation. A new dimensionless parameter s appears with the physical meaning of the square of the ratio of the sound speed to the speed of light $c$. Various self-similar dynamic solutions are constructed for a polytropic index $\\gamma>4/3$. Two (for small enough $s4/3$, representing the collapse of static singular GP spheres towards the central singularity of spacetime. Such GP spherical dynamic mass collapse is shown to be highly efficient for the rapid formation of supermassive black holes (SMBHs; mass range of $10^6-10^{10}M_{\\odot}$) in ...
Relativistic quantum revivals.
Strange, P
2010-03-26
Quantum revivals are now a well-known phenomena within nonrelativistic quantum theory. In this Letter we display the effects of relativity on revivals and quantum carpets. It is generally believed that revivals do not occur within a relativistic regime. Here we show that while this is generally true, it is possible, in principle, to set up wave packets with specific mathematical properties that do exhibit exact revivals within a fully relativistic theory.
Mean-field magnetohydrodynamics and dynamo theory
Krause, F
2013-01-01
Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen
Variational Integrators for Ideal and Reduced Magnetohydrodynamics
Kraus, Michael; Maj, Omar; Tassi, Emanuele; Grasso, Daniela
2016-10-01
Ideal and reduced magnetohydrodynamics are simplified sets of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their geometrical character. The resulting integrators preserve important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As these integrators are free of numerical resistivity, the magnetic field line topology is preserved and spurious reconnection is absent in the ideal case. Only when effects of finite electron mass are added, magnetic reconnection takes place. The excellent conservation properties of the methods are exemplified with numerical examples in 2D. We conclude with an outlook towards the treatment of general geometries in 3D and full magnetohydrodynamics.
Energy Technology Data Exchange (ETDEWEB)
Psaltis, Dimitrios; Özel, Feryal; Chan, Chi-Kwan; Marrone, Daniel P. [Astronomy Department, University of Arizona, 933 N. Cherry Ave, Tucson, AZ 85721 (United States)
2015-12-01
The half opening angle of a Kerr black hole shadow is always equal to (5 ± 0.2)GM/Dc{sup 2}, where M is the mass of the black hole and D is its distance from the Earth. Therefore, measuring the size of a shadow and verifying whether it is within this 4% range constitutes a null hypothesis test of general relativity. We show that the black hole in the center of the Milky Way, Sgr A*, is the optimal target for performing this test with upcoming observations using the Event Horizon Telescope (EHT). We use the results of optical/IR monitoring of stellar orbits to show that the mass-to-distance ratio for Sgr A* is already known to an accuracy of ∼4%. We investigate our prior knowledge of the properties of the scattering screen between Sgr A* and the Earth, the effects of which will need to be corrected for in order for the black hole shadow to appear sharp against the background emission. Finally, we explore an edge detection scheme for interferometric data and a pattern matching algorithm based on the Hough/Radon transform and demonstrate that the shadow of the black hole at 1.3 mm can be localized, in principle, to within ∼9%. All these results suggest that our prior knowledge of the properties of the black hole, of scattering broadening, and of the accretion flow can only limit this general relativistic null hypothesis test with EHT observations of Sgr A* to ≲10%.
Kuroda, Takami; Takiwaki, Tomoya
2012-01-01
We present results from the first generation of multi-dimensional hydrodynamic core-collapse simulations in full general relativity (GR) that include an approximate treatment of neutrino transport. Using a M1 closure scheme with an analytic variable Eddington factor, we solve the energy-independent set of radiation energy and momentum based on the Thorne's momentum formalism. To simplify the source terms of the transport equations, a methodology of multiflavour neutrino leakage scheme is partly employed. Our newly developed code is designed to evolve the Einstein field equation together with the GR radiation hydrodynamic equations. We follow the dynamics starting from the onset of gravitational core-collapse of a 15 $M_{\\odot}$ star, through bounce, up to about 100 ms postbounce in this study to study how the spacial multi-dimensionality and GR would affect the dynamics in the early postbounce phase. Our 3D results support the anticipation in previous 1D results that the neutrino luminosity and average neutri...
GRAVITAS : General Relativistic Astrophysics VIa Timing And Spectroscopy: An ESA M3 mission proposal
Nandra, Kirpal; Fabian, Andy; Strueder, Lothar; Willingale, Richard; Watson, Mike; Jonker, Peter; Kunieda, Hideyo; Miniutti, Giovanni; Motch, Christian; Predehl, Peter
2011-01-01
GRAVITAS is an X-ray observatory, designed and optimised to address the ESA Cosmic Vision theme of "Matter under extreme conditions". It was submitted as a response to the call for M3 mission proposals. The concept centres around an X-ray telescope of unprecedented effective area, which will focus radiation emitted from close to the event horizon of black holes or the surface of neutron stars. To reveal the nature and behaviour of matter in the most extreme astrophysical environments, GRAVITAS targets a key feature in the X-ray spectra of compact objects: the iron Kalpha line at ~6.5 keV. The energy, profile, and variability of this emission line, and the properties of the surrounding continuum emission, shaped by General Relativity (GR) effects, provide a unique probe of gravity in its strong field limit. Among its prime targets are hundreds of supermassive black holes in bright Active Galactic Nuclei (AGN), which form the perfect laboratory to help understand the physical processes behind black hole growth....
Sekhar, Aswin; Valsecchi, Giovanni B.; Asher, David; Werner, Stephanie; Vaubaillon, Jeremie; Li, Gongjie
2017-06-01
One of the greatest successes of Einstein's General Theory of Relativity (GR) was the correct prediction of the perihelion precession of Mercury. The closed form expression to compute this precession tells us that substantial GR precession would occur only if the bodies have a combination of both moderately small perihelion distance and semi-major axis. Minimum Orbit Intersection Distance (MOID) is a quantity which helps us to understand the closest proximity of two orbits in space. Hence evaluating MOID is crucial to understand close encounters and collision scenarios better. In this work, we look at the possible scenarios where a small GR precession in argument of pericentre can create substantial changes in MOID for small bodies ranging from meteoroids to comets and asteroids.Previous works have looked into neat analytical techniques to understand different collision scenarios and we use those standard expressions to compute MOID analytically. We find the nature of this mathematical function is such that a relatively small GR precession can lead to drastic changes in MOID values depending on the initial value of argument of pericentre. Numerical integrations were done with the MERCURY package incorporating GR code to test the same effects. A numerical approach showed the same interesting relationship (as shown by analytical theory) between values of argument of pericentre and the peaks or dips in MOID values. There is an overall agreement between both analytical and numerical methods.We find that GR precession could play an important role in the calculations pertaining to MOID and close encounter scenarios in the case of certain small solar system bodies (depending on their initial orbital elements) when long term impact risk possibilities are considered. Previous works have looked into impact probabilities and collision scenarios on planets from different small body populations. This work aims to find certain sub-sets of small bodies where GR could play an
Kovács, Z.; Harko, T.
2011-11-01
We present a full general relativistic numerical code for estimating the energy-momentum deposition rate (EMDR) from neutrino pair annihilation (?). The source of the neutrinos is assumed to be a neutrino-cooled accretion disc around neutron and quark stars. We calculate the neutrino trajectories by using a ray-tracing algorithm with the general relativistic Hamilton's equations for neutrinos and derive the spatial distribution of the EMDR due to the annihilations of neutrinos and antineutrinos around rotating neutron and quark stars. We obtain the EMDR for several classes of rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the Massachusetts Institute of Technology (MIT) bag model equation of state and in the colour-flavour-locked (CFL) phase. The distribution of the total annihilation rate of the neutrino-antineutrino pairs around rotating neutron and quark stars is studied for isothermal discs and accretion discs in thermodynamical equilibrium. We demonstrate both the differences in the equations of state for neutron and quark matter and rotation with the general relativistic effects significantly modify the EMDR of the electrons and positrons generated by the neutrino-antineutrino pair annihilation around compact stellar objects, as measured at infinity.
Energy Technology Data Exchange (ETDEWEB)
Müller, Bernhard [Monash Center for Astrophysics, School of Mathematical Sciences, Building 28, Monash University, Victoria 3800 (Australia); Janka, Hans-Thomas, E-mail: bernhard.mueller@monash.edu, E-mail: bjmuellr@mpa-garching.mpg.de, E-mail: thj@mpa-garching.mpg.de [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching (Germany)
2014-06-10
Considering six general relativistic, two-dimensional (2D) supernova (SN) explosion models of progenitor stars between 8.1 and 27 M {sub ☉}, we systematically analyze the properties of the neutrino emission from core collapse and bounce to the post-explosion phase. The models were computed with the VERTEX-COCONUT code, using three-flavor, energy-dependent neutrino transport in the ray-by-ray-plus approximation. Our results confirm the close similarity of the mean energies, (E), of ν-bar {sub e} and heavy-lepton neutrinos and even their crossing during the accretion phase for stars with M ≳ 10 M {sub ☉} as observed in previous 1D and 2D simulations with state-of-the-art neutrino transport. We establish a roughly linear scaling of 〈E{sub ν-bar{sub e}}〉 with the proto-neutron star (PNS) mass, which holds in time as well as for different progenitors. Convection inside the PNS affects the neutrino emission on the 10%-20% level, and accretion continuing beyond the onset of the explosion prevents the abrupt drop of the neutrino luminosities seen in artificially exploded 1D models. We demonstrate that a wavelet-based time-frequency analysis of SN neutrino signals in IceCube will offer sensitive diagnostics for the SN core dynamics up to at least ∼10 kpc distance. Strong, narrow-band signal modulations indicate quasi-periodic shock sloshing motions due to the standing accretion shock instability (SASI), and the frequency evolution of such 'SASI neutrino chirps' reveals shock expansion or contraction. The onset of the explosion is accompanied by a shift of the modulation frequency below 40-50 Hz, and post-explosion, episodic accretion downflows will be signaled by activity intervals stretching over an extended frequency range in the wavelet spectrogram.
Relativistic GLONASS and geodesy
Mazurova, E. M.; Kopeikin, S. M.; Karpik, A. P.
2016-12-01
GNSS technology is playing a major role in applications to civil, industrial and scientific areas. Nowadays, there are two fully functional GNSS: American GPS and Russian GLONASS. Their data processing algorithms have been historically based on the Newtonian theory of space and time with only a few relativistic effects taken into account as small corrections preventing the system from degradation on a fairly long time. Continuously growing accuracy of geodetic measurements and atomic clocks suggests reconsidering the overall approach to the GNSS theoretical model based on the Einstein theory of general relativity. This is essentially more challenging but fundamentally consistent theoretical approach to relativistic space geodesy. In this paper, we overview the basic principles of the relativistic GNSS model and explain the advantages of such a system for GLONASS and other positioning systems. Keywords: relativistic GLONASS, Einstein theory of general relativity.
Acceleration and collimation of relativistic MHD disk winds
Porth, O
2009-01-01
We perform axisymmetric relativistic magnetohydrodynamic (MHD) simulations to investigate the acceleration and collimation of jets and outflows from disks around compact objects. The fiducial disk surface (respectively a slow disk wind) is prescribed as boundary condition for the outflow. We apply this technique for the first time in the context of relativistic jets. The strength of this approach is that it allows us to run a parameter study in order to investigate how the accretion disk conditions govern the outflow formation. Our simulations using the PLUTO code run for 500 inner disk rotations and on a physical grid size of 100x200 inner disk radii. In general, we obtain collimated beams of mildly relativistic speed and mass-weighted half-opening angles of 3-7 degrees. When we increase the outflow Poynting flux by injecting an additional disk toroidal field into the inlet, Lorentz factors up to 6 are reached. These flows gain super-magnetosonic speed and remain Poynting flux dominated. The light surface of...
Brun-Battistini, D; Sandoval-Villalbazo, A
2016-01-01
Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman\\textquoteright s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by \\textquotedblleft suppressing\\textquotedblright{} the molecular acceleration in Boltzmann\\textquoteright s equation, that a gravitational field drives a heat flux. This procedure corresponds to the description of particle motion through geodesics, in which a Newtonian limit to the Schwarzschild metric is assumed. The effect vanishes in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.
Nakano, Masahiko; Seino, Junji; Nakai, Hiromi
2017-05-01
We have derived and implemented a universal formulation of the second-order generalized Møller-Plesset perturbation theory (GMP2) for spin-dependent (SD) two-component relativistic many-electron Hamiltonians, such as the infinite-order Douglas-Kroll-Hess Hamiltonian for many-electron systems, which is denoted as IODKH/IODKH. Numerical assessments for He- and Ne-like atoms and 16 diatomic molecules show that the MP2 correlation energies with IODKH/IODKH agree well with those calculated with the four-component Dirac-Coulomb (DC) Hamiltonian, indicating a systematic improvement on the inclusion of relativistic two-electron terms. The present MP2 scheme for IODKH/IODKH is demonstrated to be computationally more efficient than that for DC.
Mohammadi, Vahid; Chenaghlou, Alireza
2017-09-01
The two-dimensional Dirac equation with spin and pseudo-spin symmetries is investigated in the presence of the maximally superintegrable potentials. The integrals of motion and the quadratic algebras of the superintegrable quantum E3‧, anisotropic oscillator and the Holt potentials are studied. The corresponding Casimir operators and the structure functions of the mentioned superintegrable systems are found. Also, we obtain the relativistic energy spectra of the corresponding superintegrable systems. Finally, the relativistic energy eigenvalues of the generalized Yang-Coulomb monopole (YCM) superintegrable system (a SU(2) non-Abelian monopole) are calculated by the energy spectrum of the eight-dimensional oscillator which is dual to the former system by Hurwitz transformation.
Spectrum of weak magnetohydrodynamic turbulence.
Boldyrev, Stanislav; Perez, Jean Carlos
2009-11-27
Turbulence of magnetohydrodynamic waves in nature and in the laboratory is generally cross-helical or nonbalanced, in that the energies of Alfvén waves moving in opposite directions along the guide magnetic field are unequal. Based on high-resolution numerical simulations it is proposed that such turbulence spontaneously generates a condensate of the residual energy E(v) - E(b) at small field-parallel wave numbers. As a result, the energy spectra of Alfvén waves are generally not scale invariant in an inertial interval of limited extent. In the limit of an infinite Reynolds number, the universality is asymptotically restored at large wave numbers, and both spectra attain the scaling E(k) proportional to k(perpendicular)(-2). The generation of a condensate is apparently related to the breakdown of mirror symmetry in nonbalanced turbulence.
Alignment of magnetized accretion disks and relativistic jets with spinning black holes.
McKinney, Jonathan C; Tchekhovskoy, Alexander; Blandford, Roger D
2013-01-04
Accreting black holes (BHs) produce intense radiation and powerful relativistic jets, which are affected by the BH's spin magnitude and direction. Although thin disks might align with the BH spin axis via the Bardeen-Petterson effect, this does not apply to jet systems with thick disks. We used fully three-dimensional general relativistic magnetohydrodynamical simulations to study accreting BHs with various spin vectors and disk thicknesses and with magnetic flux reaching saturation. Our simulations reveal a "magneto-spin alignment" mechanism that causes magnetized disks and jets to align with the BH spin near BHs and to reorient with the outer disk farther away. This mechanism has implications for the evolution of BH mass and spin, BH feedback on host galaxies, and resolved BH images for the accreting BHs in SgrA* and M87.
Magnetohydrodynamics of the sun
Priest, Eric
2014-01-01
Magnetohydrodynamics of the Sun is a completely new up-to-date rewrite from scratch of the 1982 book Solar Magnetohydrodynamics, taking account of enormous advances in understanding since that date. It describes the subtle and complex interaction between the Sun's plasma atmosphere and its magnetic field, which is responsible for many fascinating dynamic phenomena. Chapters cover the generation of the Sun's magnetic field by dynamo action, magnetoconvection and the nature of photospheric flux tubes such as sunspots, the heating of the outer atmosphere by waves or reconnection, the structure of prominences, the nature of eruptive instability and magnetic reconnection in solar flares and coronal mass ejections, and the acceleration of the solar wind by reconnection or wave-turbulence. It is essential reading for graduate students and researchers in solar physics and related fields of astronomy, plasma physics and fluid dynamics. Problem sets and other resources are available at www.cambridge.org/9780521854719.
Thermoacoustic magnetohydrodynamic electrical generator
Wheatley, John C.; Swift, Gregory W.; Migliori, Albert
1986-01-01
A thermoacoustic magnetohydrodynamic electrical generator includes an intrinsically irreversible thermoacoustic heat engine coupled to a magnetohydrodynamic electrical generator. The heat engine includes an electrically conductive liquid metal as the working fluid and includes two heat exchange and thermoacoustic structure assemblies which drive the liquid in a push-pull arrangement to cause the liquid metal to oscillate at a resonant acoustic frequency on the order of 1,000 Hz. The engine is positioned in the field of a magnet and is oriented such that the liquid metal oscillates in a direction orthogonal to the field of the magnet, whereby an alternating electrical potential is generated in the liquid metal. Low-loss, low-inductance electrical conductors electrically connected to opposite sides of the liquid metal conduct an output signal to a transformer adapted to convert the low-voltage, high-current output signal to a more usable higher voltage, lower current signal.
Lectures on magnetohydrodynamical drives
Loigom, Villem
The paper deals with nonconventional types of electrical machines and drives - magnetohydrodynamical (MHD) machines and drives. In cardinal it is based on the research conducted with participation of the author in Tallinn Technical University at the Institute of Electrical Drives and Power Electronics, where the use of magnetohydrodynamical motors and drives in the metallurgical and casting industries have been studied for a long time. Major research interests include the qualities and applications of the induction MHD-drives for set in the motion (pumping, turning, dosing, mixing, etc.) non-ferrous molten metals like Al, Mg, Sn, Pb, Na, K, and their alloys. The first part of the paper describes induction MHD motors and their electrohydraulical qualities. In the second part energy conversion problems are described. Also, on the basis of the analogy between electromechanical and electrohydraulical phenomenas, static and dynamic qualities of MHD drives with induction MHD machines are discussed.
Adventures in magnetohydrodynamics
Johnson, John L.
1988-03-01
The material in the report was presented in a series of three lectures presented on two days, October 29 and 30, 1987, at Nagoya University. A survey of magnetohydrodynamic theory was given as it applies to toroidal confinement. The material was broken down into four sections: (1) the derivation and justification of the MHD equations; (2) the equilibrium problem; (3) linearized stability; and (4) comments on nonlinear evolution, magnetic islands and transport theory.
Relativistic viscoelastic fluid mechanics.
Fukuma, Masafumi; Sakatani, Yuho
2011-08-01
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Future of Magnetohydrodynamic Ship Propulsion,
1983-08-16
83 FOREIGN TECHNOLOGY DIVISION FUTURE OF MAGNETOHYDRODYNAMIC SHIP PROPULSION by A.P. Baranov DTIQ ~E tJ Approved for public release; 0.. distribution...MAGNETOHYDRODYNAMIC SHIP PROPULSION By: A.P. Baranov -,English pages: 10 Source: Sudostroyeniye, Nr. 12, December 1966, pp. 3-6 . Country of origin: USSR X...equations, etc. merged into this translation were extracted from the best quality copy available. FUTURE OF MAGNETOHYDRODYNAMIC SHIP PROPULSION A. P
Test particle acceleration in explosive magnetohydrodynamic reconnection
Ripperda, Bart; Xia, Chun; Keppens, Rony
2016-01-01
Magnetic reconnection is the mechanism behind many violent phenomena in the universe. We demonstrate that energy released during reconnection can lead to non-thermal particle distribution functions. We use a method in which we combine resistive magnetohydrodynamics (MHD) with relativistic test particle dynamics. Using our open-source grid-adaptive MPI-AMRVAC software, we simulate global MHD evolution combined with test particle treatments in MHD snapshots. This approach is used to evaluate particle acceleration in explosive reconnection. The reconnection is triggered by an ideal tilt instability in two-and-a-half dimensional (2.5D) scenarios and by a combination of ideal tilt and kink instabilities in three-dimensional (3D) scenarios. These instabilities occur in a system with two parallel, adjacent, repelling current channels in an initially force-free equilibrium, as a simplified representation of flux ropes in a stellar magnetosphere. The current channels undergo a rotation and a separation on Alfv\\'enic t...
Introduction to Magneto-Hydrodynamics
Pelletier, Guy
Magneto-Hydrodynamics (hereafter MHD) describes plasmas on large scales and more generally electrically conducting fluids. This description does not discriminate between the various fluids that constitute the medium. In laboratory, it allows to globally describe a plasma machine, for instance a toroidal nuclear fusion reactor like a Tokamak. In astrophysics it plays an essential role in the description of cosmic objects and their environments, as well as the media, such as the interstellar or the intergalactic medium. A set of phenomena are specific to MHD description. Some of them will be presented in this lecture such as the tension effect, confinement, magnetic diffusivity, magnetic field freezing, Alfvén waves, magneto-sonic waves, reconnection. A celebrated phenomenon of MHD will not be introduced in this brief lecture, namely the dynamo effect.
Komissarov, S S; Lyutikov, M
2015-01-01
In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with v~c the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution z=ct. Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialized code for the time-independent equations. The approach is also much cheaper and more robust compared to the relaxation method. We tested this technique against numerical and analytical solutions found in literature as well as solutions we obtained using the relaxation method and found it sufficiently accurate. In the process, we discovered the reason for the failure of the self-similar analytical model of the jet reconfinement in relatively flat atmospheres a...
Dislocations in magnetohydrodynamic waves in a stellar atmosphere.
López Ariste, A; Collados, M; Khomenko, E
2013-08-23
We describe the presence of wave front dislocations in magnetohydrodynamic waves in stratified stellar atmospheres. Scalar dislocations such as edges and vortices can appear in Alfvén waves, as well as in general magnetoacoustic waves. We detect those dislocations in observations of magnetohydrodynamic waves in sunspots in the solar chromosphere. Through the measured charge of all the dislocations observed, we can give for the first time estimates of the modal contribution in the waves propagating along magnetic fields in solar sunspots.
Dislocations in magnetohydrodynamic waves in a stellar atmosphere
Ariste, A López; Khomenko, E
2013-01-01
We describe the presence of wavefront dislocations in magnetohydrodynamic waves in stratified stellar atmospheres. Scalar dislocations such as edges and vortices can appear in Alfv\\'en waves, as well as in general magneto-acoustic waves. We detect those dislocations in observations of magnetohydrodynamic waves in sunspots in the solar chromosphere. Through the measured charge of all the dislocations observed, we can give for the first time estimates of the modal contribution in the waves propagating along magnetic fields in solar sunspots.
Remarks on the Regularity to 3-D Ideal Magnetohydrodynamic Equations
Institute of Scientific and Technical Information of China (English)
Quan Sen JIU; Cheng HE
2004-01-01
In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval [0,T]. Five sufficient conditions are given. Our results are motivated by two main ideas: one is to control the accumulation of vorticity alone; the other is to generalize the corresponding geometric conditions of 3-D Euler equations to 3-D ideal magnetohydrodynamic equations.
Relativistic theories of materials
Bressan, Aldo
1978-01-01
The theory of relativity was created in 1905 to solve a problem concerning electromagnetic fields. That solution was reached by means of profound changes in fundamental concepts and ideas that considerably affected the whole of physics. Moreover, when Einstein took gravitation into account, he was forced to develop radical changes also in our space-time concepts (1916). Relativistic works on heat, thermodynamics, and elasticity appeared as early as 1911. However, general theories having a thermodynamic basis, including heat conduction and constitutive equations, did not appear in general relativity until about 1955 for fluids and appeared only after 1960 for elastic or more general finitely deformed materials. These theories dealt with materials with memory, and in this connection some relativistic versions of the principle of material indifference were considered. Even more recently, relativistic theories incorporating finite deformations for polarizable and magnetizable materials and those in which couple s...
Iorio, Lorenzo
2005-01-01
The general relativistic Lense-Thirring precessions of the perihelia of the inner planets of the Solar System are about 10^-3 arcseconds per century. Recent improvements in planetary orbit determination may yield the first observational evidence of such a tiny effect. Indeed, corrections to the known perihelion rates of -0.0036 +/- 0.0050, -0.0002 +/- 0.0004 and 0.0001 +/- 0.0005 arcseconds per century were recently estimated by E.V. Pitjeva for Mercury, the Earth and Mars, respectively, on t...
Relabeling symmetries in hydrodynamics and magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Padhye, N.; Morrison, P.J.
1996-04-01
Lagrangian symmetries and concomitant generalized Bianchi identities associated with the relabeling of fluid elements are found for hydrodynamics and magnetohydrodynamics (MHD). In hydrodynamics relabeling results in Ertel`s theorem of conservation of potential vorticity, while in MHD it yields the conservation of cross helicity. The symmetries of the reduction from Lagrangian (material) to Eulerian variables are used to construct the Casimir invariants of the Hamiltonian formalism.
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
Evangelos Chaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
EvangelosChaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.
Solitary vortexes in magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Vainshtein, S.I.
1985-12-01
Stationary configurations in magnetohydrodynamics are investigated for the following two particular cases: (1) there is no motion, which corresponds to a state of magnetostatic equilibrium; and (2) the magnetic field intensity becomes zero, i.e., hydrodynamic vortexes are involved. It is shown that in certain cases the line-of-force topology must be sufficiently simple in order before a stationary or equilibrium state can be achieved. It is also shown that in the two-dimensional case, the magnetic surfaces of an equilibrium configuration represent coaxial cylindrical surfaces. 12 references.
Elements of magnetohydrodynamic stability theory
Energy Technology Data Exchange (ETDEWEB)
Spies, G O
1976-11-01
The nonlinear equations of ideal magnetohydrodynamics are discussed along with the following topics: (1) static equilibrium, (2) strict linear theory, (3) stability of a system with one degree of freedom, (4) spectrum and variational principles in magnetohydrodynamics, (5) elementary proof of the modified energy principle, (6) sufficient stability criteria, (7) local stability, and (8) normal modes. (MOW)
Magnetohydrodynamic process in solar activity
Directory of Open Access Journals (Sweden)
Jingxiu Wang
2014-01-01
Full Text Available Magnetohydrodynamics is one of the major disciplines in solar physics. Vigorous magnetohydrodynamic process is taking place in the solar convection zone and atmosphere. It controls the generating and structuring of the solar magnetic fields, causes the accumulation of magnetic non-potential energy in the solar atmosphere and triggers the explosive magnetic energy release, manifested as violent solar flares and coronal mass ejections. Nowadays detailed observations in solar astrophysics from space and on the ground urge a great need for the studies of magnetohydrodynamics and plasma physics to achieve better understanding of the mechanism or mechanisms of solar activity. On the other hand, the spectacular solar activity always serves as a great laboratory of magnetohydrodynamics. In this article, we reviewed a few key unresolved problems in solar activity studies and discussed the relevant issues in solar magnetohydrodynamics.
Stefańska, Patrycja
2016-01-01
The Sturmian expansion of the generalized Dirac--Coulomb Green function [R.\\/~Szmytkowski, J.\\ Phys.\\ B \\textbf{30}, 825 (1997); \\textbf{30}, 2747(E) (1997)] is exploited to derive a closed-form expression for the magnetizability of the relativistic one-electron atom in an arbitrary discrete state, with a point-like, spinless and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric functions ${}_3F_2$ of the unit argument. Our general expression agrees with formulas obtained analytically earlier by other authors for some particular states of the atom. We present also numerical values of the magnetizability for some excited states of selected hydrogenlike ions with $1 \\leqslant Z \\leqslant 137$ and compare them with data available in the literature.
A multidimensional grid-adaptive relativistic magnetofluid code
van der Holst, B.; Keppens, R.; Meliani, Z.
2008-01-01
A robust second order, shock-capturing numerical scheme for multidimensional special relativistic magnetohydrodynamics on computational domains with adaptive mesh refinement is presented. The base solver is a total variation diminishing Lax-Friedrichs scheme in a finite volume setting and is combine
Magnetohydrodynamics of blood flow.
Keltner, J R; Roos, M S; Brakeman, P R; Budinger, T F
1990-10-01
The changes in hydrostatic pressure and electrical potentials across vessels in the human vasculature in the presence of a large static magnetic field are estimated to determine the feasibility of in vivo NMR spectroscopy at fields as high as 10 T.A 10-T magnetic field changes the vascular pressure in a model of the human vasculature by less than 0.2%. An exact solution to the magnetohydrodynamic equations describing a conducting fluid flowing transverse to a static magnetic field in a nonconducting, straight, circular tube is used. This solution is compared to an approximate solution that assumes that no magnetic fields are induced in the fluid and that has led previous investigators to predict significant biological effects from static magnetic fields. Experimental results show that the exact solution accurately predicts the magnetohydrodynamic slowing of 15% NaCl flowing transverse to 2.3- and 4.7-T magnetic fields for fluxes below 0.5 liter/min while the approximate solution predicts a much more retarded flow.
Multi-region relaxed magnetohydrodynamics with flow
Dennis, G R; Dewar, R L; Hole, M J
2014-01-01
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential application to describing rotating 3D MHD structures such as 'snakes' and long-lived modes.
Multi-region relaxed magnetohydrodynamics with flow
Energy Technology Data Exchange (ETDEWEB)
Dennis, G. R., E-mail: graham.dennis@anu.edu.au; Dewar, R. L.; Hole, M. J. [Research School of Physics and Engineering, Australian National University, ACT 0200 (Australia); Hudson, S. R. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States)
2014-04-15
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite, our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential application to describing rotating 3D MHD structures such as 'snakes' and long-lived modes.
Relativistic cosmological hydrodynamics
Hwang, J
1997-01-01
We investigate the relativistic cosmological hydrodynamic perturbations. We present the general large scale solutions of the perturbation variables valid for the general sign of three space curvature, the cosmological constant, and generally evolving background equation of state. The large scale evolution is characterized by a conserved gauge invariant quantity which is the same as a perturbed potential (or three-space curvature) in the comoving gauge.
Stefańska, Patrycja
2016-01-01
We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); 30, 2747(E) (1997)], we derive a closed-form expression for the electric quadrupole moment induced in the atom in an arbitrary discrete energy eigenstate. The result, which has the form of a double finite sum involving the generalized hypergeometric functions 3F2 of the unit argument, agrees with the earlier relativistic formula for that quantity, obtained by us for the ground state of the atom.
Stefańska, Patrycja
2016-02-01
We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997), 10.1088/0953-4075/30/4/007; J. Phys. B 30, 2747 (1997), 10.1088/0953-4075/30/11/023], We derive a closed-form expression for the electric quadrupole moment induced in the atom in an arbitrary discrete energy eigenstate. The result, which has the form of a double finite sum involving the generalized hypergeometric functions 3F2 of the unit argument, agrees with the earlier relativistic formula for that quantity, obtained by us for the ground state of the atom.
Relativistic cosmology; Cosmologia Relativista
Energy Technology Data Exchange (ETDEWEB)
Bastero-Gil, M.
2015-07-01
Relativistic cosmology is nothing but the study of the evolution of our universe expanding from the General Theory of Relativity, which describes the gravitational interaction at any scale and given its character far-reaching is the force that dominate the evolution of the universe. (Author)
Fabian, A C; Parker, M L
2014-01-01
Broad emission lines, particularly broad iron-K lines, are now commonly seen in the X-ray spectra of luminous AGN and Galactic black hole binaries. Sensitive NuSTAR spectra over the energy range of 3-78 keV and high frequency reverberation spectra now confirm that these are relativistic disc lines produced by coronal irradiation of the innermost accretion flow around rapidly spinning black holes. General relativistic effects are essential in explaining the observations. Recent results are briefly reviewed here.
Introduction to magnetohydrodynamics
Thompson, Ian
2016-01-01
Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite.
Magnetohydrodynamic inertial reference system
Eckelkamp-Baker, Dan; Sebesta, Henry R.; Burkhard, Kevin
2000-07-01
Optical platforms increasingly require attitude knowledge and optical instrument pointing at sub-microradian accuracy. No low-cost commercial system exists to provide this level of accuracy for guidance, navigation, and control. The need for small, inexpensive inertial sensors, which may be employed in pointing control systems that are required to satisfy angular line-of-sight stabilization jitter error budgets to levels of 1-3 microradian rms and less, has existed for at least two decades. Innovations and evolutions in small, low-noise inertial angular motion sensor technology and advances in the applications of the global positioning system have converged to allow improvement in acquisition, tracking and pointing solutions for a wide variety of payloads. We are developing a small, inexpensive, and high-performance inertial attitude reference system that uses our innovative magnetohydrodynamic angular rate sensor technology.
Astrophysical Weighted Particle Magnetohydrodynamics
Gaburov, Evghenii
2010-01-01
This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. The divergence constraint of the latter is maintained to the truncation error by a new meshless divergence cleaning procedure. The physics of the interaction between the particles is described by an one-dimensional Riemann problem in a moving frame. As a result, necessary diffusion which is required to treat dissipative processes is added automatically. As a result, our scheme has no free parameters that controls the physics of inter-particle interaction, with the exception of the number of the interacting neighbours which control the resolution and accuracy. The resulting equations have the form similar to SPH equations, and therefore existing SPH codes can be used to implement the weighed particle scheme. The scheme is validated in several hydrodynamic and MHD test cases. In particular, we demonstrate for the first time the ability of a meshless MHD schem...
Introduction to modern magnetohydrodynamics
Galtier, Sébastien
2016-01-01
Ninety-nine percent of ordinary matter in the Universe is in the form of ionized fluids, or plasmas. The study of the magnetic properties of such electrically conducting fluids, magnetohydrodynamics (MHD), has become a central theory in astrophysics, as well as in areas such as engineering and geophysics. This textbook offers a comprehensive introduction to MHD and its recent applications, in nature and in laboratory plasmas; from the machinery of the Sun and galaxies, to the cooling of nuclear reactors and the geodynamo. It exposes advanced undergraduate and graduate students to both classical and modern concepts, making them aware of current research and the ever-widening scope of MHD. Rigorous derivations within the text, supplemented by over 100 illustrations and followed by exercises and worked solutions at the end of each chapter, provide an engaging and practical introduction to the subject and an accessible route into this wide-ranging field.
Iorio, L
2005-01-01
The post-Newtonian general relativistic gravitomagnetic Lense-Thirring precessions of the perihelia of the inner planets of the Solar System amount to 10^-3 arcseconds per century. Up to now they were always retained too small to be detected. Recent improvements in the planetary ephemerides determination yield the first observational evidence of such a tiny effect. Indeed, extra-corrections to the known perihelion advances of -0.0036\\pm 0.0050, -0.0002\\pm 0.0004 and 0.0001\\pm 0.0005 arcseconds per century were recently determined by E.V. Pitjeva for Mercury, the Earth and Mars, respectively. They were based on the EPM2004 ephemerides and a set of more than 317 000 observations of various kinds. The predicted relativistic Thirring-Lense precessions for these planets are -0.0020, -0.0001 and -3\\times 10^-5 arcseconds per century, respectively and are compatible with the measured perihelia corrections, although the experimental errors are still large. The data from the forthcoming BepiColombo mission to Mercury ...
Mueller, B; Dimmelmeier, H
2010-01-01
We present a new general relativistic (GR) code for hydrodynamic supernova simulations with neutrino transport in spherical and azimuthal symmetry (1D/2D). The code is a combination of the CoCoNuT hydro module, which is a Riemann-solver based, high-resolution shock-capturing method, and the three-flavor, energy-dependent neutrino transport scheme VERTEX. VERTEX integrates the neutrino moment equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the ray-by-ray plus approximation in 2D, assuming the neutrino distribution to be axially symmetric around the radial direction, and thus the neutrino flux to be radial. Our spacetime treatment employs the ADM 3+1 formalism with the conformal flatness condition for the spatial three-metric. This approach is exact in 1D and has been shown to yield very accurate results also for rotational stellar collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian...
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
grim: A Flexible, Conservative Scheme for Relativistic Fluid Theories
Chandra, Mani; Foucart, Francois; Gammie, Charles F.
2017-03-01
Hot, diffuse, relativistic plasmas such as sub-Eddington black-hole accretion flows are expected to be collisionless, yet are commonly modeled as a fluid using ideal general relativistic magnetohydrodynamics (GRMHD). Dissipative effects such as heat conduction and viscosity can be important in a collisionless plasma and will potentially alter the dynamics and radiative properties of the flow from that in ideal fluid models; we refer to models that include these processes as Extended GRMHD. Here we describe a new conservative code, grim, that enables all of the above and additional physics to be efficiently incorporated. grim combines time evolution and primitive variable inversion needed for conservative schemes into a single step using an algorithm that only requires the residuals of the governing equations as inputs. This algorithm enables the code to be physics agnostic as well as flexibility regarding time-stepping schemes. grim runs on CPUs, as well as on GPUs, using the same code. We formulate a performance model and use it to show that our implementation runs optimally on both architectures. grim correctly captures classical GRMHD test problems as well as a new suite of linear and nonlinear test problems with anisotropic conduction and viscosity in special and general relativity. As tests and example applications, we resolve the shock substructure due to the presence of dissipation, and report on relativistic versions of the magneto-thermal instability and heat flux driven buoyancy instability, which arise due to anisotropic heat conduction, and of the firehose instability, which occurs due to anisotropic pressure (i.e., viscosity). Finally, we show an example integration of an accretion flow around a Kerr black hole, using Extended GRMHD.
Review of magnetohydrodynamic pump applications
National Research Council Canada - National Science Library
Al-Habahbeh, O.M; Al-Saqqa, M; Safi, M; Abo Khater, T
2016-01-01
Magneto-hydrodynamic (MHD) principle is an important interdisciplinary field. One of the most important applications of this effect is pumping of materials that are hard to pump using conventional pumps...
Relativistic formulation and reference frame
Klioner, Sergei A.
2004-01-01
After a short review of experimental foundations of metric theories of gravity, the choice of general relativity as a theory to be used for the routine modeling of Gaia observations is justified. General principles of relativistic modeling of astronomical observations are then sketched and compared to the corresponding Newtonian principles. The fundamental reference system -- Barycentric Celestial Reference System, which has been chosen to be the relativistic reference system underlying the f...
Fractional Dynamics of Relativistic Particle
Tarasov, Vasily E
2011-01-01
Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to a non-potential four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u_{\\mu} u^{\\mu}+c^2=0, where c is a speed of light in vacuum. In the general case, the fractional dynamics of relativistic particle is described as non-Hamiltonian and dissipative. Conditions for fractional relativistic particle to be a Hamiltonian system are considered.
Fluid-magnetic helicity in axisymmetric stationary relativistic magnetohydrodynamics
Prasad, G.
2017-10-01
The present work is intended to gain a fruitful insight into the understanding of the formations of magneto-vortex configurations and their role in the physical processes of mutual exchange of energies associated with fluid's motion and the magnetic fields in an axisymmetric stationary hydromagnetic system subject to strong gravitational field (e.g., neutron star/magnetar). It is found that the vorticity flux vector field associated with vorticity 2-form is a linear combination of fluid's vorticity vector and of magnetic vorticity vector. The vorticity flux vector obeys Helmholtz's flux conservation. The energy equation associated with the vorticity flux vector field is deduced. It is shown that the mechanical rotation of vorticity flux surfaces contributes to the formation of vorticity flux vector field. The dynamo action for the generation of toroidal components of vorticity flux vector field is described in the presence of meridional circulations. It is shown that the stretching of twisting magnetic lines due to differential rotation leads to the breakdown of gravitational isorotation in the absence of meridional circulations. An explicit expression consists of rotation of vorticity flux surface, energy and angular momentum per baryon for the fluid-magnetic helicity current vector is obtained. The conservation of fluid-magnetic helicity is demonstrated. It is found that the fluid-magnetic helicity displays the energy spectrum arising due to the interaction between the mechanical rotation of vorticity flux surfaces and the fluid's motion obeying Euler's equations. The dissipation of a linear combination of modified fluid helicity and magnetic twist is shown to occur due to coupled effect of frame dragging and meridional circulation. It is found that the growing twist of magnetic lines causes the dissipation of modified fluid helicity in the absence of meridional circulations.
Baiotti, Luca; Shibata, Masaru; Yamamoto, Tetsuro
2010-09-01
We present the first quantitative comparison of two independent general-relativistic hydrodynamics codes, the whisky code and the sacra code. We compare the output of simulations starting from the same initial data and carried out with the configuration (numerical methods, grid setup, resolution, gauges) which for each code has been found to give consistent and sufficiently accurate results, in particular, in terms of cleanness of gravitational waveforms. We focus on the quantities that should be conserved during the evolution (rest mass, total mass energy, and total angular momentum) and on the gravitational-wave amplitude and frequency. We find that the results produced by the two codes agree at a reasonable level, with variations in the different quantities but always at better than about 10%.
Baiotti, Luca; Yamamoto, Tetsuro
2010-01-01
We present the first quantitative comparison of two independent general-relativistic hydrodynamics codes, the Whisky code and the SACRA code. We compare the output of simulations starting from the same initial data and carried out with the configuration (numerical methods, grid setup, resolution, gauges) which for each code has been found to give consistent and sufficiently accurate results, in particular in terms of cleanness of gravitational waveforms. We focus on the quantities that should be conserved during the evolution (rest mass, total mass energy, and total angular momentum) and on the gravitational-wave amplitude and frequency. We find that the results produced by the two codes agree at a reasonable level, with variations in the different quantities but always at better than about 10%.
Computational Methods for Ideal Magnetohydrodynamics
Kercher, Andrew D.
Numerical schemes for the ideal magnetohydrodynamics (MHD) are widely used for modeling space weather and astrophysical flows. They are designed to resolve the different waves that propagate through a magnetohydro fluid, namely, the fast, Alfven, slow, and entropy waves. Numerical schemes for ideal magnetohydrodynamics that are based on the standard finite volume (FV) discretization exhibit pseudo-convergence in which non-regular waves no longer exist only after heavy grid refinement. A method is described for obtaining solutions for coplanar and near coplanar cases that consist of only regular waves, independent of grid refinement. The method, referred to as Compound Wave Modification (CWM), involves removing the flux associated with non-regular structures and can be used for simulations in two- and three-dimensions because it does not require explicitly tracking an Alfven wave. For a near coplanar case, and for grids with 213 points or less, we find root-mean-square-errors (RMSEs) that are as much as 6 times smaller. For the coplanar case, in which non-regular structures will exist at all levels of grid refinement for standard FV schemes, the RMSE is as much as 25 times smaller. A multidimensional ideal MHD code has been implemented for simulations on graphics processing units (GPUs). Performance measurements were conducted for both the NVIDIA GeForce GTX Titan and Intel Xeon E5645 processor. The GPU is shown to perform one to two orders of magnitude greater than the CPU when using a single core, and two to three times greater than when run in parallel with OpenMP. Performance comparisons are made for two methods of storing data on the GPU. The first approach stores data as an Array of Structures (AoS), e.g., a point coordinate array of size 3 x n is iterated over. The second approach stores data as a Structure of Arrays (SoA), e.g. three separate arrays of size n are iterated over simultaneously. For an AoS, coalescing does not occur, reducing memory efficiency
Wuthrich, Christian
2014-01-01
There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in principle) can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istv\\'an N\\'emeti and Gyula D\\'avid (2006) have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this essay, I will honour Istv\\'an's seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in N\\'emeti and D\\'avid (2006) might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing ...
Haba, Z
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.
Sahoo, Raghunath
2016-01-01
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.
Magnetohydrodynamic Augmented Propulsion Experiment
Litchford, Ron J.; Cole, John; Lineberry, John; Chapman, Jim; Schmidt, Harold; Cook, Stephen (Technical Monitor)
2002-01-01
A fundamental obstacle to routine space access is the specific energy limitations associated with chemical fuels. In the case of vertical take-off, the high thrust needed for vertical liftoff and acceleration to orbit translates into power levels in the 10 GW range. Furthermore, useful payload mass fractions are possible only if the exhaust particle energy (i.e., exhaust velocity) is much greater than that available with traditional chemical propulsion. The electronic binding energy released by the best chemical reactions (e.g., LOX/LH2 for example, is less than 2 eV per product molecule (approx. 1.8 eV per H2O molecule), which translates into particle velocities less than 5 km/s. Useful payload fractions, however, will require exhaust velocities exceeding 15 km/s (i.e., particle energies greater than 20 eV). As an added challenge, the envisioned hypothetical RLV (reusable launch vehicle) should accomplish these amazing performance feats while providing relatively low acceleration levels to orbit (2-3g maximum). From such fundamental considerations, it is painfully obvious that planned and current RLV solutions based on chemical fuels alone represent only a temporary solution and can only result in minor gains, at best. What is truly needed is a revolutionary approach that will dramatically reduce the amount of fuel and size of the launch vehicle. This implies the need for new compact high-power energy sources as well as advanced accelerator technologies for increasing engine exhaust velocity. Electromagnetic acceleration techniques are of immense interest since they can be used to circumvent the thermal limits associated with conventional propulsion systems. This paper describes the Magnetohydrodynamic Augmented Propulsion Experiment (MAPX) being undertaken at NASA Marshall Space Flight Center (MSFC). In this experiment, a 1-MW arc heater is being used as a feeder for a 1-MW magnetohydrodynamic (MHD) accelerator. The purpose of the experiment is to demonstrate
Buoyancy-driven Magnetohydrodynamic Waves
Hague, A.; Erdélyi, R.
2016-09-01
Turbulent motions close to the visible solar surface may generate low-frequency internal gravity waves (IGWs) that propagate through the lower solar atmosphere. Magnetic activity is ubiquitous throughout the solar atmosphere, so it is expected that the behavior of IGWs is to be affected. In this article we investigate the role of an equilibrium magnetic field on propagating and standing buoyancy oscillations in a gravitationally stratified medium. We assume that this background magnetic field is parallel to the direction of gravitational stratification. It is known that when the equilibrium magnetic field is weak and the background is isothermal, the frequencies of standing IGWs are sensitive to the presence of magnetism. Here, we generalize this result to the case of a slowly varying temperature. To do this, we make use of the Boussinesq approximation. A comparison between the hydrodynamic and magnetohydrodynamic cases allows us to deduce the effects due to a magnetic field. It is shown that the frequency of IGWs may depart significantly from the Brunt-Väisälä frequency, even for a weak magnetic field. The mathematical techniques applied here give a clearer picture of the wave mode identification, which has previously been misinterpreted. An observational test is urged to validate the theoretical findings.
Parker, Edward
2017-08-01
A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl's theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.
What is "Relativistic Canonical Quantization"?
Arbatsky, D. A.
2005-01-01
The purpose of this review is to give the most popular description of the scheme of quantization of relativistic fields that was named relativistic canonical quantization (RCQ). I do not give here the full exact account of this scheme. But with the help of this review any physicist, even not a specialist in the relativistic quantum theory, will be able to get a general view of the content of RCQ, of its connection with other known approaches, of its novelty and of its fruitfulness.
Relativistic effects in atom gravimeters
Tan, Yu-Jie; Shao, Cheng-Gang; Hu, Zhong-Kun
2017-01-01
Atom interferometry is currently developing rapidly, which is now reaching sufficient precision to motivate laboratory tests of general relativity. Thus, it is extremely significant to develop a general relativistic model for atom interferometers. In this paper, we mainly present an analytical derivation process and first give a complete vectorial expression for the relativistic interferometric phase shift in an atom interferometer. The dynamics of the interferometer are studied, where both the atoms and the light are treated relativistically. Then, an appropriate coordinate transformation for the light is performed crucially to simplify the calculation. In addition, the Bordé A B C D matrix combined with quantum mechanics and the "perturbation" approach are applied to make a methodical calculation for the total phase shift. Finally, we derive the relativistic phase shift kept up to a sensitivity of the acceleration ˜1 0-14 m/s 2 for a 10 -m -long atom interferometer.
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
Solar Flares: Magnetohydrodynamic Processes
Directory of Open Access Journals (Sweden)
Kazunari Shibata
2011-12-01
Full Text Available This paper outlines the current understanding of solar flares, mainly focused on magnetohydrodynamic (MHD processes responsible for producing a flare. Observations show that flares are one of the most explosive phenomena in the atmosphere of the Sun, releasing a huge amount of energy up to about 10^32 erg on the timescale of hours. Flares involve the heating of plasma, mass ejection, and particle acceleration that generates high-energy particles. The key physical processes for producing a flare are: the emergence of magnetic field from the solar interior to the solar atmosphere (flux emergence, local enhancement of electric current in the corona (formation of a current sheet, and rapid dissipation of electric current (magnetic reconnection that causes shock heating, mass ejection, and particle acceleration. The evolution toward the onset of a flare is rather quasi-static when free energy is accumulated in the form of coronal electric current (field-aligned current, more precisely, while the dissipation of coronal current proceeds rapidly, producing various dynamic events that affect lower atmospheres such as the chromosphere and photosphere. Flares manifest such rapid dissipation of coronal current, and their theoretical modeling has been developed in accordance with observations, in which numerical simulations proved to be a strong tool reproducing the time-dependent, nonlinear evolution of a flare. We review the models proposed to explain the physical mechanism of flares, giving an comprehensive explanation of the key processes mentioned above. We start with basic properties of flares, then go into the details of energy build-up, release and transport in flares where magnetic reconnection works as the central engine to produce a flare.
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE
Directory of Open Access Journals (Sweden)
Francisco Frutos Alfaro
2017-04-01
Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.
Particle energisation in a collapsing magnetic trap model: the relativistic regime
Oskoui, Solmaz Eradat
2014-01-01
In solar flares, a large number of charged particles is accelerated to high energies. By which physical processes this is achieved is one of the main open problems in solar physics. It has been suggested that during a flare, regions of the rapidly relaxing magnetic field can form a collapsing magnetic trap (CMT) and that this trap may contribute to particle energisation.} In this Research Note we focus on a particular analytical CMT model based on kinematic magnetohydrodynamics. Previous investigations of particle acceleration for this CMT model focused on the non-relativistic energy regime. It is the specific aim of this Research Note to extend the previous work to relativistic particle energies. Particle orbits were calculated numerically using the relativistic guiding centre equations. We also calculated particle orbits using the non-relativistic guiding centre equations for comparison. For mildly relativistic energies the relativistic and non-relativistic particle orbits mainly agree well, but clear devia...
Strings and large scale magnetohydrodynamics
Olesen, P
1995-01-01
From computer simulations of magnetohydrodynamics one knows that a turbulent plasma becomes very intermittent, with the magnetic fields concentrated in thin flux tubes. This situation looks very "string-like", so we investigate whether strings could be solutions of the magnetohydrodynamics equations in the limit of infinite conductivity. We find that the induction equation is satisfied, and we discuss the Navier-Stokes equation (without viscosity) with the Lorentz force included. We argue that the string equations (with non-universal maximum velocity) should describe the large scale motion of narrow magnetic flux tubes, because of a large reparametrization (gauge) invariance of the magnetic and electric string fields.
On the continua in two-dimensional nonadiabatic magnetohydrodynamic spectra
De Ploey, A.; Van der Linden, R. A. M.; Belien, A. J. C.
2000-01-01
The equations for the continuous subspectra of the linear magnetohydrodynamic (MHD) normal modes spectrum of two-dimensional (2D) plasmas are derived in general curvilinear coordinates, taking nonadiabatic effects in the energy equation into account. Previously published derivations of continuous sp
On magnetohydrodynamic gauge field theory
Webb, G. M.; Anco, S. C.
2017-06-01
Clebsch potential gauge field theory for magnetohydrodynamics is developed based in part on the theory of Calkin (1963 Can. J. Phys. 41 2241-51). It is shown how the polarization vector {P} in Calkin’s approach naturally arises from the Lagrange multiplier constraint equation for Faraday’s equation for the magnetic induction {B} , or alternatively from the magnetic vector potential form of Faraday’s equation. Gauss’s equation, (divergence of {B} is zero) is incorporated in the variational principle by means of a Lagrange multiplier constraint. Noether’s theorem coupled with the gauge symmetries is used to derive the conservation laws for (a) magnetic helicity, (b) cross helicity, (c) fluid helicity for non-magnetized fluids, and (d) a class of conservation laws associated with curl and divergence equations which applies to Faraday’s equation and Gauss’s equation. The magnetic helicity conservation law is due to a gauge symmetry in MHD and not due to a fluid relabelling symmetry. The analysis is carried out for the general case of a non-barotropic gas in which the gas pressure and internal energy density depend on both the entropy S and the gas density ρ. The cross helicity and fluid helicity conservation laws in the non-barotropic case are nonlocal conservation laws that reduce to local conservation laws for the case of a barotropic gas. The connections between gauge symmetries, Clebsch potentials and Casimirs are developed. It is shown that the gauge symmetry functionals in the work of Henyey (1982 Phys. Rev. A 26 480-3) satisfy the Casimir determining equations.
Electron magnetohydrodynamics: dynamics and turbulence.
Lyutikov, Maxim
2013-11-01
We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron magnetohydrodynamics (EMHD). We argue that there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. On the other hand, the relaxation principle, the long term evolution of a weakly dissipative system towards Taylor-Beltrami state, remains valid in EMHD. We consider the turbulent cascade of whistler modes. We show that (i) harmonic whistlers are exact nonlinear solutions; (ii) collinear whistlers do not interact (including counterpropagating); (iii) waves with the same value of the wave vector k(1)=k(2) do not interact; (iv) whistler modes have a dispersion that allows a three-wave decay, including into a zero frequency mode; (v) the three-wave interaction effectively couples modes with highly different wave numbers and propagation angles. In addition, linear interaction of a whistler with a single zero mode can lead to spatially divergent structures via parametric instability. All these properties are drastically different from MHD, so that the qualitative properties of the Alfvén turbulence can not be transferred to the EMHD turbulence. We derive the Hamiltonian formulation of EMHD, and using Bogoliubov transformation reduce it to the canonical form; we calculate the matrix elements for the three-wave interaction of whistlers. We solve numerically the kinetic equation and show that, generally, the EMHD cascade develops within a broad range of angles, while transiently it may show anisotropic, nearly two-dimensional structures. Development of a cascade depends on the forcing (nonuniversal) and often fails to reach a steady state. Analytical estimates predict the spectrum of magnetic fluctuations for the quasi-isotropic cascade [proportionality]k(-2). The cascade remains weak (not critically balanced). The cascade is UV local, while the infrared locality is weakly (logarithmically) violated.
GRay: a Massively Parallel GPU-Based Code for Ray Tracing in Relativistic Spacetimes
Chan, Chi-kwan; Ozel, Feryal
2013-01-01
We introduce GRay, a massively parallel integrator designed to trace the trajectories of billions of photons in a curved spacetime. This GPU-based integrator employs the stream processing paradigm, is implemented in CUDA C/C++, and runs on nVidia graphics cards. The peak performance of GRay using single precision floating-point arithmetic on a single GPU exceeds 300 GFLOP (or 1 nanosecond per photon per time step). For a realistic problem, where the peak performance cannot be reached, GRay is two orders of magnitude faster than existing CPU-based ray tracing codes. This performance enhancement allows more effective searches of large parameter spaces when comparing theoretical predictions of images, spectra, and lightcurves from the vicinities of compact objects to observations. GRay can also perform on-the-fly ray tracing within general relativistic magnetohydrodynamic algorithms that simulate accretion flows around compact objects. Making use of this algorithm, we calculate the properties of the shadows of K...
Relativistic MHD in dynamical spacetimes: Improved EM gauge condition for AMR grids
Etienne, Zachariah B; Liu, Yuk Tung; Shapiro, Stuart L
2011-01-01
We recently developed a new general relativistic magnetohydrodynamic code with adaptive mesh refinement that evolves the electromagnetic (EM) vector potential (A) instead of the magnetic fields directly. Evolving A enables one to use any interpolation scheme on refinement level boundaries and still guarantee that the magnetic field remains divergenceless. As in classical EM, a gauge choice must be made when evolving A, and we chose a straightforward "algebraic" gauge condition to simplify the A evolution equation. However, magnetized black hole-neutron star (BHNS) simulations in this gauge exhibit unphysical behavior, including the spurious appearance of strong magnetic fields on refinement level boundaries. This spurious behavior is exacerbated when matter crosses refinement boundaries during tidal disruption of the NS. Applying Kreiss-Oliger dissipation to the evolution of the magnetic vector potential A slightly weakens this spurious magnetic effect, but with undesired consequences. We demonstrate via an e...
Action principles for extended magnetohydrodynamic models
Energy Technology Data Exchange (ETDEWEB)
Keramidas Charidakos, I.; Lingam, M.; Morrison, P. J.; White, R. L. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, Texas 78712 (United States); Wurm, A. [Department of Physical and Biological Sciences, Western New England University, Springfield, Massachusetts 01119 (United States)
2014-09-15
The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of motion. To ensure that the reduced models are Hamiltonian, we start with the general two-fluid action functional, and make all the approximations, changes of variables, and expansions directly within the action context. The resulting equations are then mapped to the Eulerian fluid variables using a novel nonlocal Lagrange-Euler map. Using this method, we recover Lüst's general two-fluid model, extended magnetohydrodynamic (MHD), Hall MHD, and electron MHD from a unified framework. The variational formulation allows us to use Noether's theorem to derive conserved quantities for each symmetry of the action.
Leiter, D; Robertson, S; Leiter, Darryl; Mitra, Abhas; Robertson, Stanley
2001-01-01
It has been recently shown (Mitra, 2000 - astro-ph/9910408) that the timelike spherical collapse of a radiating, physical fluid in General Relativity, as seen by an interior co-moving observer at rest in the physical fluid, does not permit formation of ``trapped surfaces''. This followed from the fact that the formation of a trapped surface in a physical fluid would cause the timelike world lines of the collapsing fluid to become null at the would be trapped surface, thus violating the Principle of Equivalence in General Theory of Relativity. In this paper we generalize and extend this result by studying the problem from the point of view of the exterior Vaidya metric of a collapsing radiating fluid as seen by an exterior stationary observer, and find that the "no trapped surface condition" becomes g00 > 0 consistent with that obtained for the interior co-moving metric. Since we have shown that the Principle of Equivalence prevents trapped surfaces from being formed in collapsing, radiating objects, then true...
Spectral analysis in magnetohydrodynamic equilibria
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel; Galindo, Felix [Departamento de Analisis Matematico, Universidad de Valladolid, Valladolid (Spain)
1998-12-11
It has been universally assumed that the spectrum of the magnetohydrodynamics equations, linearized around an equilibrium state, provides enough information on the short-term evolution of the plasma to study certain stability properties. We show that this is true if one takes into account viscous and resistive effects and the equilibrium satisfies certain regularity conditions. (author)
MAGNETOHYDRODYNAMIC MODELING FOR FUSION PLASMAS
Keppens, R.; Goedbloed, J. P.; Blokland, J. W. S.
2010-01-01
The magnetohydrodynamic model for fusion plasma dynamics governs the large-scale equilibrium properties, and sets the most stringent constraints on the parameter space accessible without violent disruptions. In conjunction with linear stability analysis in the complex tokamak geometry, the MHD parad
TURBULENT RECONNECTION IN RELATIVISTIC PLASMAS AND EFFECTS OF COMPRESSIBILITY
Energy Technology Data Exchange (ETDEWEB)
Takamoto, Makoto [Max-Planck-Institut für Kernphysik, Heidelberg (Germany); Inoue, Tsuyoshi [Division of Theoretical Astronomy, National Astronomical Observatory of Japan (Japan); Lazarian, Alexandre, E-mail: mtakamoto@eps.s.u-tokyo.ac.jp, E-mail: tsuyoshi.inoue@nao.ac.jp, E-mail: alazarian@facstaff.wisc.edu [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States)
2015-12-10
We report on the turbulence effects on magnetic reconnection in relativistic plasmas using three-dimensional relativistic resistive magnetohydrodynamics simulations. We found that the reconnection rate became independent of the plasma resistivity due to turbulence effects similarly to non-relativistic cases. We also found that compressible turbulence effects modified the turbulent reconnection rate predicted in non-relativistic incompressible plasmas; the reconnection rate saturates, and even decays, as the injected velocity approaches to the Alfvén velocity. Our results indicate that compressibility cannot be neglected when a compressible component becomes about half of the incompressible mode, occurring when the Alfvén Mach number reaches about 0.3. The obtained maximum reconnection rate is around 0.05–0.1, which will be able to reach around 0.1–0.2 if injection scales are comparable to the sheet length.
Numerical Simulations of Driven Supersonic Relativistic MHD Turbulence
Zrake, Jonathan; 10.1063/1.3621748
2011-01-01
Models for GRB outflows invoke turbulence in relativistically hot magnetized fluids. In order to investigate these conditions we have performed high-resolution three-dimensional numerical simulations of relativistic magneto-hydrodynamical (RMHD) turbulence. We find that magnetic energy is amplified to several percent of the total energy density by turbulent twisting and folding of magnetic field lines. Values of epsilon_B near 1% are thus naturally expected. We study the dependence of saturated magnetic field energy fraction as a function of Mach number and relativistic temperature. We then present power spectra of the turbulent kinetic and magnetic energies. We also present solenoidal (curl-like) and dilatational (divergence-like) power spectra of kinetic energy. We propose that relativistic effects introduce novel couplings between these spectral components. The case we explore in most detail is for equal amounts of thermal and rest mass energy, corresponding to conditions after collisions of shells with re...
Relativistic gravity gradiometry
Bini, Donato; Mashhoon, Bahram
2016-12-01
In general relativity, relativistic gravity gradiometry involves the measurement of the relativistic tidal matrix, which is theoretically obtained from the projection of the Riemann curvature tensor onto the orthonormal tetrad frame of an observer. The observer's 4-velocity vector defines its local temporal axis and its local spatial frame is defined by a set of three orthonormal nonrotating gyro directions. The general tidal matrix for the timelike geodesics of Kerr spacetime has been calculated by Marck [Proc. R. Soc. A 385, 431 (1983)]. We are interested in the measured components of the curvature tensor along the inclined "circular" geodesic orbit of a test mass about a slowly rotating astronomical object of mass M and angular momentum J . Therefore, we specialize Marck's results to such a "circular" orbit that is tilted with respect to the equatorial plane of the Kerr source. To linear order in J , we recover the gravitomagnetic beating phenomenon [B. Mashhoon and D. S. Theiss, Phys. Rev. Lett. 49, 1542 (1982)], where the beat frequency is the frequency of geodetic precession. The beat effect shows up as a special long-period gravitomagnetic part of the relativistic tidal matrix; moreover, the effect's short-term manifestations are contained in certain post-Newtonian secular terms. The physical interpretation of this effect is briefly discussed.
Knecht, Stefan; Jensen, Hans Jorgen Aa; Fleig, Timo
2008-01-07
We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.
Redkov, V M
1998-01-01
Some attention in the literature has been given to the case of a particle of spin 1/2 on the background of the external monopole potential. Some aspects of this problem are reexamined here. The primary technical novelty is that the tetrad generally relativistic method of Tetrode-Weyl-Fock-Ivanenko for describing a spinor particle is exploited. The choice of the formalism has turned out to be of great fruitfulness for examining the system. It is matter that, as known, the use of a special spherical tetrad in the theory of a spin 1/2 particle had led Schrodinger to a basis of remarkable features. The basis has been used with great efficiency by Pauli in his investigation on the pro- blem of allowed spherically symmetric wave functions in quantum mechanics. For our purposes, just several simple rules extracted from the much more com- prehensive Pauli's analysis will be quite sufficient; those are almost mnemo- nic working regulations. So, one may remember some very primary facts of D- functions theory and then p...
Relativistic and non-relativistic geodesic equations
Energy Technology Data Exchange (ETDEWEB)
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Ghosh, Shubhrangshu; Banik, Prabir
2015-07-01
In this paper, we present a complete work on steady state spherically symmetric Bondi type accretion flow in the presence of cosmological constant (Λ) in both Schwarzschild-de Sitter (SDS) and Schwarzschild anti-de Sitter (SADS) backgrounds considering an isolated supermassive black hole (SMBH), with the inclusion of a simple radiative transfer scheme, in the pseudo-general relativistic paradigm. We do an extensive analysis on the transonic behavior of the Bondi type accretion flow onto the cosmological BHs including a complete analysis of the global parameter space and the stability of flow, and do a complete study of the global family of solutions for a generic polytropic flow. Bondi type accretion flow in SADS background renders multiplicity in its transonic behavior with inner "saddle" type and outer "center" type sonic points, with the transonic solutions forming closed loops or contours. There is always a limiting value for ∣Λ∣ up to which we obtain valid stationary transonic solutions, which correspond to both SDS and SADS geometries; this limiting value moderately increases with the increasing radiative efficiency of the flow, especially correspond to Bondi type accretion flow in SADS background. Repulsive Λ suppresses the Bondi accretion rate by an order of magnitude for relativistic Bondi type accretion flow for a certain range in temperature, and with a marginal increase in the Bondi accretion rate if the corresponding accretion flow occurs in SADS background. However, for a strongly radiative Bondi type accretion flow with high mass accretion rate, the presence of cosmological constant do not much influence the corresponding Bondi accretion rate of the flow. Our analysis show that the relic cosmological constant has a substantial effect on Bondi type accretion flow onto isolated SMBHs and their transonic solutions beyond length-scale of kiloparsecs, especially if the Bondi type accretion occurs onto the host supergiant ellipticals or central
Muronga, A
2007-01-01
Relativistic non-ideal fluid dynamics is formulated in 3+1 space--time dimensions. The equations governing dissipative relativistic hydrodynamics are given in terms of the time and the 3-space quantities which correspond to those familiar from non-relativistic physics. Dissipation is accounted for by applying the causal theory of relativistic dissipative fluid dynamics. As a special case we consider a fluid without viscous/heat couplings in the causal system of transport/relaxation equations. For the study of physical systems we consider pure (1+1)-dimensional expansion in planar geometry, (1+1)-dimensional spherically symmetric ({\\em fireball}) expansion, (1+1)-dimensional cylindrically symmetric expansion and a (2+1)-dimensional expansion with cylindrical symmetry in the transverse plane ({\\em firebarell} expansion). The transport/relaxation equations are given in terms of the spatial components of the dissipative fluxes, since these are not independent. The choice for the independent components is analogou...
Scattering in Relativistic Particle Mechanics.
de Bievre, Stephan
The problem of direct interaction in relativistic particle mechanics has been extensively studied and a variety of models has been proposed avoiding the conclusions of the so-called no-interaction theorems. In this thesis we study scattering in the relativistic two-body problem. We use our results to analyse gauge invariance in Hamiltonian constraint models and the uniqueness of the symplectic structure in manifestly covariant relativistic particle mechanics. We first present a general geometric framework that underlies approaches to relativistic particle mechanics. This permits a model-independent and geometric definition of the notions of asymptotic completeness and of Moller and scattering operators. Subsequent analysis of these concepts divides into two parts. First, we study the kinematic properties of the scattering transformation, i.e. those properties that arise solely from the invariance of the theory under the Poincare group. We classify all canonical (symplectic) scattering transformations on the relativistic phase space for two free particles in terms of a single function of the two invariants of the theory. We show how this function is determined by the center of mass time delay and scattering angle and vice versa. The second part of our analysis of the relativistic two-body scattering problem is devoted to the dynamical properties of the scattering process. Hence, we turn to two approaches to relativistic particle mechanics: the Hamiltonian constraint models and the manifestly covariant formalism. Using general geometric arguments, we prove "gauge invariance" of the scattering transformation in the Todorov -Komar Hamiltonian constraint model. We conclude that the scattering cross sections of the Todorov-Komar models have the same angular dependence as their non-relativistic counterpart, irrespective of a choice of gauge. This limits the physical relevance of those models. We present a physically non -trivial Hamiltonian constraint model, starting from
The internal structure of magnetized relativistic jets
Martí, José M; Gómez, José L
2016-01-01
This work presents the first characterization of the internal structure of overpressured steady superfast magnetosonic relativistic jets in connection with their dominant type of energy. To this aim, relativistic magnetohydrodynamic simulations of different jet models threaded by a helical magnetic field have been analyzed covering a wide region in the magnetosonic Mach number - specific internal energy plane. The merit of this plane is that models dominated by different types of energy (internal energy: hot jets; rest-mass energy: kinetically dominated jets; magnetic energy: Poynting-flux dominated jets) occupy well separated regions. The analyzed models also cover a wide range of magnetizations. Models dominated by the internal energy (i.e., hot models, or Poynting-flux dominated jets with magnetizations larger than but close to 1) have a rich internal structure characterized by a series of recollimation shocks and present the largest variations in the flow Lorentz factor (and internal energy density). Conv...
Psaltis, Dimitrios; Chan, Chi-Kwan; Marrone, Daniel P
2014-01-01
(Abridged) In General Relativity, the shadow cast by a black hole has a size that depends very weakly on its spin or the orientation of the observer. The half opening angle of the shadow is always equal to 5+-0.2 GM/Dc^2, where M is the mass of the black hole and D is its distance from the Earth. Therefore, measuring the size of the shadow of a black hole of known mass-to-distance ratio and verifying whether it is within the 4% predicted range constitutes a null hypothesis test of GR. We show that Sgr A* is the optimal target for performing this test with the Event Horizon Telescope. We use the results of monitoring of stellar orbits to show that the ratio M/D for Sgr A* is already known to an accuracy of ~6%. We investigate our prior knowledge of the scattering screen towards Sgr A, the effects of which will need to be corrected for in order for the black-hole shadow to appear sharp against the background emission. We argue that, even though the properties of the scattering ellipse at longer wavelengths are ...
Shear instabilities in shallow-water magnetohydrodynamics
Mak, Julian; Hughes, D W
2016-01-01
Within the framework of shallow-water magnetohydrodynamics, we investigate the linear instability of horizontal shear flows, influenced by an aligned magnetic field and stratification. Various classical instability results, such as H{\\o}iland's growth rate bound and Howard's semi-circle theorem, are extended to this shallow-water system for quite general profiles. Two specific piecewise-constant velocity profiles, the vortex sheet and the rectangular jet, are studied analytically and asymptotically; it is found that the magnetic field and stratification (as measured by the Froude number) are generally both stabilising, but weak instabilities can be found at arbitrarily large Froude number. Numerical solutions are computed for corresponding smooth velocity profiles, the hyperbolic-tangent shear layer and the Bickley jet, for a uniform background field. A generalisation of the long-wave asymptotic analysis of Drazin & Howard (1962) is employed in order to understand the instability characteristics for both ...
Extended inertial range phenomenology of magnetohydrodynamic turbulence
Matthaeus, William H.; Zhou, YE
1989-01-01
A phenomenological treatment of the inertial range of isotropic statistically steady magnetohydrodynamic turbulence is presented, extending the theory of Kraichnan (1965). The role of Alfven wave propagation is treated on equal footing with nonlinear convection, leading to a simple generalization of the relations between the times characteristic of wave propagation, convection, energy transfer, and decay of triple correlations. The theory leads to a closed-form steady inertial range spectral law that reduces to the Kraichnan and Kolmogorov laws in appropriate limits. The Kraichnan constant is found to be related in a simple way to the Kolmogorov constant; for typical values of the latter constant, the former has values in the range 1.22-1.87. Estimates of the time scale associated with spectral transfer of energy also emerge from the new approach, generalizing previously presented 'golden rules' for relating the spectral transfer time scale to the Alfven and eddy-turnover time scales.
Leardini, Fabrice
2013-01-01
This manuscript presents a problem on special relativity theory (SRT) which embodies an apparent paradox relying on the concept of simultaneity. The problem is represented in the framework of Greek epic poetry and structured in a didactic way. Owing to the characteristic properties of Lorenz transformations, three events which are simultaneous in a given inertial reference system, occur at different times in the other two reference frames. In contrast to the famous twin paradox, in the present case there are three, not two, different inertial observers. This feature provides a better framework to expose some of the main characteristics of SRT, in particular, the concept of velocity and the relativistic rule of addition of velocities.
Geometric Models of the Relativistic Harmonic Oscillator
Cotaescu, I I
1997-01-01
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.
Special Relativistic Hydrodynamics with Gravitation
Hwang, Jai-chan; Noh, Hyerim
2016-12-01
Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.
Special relativistic hydrodynamics with gravitation
Hwang, Jai-chan
2016-01-01
The special relativistic hydrodynamics with weak gravity is hitherto unknown in the literature. Whether such an asymmetric combination is possible was unclear. Here, the hydrodynamic equations with Poisson-type gravity considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit are consistently derived from Einstein's general relativity. Analysis is made in the maximal slicing where the Poisson's equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the {\\it general} hypersurface condition. Our formulation includes the anisotropic stress.
Physico-mathematical foundations of relativistic cosmology
Soares, Domingos
2013-01-01
I briefly present the foundations of relativistic cosmology, which are, General Relativity Theory and the Cosmological Principle. I discuss some relativistic models, namely, "Einstein static universe" and "Friedmann universes". The classical bibliographic references for the relevant tensorial demonstrations are indicated whenever necessary, although the calculations themselves are not shown.
BOOK REVIEW: Nonlinear Magnetohydrodynamics
Shafranov, V.
1998-08-01
Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas. The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are the plasma magnetic confinement systems for nuclear fusion and space plasmas, mainly the solar plasma. A significant number of the examples of the dynamic processes considered are taken from laboratory plasmas, for which an experimental check of the theory is possible. Therefore, though the book is intended for researchers and students interested in both laboratory, including nuclear fusion, and astrophysical plasmas, it is most probably closer to the first category of reader. In the Introduction the author notes that unlike the hydrodynamics of non-conducting fluids, where the phenomena caused by rapid fluid motions are the most interesting, for plasmas in a strong magnetic field the quasi-static configurations inside which the local dynamic processes occur are often the most important. Therefore, the reader will also find in this book rather traditional material on the theory of plasma equilibrium and stability in magnetic fields. In addition, it is notable that, as opposed to a linear theory, the non-linear theory, as a rule, cannot give quite definite explanations or predictions of phenomena, and consequently there are in the book many results obtained by consideration of numerical models with the use of supercomputers. The treatment of non-linear dynamics is preceded by Chapters 2 to 4, in which the basics of MHD theory are presented with an emphasis on the role of integral invariants of the magnetic helicity type, a derivation of the reduced MHD equations is given, together with examples of the exact solutions of the equilibrium
Variational Integrators for Reduced Magnetohydrodynamics
Kraus, Michael; Grasso, Daniela
2015-01-01
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws are described both at the continuous and discrete level. We verify...
CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD
Anninos, Peter; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Lau, Cheuk; Nemergut, Daniel
2017-08-01
We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge-Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.
Acceleration of positrons by a relativistic electron beam in the presence of quantum effects
Energy Technology Data Exchange (ETDEWEB)
Niknam, A. R. [Laser and Plasma Research Institute, Shahid Beheshti University, G.C., Tehran (Iran, Islamic Republic of); Aki, H.; Khorashadizadeh, S. M. [Physics Department, Birjand University, Birjand (Iran, Islamic Republic of)
2013-09-15
Using the quantum magnetohydrodynamic model and obtaining the dispersion relation of the Cherenkov and cyclotron waves, the acceleration of positrons by a relativistic electron beam is investigated. The Cherenkov and cyclotron acceleration mechanisms of positrons are compared together. It is shown that growth rate and, therefore, the acceleration of positrons can be increased in the presence of quantum effects.
Shukla, Chandrasekhar; Patel, Kartik
2016-01-01
We carry out Particle-in-Cell (PIC) simulations to study the instabilities associated with a 2-D sheared electron flow configuration against a neutralizing background of ions. Both weak and strong relativistic flow velocities are considered. In the weakly relativistic case, we observe the development of electromagnetic Kelvin Helmholtz instability with similar characteristics as that predicted by the electron Magnetohydrodynamic (EMHD) model. On other hand, in strong relativistic case the compressibility effects of electron fluid dominate and introduce upper hybrid electrostatic oscillations transverse to the flow which are very distinct from EMHD fluid behaviour. In the nonlinear regime, both weak and strong relativistic cases lead to turbulence with broad power law spectrum.
Magnetohydrodynamics simulations on graphics processing units
Wong, Hon-Cheng; Feng, Xueshang; Tang, Zesheng
2009-01-01
Magnetohydrodynamics (MHD) simulations based on the ideal MHD equations have become a powerful tool for modeling phenomena in a wide range of applications including laboratory, astrophysical, and space plasmas. In general, high-resolution methods for solving the ideal MHD equations are computationally expensive and Beowulf clusters or even supercomputers are often used to run the codes that implemented these methods. With the advent of the Compute Unified Device Architecture (CUDA), modern graphics processing units (GPUs) provide an alternative approach to parallel computing for scientific simulations. In this paper we present, to the authors' knowledge, the first implementation to accelerate computation of MHD simulations on GPUs. Numerical tests have been performed to validate the correctness of our GPU MHD code. Performance measurements show that our GPU-based implementation achieves speedups of 2 (1D problem with 2048 grids), 106 (2D problem with 1024^2 grids), and 43 (3D problem with 128^3 grids), respec...
Relativistic recursion relations for transition matrix elements
Martínez y Romero, R P; Salas-Brito, A L
2004-01-01
We review some recent results on recursion relations which help evaluating arbitrary non-diagonal, radial hydrogenic matrix elements of $r^\\lambda$ and of $\\beta r^\\lambda$ ($\\beta$ a Dirac matrix) derived in the context of Dirac relativistic quantum mechanics. Similar recursion relations were derived some years ago by Blanchard in the non relativistic limit. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\\"odinger case. An extension of the relations to the case of two potentials in the so-called unshifted case, but using an arbitrary radial function instead of a power one, is also given. Several important results are obtained as special instances of our recurrence relations, such as a generalization to the relativistic case of the Pasternack-Sternheimer rule. Our results are useful in any atomic or molecular calculation which take into account relativistic corrections.
Jiang, Song; Li, Fucai
2011-01-01
We study the incompressible limit of the compressible non-isentropic magnetohydrodynamic equations with zero magnetic diffusivity and general initial data in the whole space $\\mathbb{R}^d$ $(d=2,3)$. We first establish the existence of classic solutions on a time interval independent of the Mach number. Then, by deriving uniform a priori estimates, we obtain the convergence of the solution to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero.
Magnetohydrodynamic stability of tokamaks
Zohm, Hartmut
2014-01-01
This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong lin
Bar-mode instability suppression in magnetized relativistic stars
Franci, Luca; Dionysopoulou, Kyriaki; Rezzolla, Luciano
2013-01-01
We show that magnetic fields stronger than about $10^{15}$ G are able to suppress the development of the hydrodynamical bar-mode instability in relativistic stars. The suppression is due to a change in the rest-mass density and angular velocity profiles due to the formation and to the linear growth of a toroidal component that rapidly overcomes the original poloidal one, leading to an amplification of the total magnetic energy. The study is carried out performing three-dimensional ideal-magnetohydrodynamics simulations in full general relativity, superimposing to the initial (matter) equilibrium configurations a purely poloidal magnetic field in the range $10^{14}-10^{16}$ G. When the seed field is a few parts in $10^{15}$ G or above, all the evolved models show the formation of a low-density envelope surrounding the star. For much weaker fields, no effect on the matter evolution is observed, while magnetic fields which are just below the suppression threshold are observed to slow down the growth-rate of the ...
The Formation of Relativistic Jets from Kerr Black Holes
Nishikawa, K.-I.; Richardson, G.; Preece, R.; Hardee, P.; Koide, S.; Shibata, K.; Kudoh, T.; Sol, H.; Fishman, G. J.
2003-01-01
We have performed the first fully three-dimensional general relativistic magnetohydrodynamics (GRMHD) simulation for Schwarzschild and Kerr black holes with a free falling corona and thin accretion disk. The initial simulation results with a Schwarzschild metric show that a jet is created as in the previous axisymmetric simulations with mirror symmetry at the equator. However, the time to form the jet is slightly longer than in the 2-D axisymmetric simulation. We expect that the dynamics of jet formation are modified due to the additional freedom in the azimuth dimension without axisymmetry with respect to the Z axis and reflection symmetry respect to the equatorial plane. The jet which is initially formed due to the twisted magnetic fields and shocks becomes a wind at the later time. The wind flows out with a much wider angle than the initial jet. The twisted magnetic fields at the earlier time were untwisted and less pinched. The accretion disk became thicker than the initial condition. Further simulations with initial perturbations will provide insights for accretion dynamics with instabilities such as magneto-rotational instability (MRI) and accretion-eject instability (AEI). These instabilities may contribute to variabilities observed in microquasars and AGN jets.
Frontiers in relativistic celestial mechanics
2014-01-01
Relativistic celestial mechanics – investigating the motion celestial bodies under the influence of general relativity – is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics – starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area.
Empirical Foundations of Relativistic Gravity
Ni, W T
2005-01-01
In 1859, Le Verrier discovered the mercury perihelion advance anomaly. This anomaly turned out to be the first relativistic-gravity effect observed. During the 141 years to 2000, the precisions of laboratory and space experiments, and astrophysical and cosmological observations on relativistic gravity have been improved by 3 orders of magnitude. In 1999, we envisaged a 3-6 order improvement in the next 30 years in all directions of tests of relativistic gravity. In 2000, the interferometric gravitational wave detectors began their runs to accumulate data. In 2003, the measurement of relativistic Shapiro time-delay of the Cassini spacecraft determined the relativistic-gravity parameter gammaγ with a 1.5-order improvement. In October 2004, Ciufolini and Pavlis reported a measurement of the Lense-Thirring effect on the LAGEOS and LAGEOS2 satellites to 10 percent of the value predicted by general relativity. In April 2004, Gravity Probe B was launched and has been accumulating science data for more than ...
Relativistic causality and clockless circuits
Matherat, Philippe; 10.1145/2043643.2043650
2011-01-01
Time plays a crucial role in the performance of computing systems. The accurate modelling of logical devices, and of their physical implementations, requires an appropriate representation of time and of all properties that depend on this notion. The need for a proper model, particularly acute in the design of clockless delay-insensitive (DI) circuits, leads one to reconsider the classical descriptions of time and of the resulting order and causal relations satisfied by logical operations. This questioning meets the criticisms of classical spacetime formulated by Einstein when founding relativity theory and is answered by relativistic conceptions of time and causality. Applying this approach to clockless circuits and considering the trace formalism, we rewrite Udding's rules which characterize communications between DI components. We exhibit their intrinsic relation with relativistic causality. For that purpose, we introduce relativistic generalizations of traces, called R-traces, which provide a pertinent des...
Whittaker Order Reduction Method of Relativistic Birkhoffian Systems
Institute of Scientific and Technical Information of China (English)
LUOShao-Kai; HUANGFei-Jiang; LUYi-Bing
2004-01-01
The order reduction method of the relativistic Birkhollian equations is studied. For a relativistic autonomous Birkhotffian system, if the conservative law of the Birkhotffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the relativisticBirkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least twodegrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics and the relativistic Lagrangian mechanics are discussed, and the Whittaker order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of theresult.
Whittaker Order Reduction Method of Relativistic Birkhoffian Systems
Institute of Scientific and Technical Information of China (English)
LUO Shao-Kai; HUANG Fei-Jiang; LU Yi-Bing
2004-01-01
The order reduction method of the relativistic Birkhoffian equations is studied. For a relativistic autonomous Birkhoffian system, if the conservative law of the Birkhoffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the relativistic Birkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics and the relativistic Lagrangian mechanics are discussed, and the Whittaker order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of the result.
Sądowski, Aleksander; Wielgus, Maciek; Narayan, Ramesh; Abarca, David; McKinney, Jonathan C.; Chael, Andrew
2017-04-01
We present a numerical method that evolves a two-temperature, magnetized, radiative, accretion flow around a black hole, within the framework of general relativistic radiation magnetohydrodynamics. As implemented in the code KORAL, the gas consists of two sub-components - ions and electrons - which share the same dynamics but experience independent, relativistically consistent, thermodynamical evolution. The electrons and ions are heated independently according to a prescription from the literature for magnetohydrodynamical turbulent dissipation. Energy exchange between the particle species via Coulomb collisions is included. In addition, electrons gain and lose energy and momentum by absorbing and emitting synchrotron and bremsstrahlung radiation and through Compton scattering. All evolution equations are handled within a fully covariant framework in the relativistic fixed-metric space-time of the black hole. Numerical results are presented for five models of low-luminosity black hole accretion. In the case of a model with a mass accretion rate dot{M}˜ 4× 10^{-8} dot{M}_Edd, we find that radiation has a negligible effect on either the dynamics or the thermodynamics of the accreting gas. In contrast, a model with a larger dot{M}˜ 4× 10^{-4} dot{M}_Edd behaves very differently. The accreting gas is much cooler and the flow is geometrically less thick, though it is not quite a thin accretion disc.
Data assimilation for magnetohydrodynamics systems
Mendoza, O. Barrero; de Moor, B.; Bernstein, D. S.
2006-05-01
Prediction of solar storms has become a very important issue due to the fact that they can affect dramatically the telecommunication and electrical power systems at the earth. As a result, a lot of research is being done in this direction, space weather forecast. Magnetohydrodynamics systems are being studied in order to analyse the space plasma dynamics, and techniques which have been broadly used in the prediction of earth environmental variables like the Kalman filter (KF), the ensemble Kalman filter (EnKF), the extended Kalman filter (EKF), etc., are being studied and adapted to this new framework. The assimilation of a wide range of space environment data into first-principles-based global numerical models will improve our understanding of the physics of the geospace environment and the forecasting of its behaviour. Therefore, the aim of this paper is to study the performance of nonlinear observers in magnetohydrodynamics systems, namely, the EnKF.The EnKF is based on a Monte Carlo simulation approach for propagation of process and measurement errors. In this paper, the EnKF for a nonlinear two-dimensional magnetohydrodynamic (2D-MHD) system is considered. For its implementation, two software packages are merged, namely, the Versatile Advection Code (VAC) written in Fortran and Matlab of Mathworks. The 2D-MHD is simulated with the VAC code while the EnKF is computed in Matlab. In order to study the performance of the EnKF in MHD systems, different number of measurement points as well as ensemble members are set.
Current-sheet formation in incompressible electron magnetohydrodynamics.
Ruban, V P
2002-04-01
The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local and nonlocal nonlinear approximations are introduced and partially analyzed that are generalizations of the previously known exactly solvable local model neglecting electron inertia.
Relativistic quantum information
Mann, R. B.; Ralph, T. C.
2012-11-01
Over the past few years, a new field of high research intensity has emerged that blends together concepts from gravitational physics and quantum computing. Known as relativistic quantum information, or RQI, the field aims to understand the relationship between special and general relativity and quantum information. Since the original discoveries of Hawking radiation and the Unruh effect, it has been known that incorporating the concepts of quantum theory into relativistic settings can produce new and surprising effects. However it is only in recent years that it has become appreciated that the basic concepts involved in quantum information science undergo significant revision in relativistic settings, and that new phenomena arise when quantum entanglement is combined with relativity. A number of examples illustrate that point. Quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement is an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Entanglement can also be extracted from the vacuum of relativistic quantum field theories, and used to distinguish peculiar motion from cosmological expansion. The new quantum information-theoretic framework of quantum channels in terms of completely positive maps and operator algebras now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes. This focus issue provides a sample of the state of the art in research in RQI. Some of the articles in this issue review the subject while others provide interesting new results that will stimulate further research. What makes the subject all the more exciting is that it is beginning to enter the stage at which actual experiments can be contemplated, and some of the articles appearing in this issue discuss some of these exciting new developments. The subject of RQI pulls together concepts and ideas from
Plasma Relaxation in Hall Magnetohydrodynamics
Shivamoggi, B K
2011-01-01
Parker's formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient alpha in the Hall MHD Beltrami condition turns out now to be proportional to the "potential vorticity." The Hall MHD Beltrami condition becomes equivalent to the "potential vorticity" conservation equation in two-dimensional hydrodynamics if the Hall MHD Lagrange multiplier beta is taken to be proportional to the "potential vorticity" as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as "potential vorticity" lines in 2D hydrodynamics.
Fundamental fluid mechanics and magnetohydrodynamics
Hosking, Roger J
2016-01-01
This book is primarily intended to enable postgraduate research students to enhance their understanding and expertise in Fluid Mechanics and Magnetohydrodynamics (MHD), subjects no longer treated in isolation. The exercises throughout the book often serve to provide additional and quite significant knowledge or to develop selected mathematical skills, and may also fill in certain details or enhance readers’ understanding of essential concepts. A previous background or some preliminary reading in either of the two core subjects would be advantageous, and prior knowledge of multivariate calculus and differential equations is expected.
Magnetohydrodynamic mechanism for pedestal formation.
Guazzotto, L; Betti, R
2011-09-16
Time-dependent two-dimensional magnetohydrodynamic simulations are carried out for tokamak plasmas with edge poloidal flow. Differently from conventional equilibrium theory, a density pedestal all around the edge is obtained when the poloidal velocity exceeds the poloidal sound speed. The outboard pedestal is induced by the transonic discontinuity, the inboard one by mass redistribution. The density pedestal follows the formation of a highly sheared flow at the transonic surface. These results may be relevant to the L-H transition and pedestal formation in high performance tokamak plasmas.
Parametric resonance in ideal magnetohydrodynamics
Zaqarashvili
2000-08-01
We show that an external nonelectromagnetic periodic inhomogeneous force sets up a parametric resonance in an ideal magnetohydrodynamics. Alfven waves with certain wavelengths grow exponentially in amplitude. Nonlinear interaction between the resonant harmonics produces the long-term modulation of amplitudes. The mechanism of the energy transformation from an external nonelectromagnetic force to magnetic oscillations of the system presented here can be used in understanding the physical background of the gravitational action on the magnetized medium. Future application of this theory to several astrophysical problems is briefly discussed.
Synchrotron radiation of self-collimating relativistic MHD jets
Porth, Oliver; Meliani, Zakaria; Vaidya, Bhargav
2011-01-01
The goal of this paper is to derive signatures of synchrotron radiation from state-of-the-art simulation models of collimating relativistic magnetohydrodynamic (MHD) jets featuring a large-scale helical magnetic field. We perform axisymmetric special relativistic MHD simulations of the jet acceleration region using the PLUTO code. The computational domain extends from the slow magnetosonic launching surface of the disk up to 6000^2 Schwarzschild radii allowing to reach highly relativistic Lorentz factors. The Poynting dominated disk wind develops into a jet with Lorentz factors of 8 and is collimated to 1 degree. In addition to the disk jet, we evolve a thermally driven spine jet, emanating from a hypothetical black hole corona. Solving the linearly polarized synchrotron radiation transport within the jet, we derive VLBI radio and (sub-) mm diagnostics such as core shift, polarization structure, intensity maps, spectra and Faraday rotation measure (RM), directly from the Stokes parameters. We also investigate...
The First Principle Formula of the Relativistic Heat Conductivity of Coulomb Electronic Plasmas
Institute of Scientific and Technical Information of China (English)
TIAN Chu-Shun; ZHANG Chi; LU Quan-Kang
2001-01-01
Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is obtained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrodynamic wave number.Combining Résibois' method,we present the first principle formula of the relativistic heat conductivity of Coulomb electronic plasmas for low-order corrections.
On the relativistic mass function and averaging in cosmology
Ostrowski, Jan J; Roukema, Boudewijn F
2016-01-01
The general relativistic description of cosmological structure formation is an important challenge from both the theoretical and the numerical point of views. In this paper we present a brief prescription for a general relativistic treatment of structure formation and a resulting mass function on galaxy cluster scales in a highly generic scenario. To obtain this we use an exact scalar averaging scheme together with the relativistic generalization of Zel'dovich's approximation (RZA) that serves as a closure condition for the averaged equations.
Multicomponent diffusion in two-temperature magnetohydrodynamics
Ramshaw, J. D.; Chang, C. H.
1996-06-01
A recent hydrodynamic theory of multicomponent diffusion in multitemperature gas mixtures [J. D. Ramshaw, J. Non-Equilib. Thermodyn. 18, 121 (1993)] is generalized to include the velocity-dependent Lorentz force on charged species in a magnetic field B. This generalization is used to extend a previous treatment of ambipolar diffusion in two-temperature multicomponent plasmas [J. D. Ramshaw and C. H. Chang, Plasma Chem. Plasma Process. 13, 489 (1993)] to situations in which B and the electrical current density are nonzero. General expressions are thereby derived for the species diffusion fluxes, including thermal diffusion, in both single- and two-temperature multicomponent magnetohydrodynamics (MHD). It is shown that the usual zero-field form of the Stefan-Maxwell equations can be preserved in the presence of B by introducing generalized binary diffusion tensors dependent on B. A self-consistent effective binary diffusion approximation is presented that provides explicit approximate expressions for the diffusion fluxes. Simplifications due to the small electron mass are exploited to obtain an ideal MHD description in which the electron diffusion coefficients drop out, resistive effects vanish, and the electric field reduces to a particularly simple form. This description should be well suited for numerical calculations.
Chaos and Maps in Relativistic Dynamical Systems
Horwitz, L P
1999-01-01
The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistic charged particle in interaction with the electromagnetic field. We review the structure of the covariant Lorentz force used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field, establishing a connection between these equations and mass shell constraints. We argue that these relativistic generalizations of the problem are intrinsically inaccurate due to an inconsistency in the structure of the relativistic Lorentz force, and show that a reformulation of the relativistic problem, permitting variations (classically) in both the particle mass and the effective...
Variational integrators for reduced magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Kraus, Michael, E-mail: michael.kraus@ipp.mpg.de [Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, 85748 Garching (Germany); Technische Universität München, Zentrum Mathematik, Boltzmannstraße 3, 85748 Garching (Germany); Tassi, Emanuele, E-mail: tassi@cpt.univ-mrs.fr [Aix-Marseille Université, Université de Toulon, CNRS, CPT, UMR 7332, 163 avenue de Luminy, case 907, 13288 cedex 9 Marseille (France); Grasso, Daniela, E-mail: daniela.grasso@infm.polito.it [ISC-CNR and Politecnico di Torino, Dipartimento Energia, C.so Duca degli Abruzzi 24, 10129 Torino (Italy)
2016-09-15
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws is described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.
Variational integrators for reduced magnetohydrodynamics
Kraus, Michael; Tassi, Emanuele; Grasso, Daniela
2016-09-01
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws is described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.
Relativistic Gravothermal Instabilities
Roupas, Zacharias
2014-01-01
The thermodynamic instabilities of the self-gravitating, classical ideal gas are studied in the case of static, spherically symmetric configurations in General Relativity taking into account the Tolman-Ehrenfest effect. One type of instabilities is found at low energies, where thermal energy becomes too weak to halt gravity and another at high energies, where gravitational attraction of thermal pressure overcomes its stabilizing effect. These turning points of stability are found to depend on the total rest mass $\\mathcal{M}$ over the radius $R$. The low energy instability is the relativistic generalization of Antonov instability, which is recovered in the limit $G\\mathcal{M} \\ll R c^2$ and low temperatures, while in the same limit and high temperatures, the high energy instability recovers the instability of the radiation equation of state. In the temperature versus energy diagram of series of equilibria, the two types of gravothermal instabilities make themselves evident as a double spiral! The two energy l...
Mueller, Bernhard; Marek, Andreas
2012-01-01
We present a detailed theoretical analysis of the gravitational-wave (GW) signal of the post-bounce evolution of core-collapse supernovae (SNe), employing for the first time relativistic, two-dimensional (2D) explosion models with multi-group, three-flavor neutrino transport based on the ray-by-ray-plus approximation. The waveforms reflect the accelerated mass motions associated with the characteristic evolutionary stages that were also identified in previous works: A quasi-periodic modulation by prompt postshock convection is followed by a phase of relative quiescence before growing amplitudes signal violent hydrodynamical activity due to convection and the standing accretion shock instability during the accretion period of the stalled shock. Finally, a high-frequency, low-amplitude variation from proto-neutron star (PNS) convection below the neutrinosphere appears superimposed on the low-frequency trend associated with the aspherical expansion of the SN shock after the onset of the explosion. Relativistic e...
Relativistic radiative transfer in relativistic spherical flows
Fukue, Jun
2017-02-01
Relativistic radiative transfer in relativistic spherical flows is numerically examined under the fully special relativistic treatment. We first derive relativistic formal solutions for the relativistic radiative transfer equation in relativistic spherical flows. We then iteratively solve the relativistic radiative transfer equation, using an impact parameter method/tangent ray method, and obtain specific intensities in the inertial and comoving frames, as well as moment quantities, and the Eddington factor. We consider several cases; a scattering wind with a luminous central core, an isothermal wind without a core, a scattering accretion on to a luminous core, and an adiabatic accretion on to a dark core. In the typical wind case with a luminous core, the emergent intensity is enhanced at the center due to the Doppler boost, while it reduces at the outskirts due to the transverse Doppler effect. In contrast to the plane-parallel case, the behavior of the Eddington factor is rather complicated in each case, since the Eddington factor depends on the optical depth, the flow velocity, and other parameters.
Magnetohydrodynamic Turbulence and the Geodynamo
Shebalin, John V.
2016-01-01
Recent research results concerning forced, dissipative, rotating magnetohydrodynamic (MHD) turbulence will be discussed. In particular, we present new results from long-time Fourier method (periodic box) simulations in which forcing contains varying amounts of magnetic and kinetic helicity. Numerical results indicate that if MHD turbulence is forced so as to produce a state of relatively constant energy, then the largest-scale components are dominant and quasistationary, and in fact, have an effective dipole moment vector that aligns closely with the rotation axis. The relationship of this work to established results in ideal MHD turbulence, as well as to models of MHD turbulence in a spherical shell will also be presented. These results appear to be very pertinent to understanding the Geodynamo and the origin of its dominant dipole component. Our conclusion is that MHD turbulence, per se, may well contain the origin of the Earth's dipole magnetic field.
Vortex disruption by magnetohydrodynamic feedback
Mak, Julian; Hughes, D W
2016-01-01
In an electrically conducting fluid, vortices stretch out a weak, large-scale magnetic field to form strong current sheets on their edges. Associated with these current sheets are magnetic stresses, which are subsequently released through reconnection, leading to vortex disruption, and possibly even destruction. This disruption phenomenon is investigated here in the context of two-dimensional, homogeneous, incompressible magnetohydrodynamics. We derive a simple order of magnitude estimate for the magnetic stresses --- and thus the degree of disruption --- that depends on the strength of the background magnetic field (measured by the parameter $M$, a ratio between the Alfv\\'en speed and a typical flow speed) and on the magnetic diffusivity (measured by the magnetic Reynolds number $\\mbox{Rm}$). The resulting estimate suggests that significant disruption occurs when $M^{2}\\mbox{Rm} = O(1)$. To test our prediction, we analyse direct numerical simulations of vortices generated by the breakup of unstable shear flo...
Shell Models of Magnetohydrodynamic Turbulence
Plunian, Franck; Frick, Peter
2012-01-01
Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accu...
Method for manufacturing magnetohydrodynamic electrodes
Killpatrick, Don H.; Thresh, Henry R.
1982-01-01
A method of manufacturing electrodes for use in a magnetohydrodynamic (MHD) generator comprising the steps of preparing a billet having a core 10 of a first metal, a tubular sleeve 12 of a second metal, and an outer sheath 14, 16, 18 of an extrusile metal; evacuating the space between the parts of the assembled billet; extruding the billet; and removing the outer jacket 14. The extruded bar may be made into electrodes by cutting and bending to the shape required for an MDH channel frame. The method forms a bond between the first metal of the core 10 and the second metal of the sleeve 12 strong enough to withstand a hot and corrosive environment.
Scale locality of magnetohydrodynamic turbulence.
Aluie, Hussein; Eyink, Gregory L
2010-02-26
We investigate the scale locality of cascades of conserved invariants at high kinetic and magnetic Reynold's numbers in the "inertial-inductive range" of magnetohydrodynamic (MHD) turbulence, where velocity and magnetic field increments exhibit suitable power-law scaling. We prove that fluxes of total energy and cross helicity-or, equivalently, fluxes of Elsässer energies-are dominated by the contributions of local triads. Flux of magnetic helicity may be dominated by nonlocal triads. The magnetic stretching term may also be dominated by nonlocal triads, but we prove that it can convert energy only between velocity and magnetic modes at comparable scales. We explain the disagreement with numerical studies that have claimed conversion nonlocally between disparate scales. We present supporting data from a 1024{3} simulation of forced MHD turbulence.
Micromachined magnetohydrodynamic actuators and sensors
Lee, Abraham P.; Lemoff, Asuncion V.
2000-01-01
A magnetohydrodynamic (MHD) micropump and microsensor which utilizes micromachining to integrate the electrodes with microchannels and includes a magnet for producing magnetic fields perpendicular to both the electrical current direction and the fluid flow direction. The magnet can also be micromachined and integrated with the micropump using existing technology. The MHD micropump, for example, can generate continuous, reversible flow, with readily controllable flow rates. The flow can be reversed by either reversing the electrical current flow or reversing the magnetic field. By mismatching the electrodes, a swirling vortex flow can be generated for potential mixing applications. No moving parts are necessary and the dead volume is minimal. The micropumps can be placed at any position in a fluidic circuit and a combination of micropumps can generate fluidic plugs and valves.
Magnetohydrodynamic turbulence: Observation and experiment
Energy Technology Data Exchange (ETDEWEB)
Brown, M. R.; Schaffner, D. A.; Weck, P. J. [Department of Physics and Astronomy, Swarthmore College, 500 College Avenue, Swarthmore, Pennsylvania 19081 (United States)
2015-05-15
We provide a tutorial on the paradigms and tools of magnetohydrodynamic (MHD) turbulence. The principal paradigm is that of a turbulent cascade from large scales to small, resulting in power law behavior for the frequency power spectrum for magnetic fluctuations E{sub B}(f). We will describe five useful statistical tools for MHD turbulence in the time domain: the temporal autocorrelation function, the frequency power spectrum, the probability distribution function of temporal increments, the temporal structure function, and the permutation entropy. Each of these tools will be illustrated with an example taken from MHD fluctuations in the solar wind. A single dataset from the Wind satellite will be used to illustrate all five temporal statistical tools.
Holographic Aspects of a Relativistic Nonconformal Theory
Directory of Open Access Journals (Sweden)
Chanyong Park
2013-01-01
Full Text Available We study a general D-dimensional Schwarzschild-type black brane solution of the Einstein-dilaton theory and derive, by using the holographic renormalization, its thermodynamics consistent with the geometric results. Using the membrane paradigm, we calculate the several hydrodynamic transport coefficients and compare them with the results obtained by the Kubo formula, which shows the self-consistency of the gauge/gravity duality in the relativistic nonconformal theory. In order to understand more about the relativistic non-conformal theory, we further investigate the binding energy, drag force, and holographic entanglement entropy of the relativistic non-conformal theory.
Lock, Maximilian P E
2016-01-01
The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories. The results obtained with this clock model in flat spacetime are reviewed, and the problem of generalizing the model to curved spacetime is discussed, before briefly describing an experimental setup which could be used to test of the model. Taking an operationalist view, where time is that which is measured by a clock, we discuss the conclusions that can be drawn from these results, and what clues they contain for a full quantum relativistic theory of time.
Ruder, Hanns; Nollert, Hans-Peter; Hehl, Friedrich
1998-01-01
This book summarizes the lectures given at the 162. WE-Heraeus Seminar which took place in the house of the German Physical Society in Bad Honnefin August 1996. Already the number 162 shows the activity and effectiveness of the WE-Heraeus Foundation. We would like to express our thanks to Jutta Adam and Dr. Volker Schafer for the almost incredibly simple and unbureaucratical procedure of funding, organization and realization, and, of course, to the founders. Similar to the 152. WE-Heraeus Seminar Relativity and Scientific Computing (Springer Verlag 1996), this seminar was a joint venture of the Astronomical Society (AG) and of the Section 'Gravitation und Relativity Theory' of the German Physical Society (DPG). Since Einstein has developed his Theory of General Relativity more than 80 years ago, the situation has changed dramatically. In the first decades main efforts were untertaken for a better understanding and for the experimental verification of the theory. Mean while General Relativity (GR) is one of ...
Stably stratified magnetized stars in general relativity
Yoshida, Shijun; Shibata, Masaru
2012-01-01
We construct magnetized stars composed of a fluid stably stratified by entropy gradients in the framework of general relativity, assuming ideal magnetohydrodynamics and employing a barotropic equation of state. We first revisit basic equations for describing stably-stratified stationary axisymmetric stars containing both poloidal and toroidal magnetic fields. As sample models, the magnetized stars considered by Ioka and Sasaki (2004), inside which the magnetic fields are confined, are modified to the ones stably stratified. The magnetized stars newly constructed in this study are believed to be more stable than the existing relativistic models because they have both poloidal and toroidal magnetic fields with comparable strength, and magnetic buoyancy instabilities near the surface of the star, which can be stabilized by the stratification, are suppressed.
Stability of relativistic plasma-vacuum interfaces
Trakhinin, Yuri
2010-01-01
We study the plasma-vacuum interface problem in relativistic magnetohydrodynamics for the case when the plasma density does not go to zero continuously, but jumps. Unlike the nonrelativistic version of this problem, we have to assume that the plasma expands into the vacuum (otherwise, the problem is underdetermined). We show that even if this necessary condition is satisfied the planar interface can be still violently unstable. By using a suitable secondary symmetrization of the Maxwell equations in vacuum, we find a sufficient condition that precludes violent instabilities. Under this condition we derive a basic a priori estimate in the anisotropic weighted Sobolev space $H^1_*$ for the variable coefficients linearized problem for nonplanar plasma-vacuum interfaces and prove the well-posedness of this problem.
Al-Hashimi, M H; Shalaby, A M
2016-01-01
A general method has been developed to solve the Schr\\"odinger equation for an arbitrary derivative of the $\\delta$-function potential in 1-d using cutoff regularization. The work treats both the relativistic and nonrelativistic cases. A distinction in the treatment has been made between the case when the derivative $n$ is an even number from the one when $n$ is an odd number. A general gap equations for each case has been derived. The case of $\\delta^{(2)}$-function potential has been used as an example. The results from the relativistic case show that the $\\delta^{(2)}$-function system behaves exactly like the $\\delta$-function and the $\\delta'$-function potentials, which means it also shares the same features with quantum field theories, like being asymptotically free, in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. As a result the evidence of universality of contact interactions has been extended further to include the $\\delta^{(2)}$-functi...
New Developments in Relativistic Viscous Hydrodynamics
Romatschke, Paul
2009-01-01
Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized second law of thermodynamics, kinetic theory, and a complete second-order gradient expansion are reviewed. The resulting fluid dynamic equations are shown to be consistent for all these derivations, when properly accounting for the respective region of appl...
Relativistic quantum mechanics
Wachter, Armin
2010-01-01
Which problems do arise within relativistic enhancements of the Schrödinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way. The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the...
Institute of Scientific and Technical Information of China (English)
ZHANG Peng-Fei; RUAN Tu-Nan
2001-01-01
A systematic theory on the appropriate spin operators for the relativistic states is developed. For a massive relativistic particle with arbitrary nonzero spin, the spin operator should be replaced with the relativistic one, which is called in this paper as moving spin. Further the concept of moving spin is discussed in the quantum field theory. A new is constructed. It is shown that, in virtue of the two operators, problems in quantum field concerned spin can be neatly settled.
Relativistic Guiding Center Equations
Energy Technology Data Exchange (ETDEWEB)
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Relativistic Linear Restoring Force
Clark, D.; Franklin, J.; Mann, N.
2012-01-01
We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…
Multi-D magnetohydrodynamic modelling of pulsar wind nebulae: recent progress and open questions
Olmi, B.; Del Zanna, L.; Amato, E.; Bucciantini, N.; Mignone, A.
2016-12-01
In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of pulsar wind nebulae, and of the Crab nebula in particular, has been highly successful, with many of the observed dynamical and emission properties reproduced down to the finest detail. Here, we critically discuss the results of some of the most recent studies: namely the investigation of the origin of the radio emitting particles and the quest for the acceleration sites of particles of different energies along the termination shock, by using wisp motions as a diagnostic tool; the study of the magnetic dissipation process in high magnetization nebulae by means of new long-term three-dimensional simulations of the pulsar wind nebula evolution; the investigation of the relativistic tearing instability in thinning current sheets, leading to fast reconnection events that might be at the origin of the Crab nebula gamma-ray flares.
Multi-D magnetohydrodynamic modelling of pulsar wind nebulae: recent progress and open questions
Olmi, B; Amato, E; Bucciantini, N; Mignone, A
2016-01-01
In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of pulsar wind nebulae, and of the Crab nebula in particular, has been highly successful, with many of the observed dynamical and emission properties reproduced down to the finest detail. Here, we critically discuss the results of some of the most recent studies: namely the investigation of the origin of the radio emitting particles and the quest for the acceleration sites of particles of different energies along the termination shock, by using wisps motion as a diagnostic tool; the study of the magnetic dissipation process in high magnetization nebulae by means of new long-term three-dimensional simulations of the pulsar wind nebula evolution; the investigation of the relativistic tearing instability in thinning current sheets, leading to fast reconnection events that might be at the origin of the Crab nebula gamma-ray flares.
MALFLIET, R
1993-01-01
We discuss the present status of relativistic transport theory. Special emphasis is put on problems of topical interest: hadronic features, thermodynamical consistent approximations and spectral properties.
Magnetohydrodynamic waves in fusion and astrophysical plasmas.
Goedbloed, J. P.
Macroscopic plasma dynamics in both controlled thermonuclear confinement machines and in the atmospheres of X-ray emitting stars is described by the equations of magnetohydrodynamics. This provides a vast area of overlapping research activities which is presently actively pursued. In this lecture the author concentrates on some important differences in the dynamics of the two confined plasma systems related to the very different geometries that are encountered and, thus, the role of the different boundary conditions that have to be posed. As a result, the basic MHD waves in a tokamak are quite different from those found in a solar magnetic flux tube. The result is that, whereas the three well-known MHD waves can be traced stepwise in the curved geometry of a tokamak, their separate existence is eliminated right from the start in a line-tied coronal loop because line-tying in general conflicts with the phase relationships between the vector components of the three velocity fields. The consequences are far-reaching, viz. completely different resonant frequencies and continuous spectra, absence of rational magnetic surfaces, and irrelevance of local marginal stability theory for coronal magnetic loops.
Geometrical shock dynamics for magnetohydrodynamic fast shocks
Mostert, W.
2016-12-12
We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press
Relativistic Runaway Electrons
Breizman, Boris
2014-10-01
This talk covers recent developments in the theory of runaway electrons in a tokamak with an emphasis on highly relativistic electrons produced via the avalanche mechanism. The rapidly growing population of runaway electrons can quickly replace a large part of the initial current carried by the bulk plasma electrons. The magnetic energy associated with this current is typically much greater than the particle kinetic energy. The current of a highly relativistic runaway beam is insensitive to the particle energy, which separates the description of the runaway current evolution from the description of the runaway energy spectrum. A strongly anisotropic distribution of fast electrons is generally prone to high-frequency kinetic instabilities that may cause beneficial enhancement of runaway energy losses. The relevant instabilities are in the frequency range of whistler waves and electron plasma waves. The instability thresholds reported in earlier work have been revised considerably to reflect strong dependence of collisional damping on the wave frequency and the role of plasma non-uniformity, including radial trapping of the excited waves in the plasma. The talk also includes a discussion of enhanced scattering of the runaways as well as the combined effect of enhanced scattering and synchrotron radiation. A noteworthy feature of the avalanche-produced runaway current is a self-sustained regime of marginal criticality: the inductive electric field has to be close to its critical value (representing avalanche threshold) at every location where the runaway current density is finite, and the current density should vanish at any point where the electric field drops below its critical value. This nonlinear Ohm's law enables complete description of the evolving current profile. Work supported by the U.S. Department of Energy Contract No. DEFG02-04ER54742 and by ITER contract ITER-CT-12-4300000273. The views and opinions expressed herein do not necessarily reflect those of
Relativistic calculations of coalescing binary neutron stars
Indian Academy of Sciences (India)
Joshua Faber; Phillippe Grandclément; Frederic Rasio
2004-10-01
We have designed and tested a new relativistic Lagrangian hydrodynamics code, which treats gravity in the conformally flat approximation to general relativity. We have tested the resulting code extensively, finding that it performs well for calculations of equilibrium single-star models, collapsing relativistic dust clouds, and quasi-circular orbits of equilibrium solutions. By adding a radiation reaction treatment, we compute the full evolution of a coalescing binary neutron star system. We find that the amount of mass ejected from the system, much less than a per cent, is greatly reduced by the inclusion of relativistic gravitation. The gravity wave energy spectrum shows a clear divergence away from the Newtonian point-mass form, consistent with the form derived from relativistic quasi-equilibrium fluid sequences.
Relabeling symmetry in relativistic fluids and plasmas
Kawazura, Yohei; Fukumoto, Yasuhide
2014-01-01
The conservation of the recently formulated relativistic canonical helicity [Yoshida Z, Kawazura Y, and Yokoyama T 2014 J. Math. Phys. 55 043101] is derived from Noether's theorem by constructing an action principle on the relativistic Lagrangian coordinates (we obtain general cross helicities that include the helicity of the canonical vorticity). The conservation law is, then, explained by the relabeling symmetry pertinent to the Lagrangian label of fluid elements. Upon Eulerianizing the Noether current, the purely spatial volume integral on the Lagrangian coordinates is mapped to a space-time mixed three-dimensional integral on the four-dimensional Eulerian coordinates. The relativistic conservation law in the Eulerian coordinates is no longer represented by any divergence-free current; hence, it is not adequate to regard the relativistic helicity (represented by the Eulerian variables) as a Noether charge, and this stands the reason why the "conventional helicity" is no longer a constant of motion. We have...
Relativistic diffusion equation from stochastic quantization
Kazinski, P O
2007-01-01
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck constant). We apply this method to the models of nonrelativistic and relativistic particles interacting with an electromagnetic field. In the first case we establish the equivalence of such a quantization to the Fokker-Planck equation with a special force. The application of the proposed quantization procedure to the model of a relativistic particle results in a relativistic generalization of the Fokker-Planck equation in the coordinate space, which in the absence of the electromagnetic field reduces to the relativistic diffusion (heat) equation. The stationary probability distribution functions for a stochastically quantized particle diffusing under a barrier and a particle in the potential of a harmonic oscillator are derived.
Magnetohydrodynamics turbulence: An astronomical perspective
Indian Academy of Sciences (India)
S Sridhar
2011-07-01
Early work on magnetohydrodynamic (MHD) turbulence in the 1960s due, independently, to Iroshnikov and Kraichnan (IK) considered isotropic inertial-range spectra. Whereas laboratory experiments were not in a position to measure the spectral index, they showed that the turbulence was strongly anisotropic. Theoretical horizons correspondingly expanded in the 1980s, to accommodate both the isotropy of the IK theory and the anisotropy suggested by the experiments. Since the discovery of pulsars in 1967, many years of work on interstellar scintillation suggested that small-scale interstellar turbulence must have a hydromagnetic origin; but the IK spectrum was too ﬂat and the ideas on anisotropic spectra too qualitative to explain the observations. In response, new theories of balanced MHD turbulence were proposed in the 1990s, which argued that the IK theory was incorrect, and made quantitative predictions of anisotropic inertial-range spectra; these theories have since found applications in many areas of astrophysics. Spacecraft measurements of solar-wind turbulence show that there is more power in Alfvén waves that travel away from the Sun than towards it. Theories of imbalanced MHD turbulence have now been proposed to address interplanetary turbulence. This very active area of research continues to be driven by astronomy.
Magnetohydrodynamic (MHD) driven droplet mixer
Lee, Abraham P.; Lemoff, Asuncion V.; Miles, Robin R.
2004-05-11
A magnetohydrodynamic fluidic system mixes a first substance and a second substance. A first substrate section includes a first flow channel and a first plurality of pairs of spaced electrodes operatively connected to the first flow channel. A second substrate section includes a second flow channel and a second plurality of pairs of spaced electrodes operatively connected to the second flow channel. A third substrate section includes a third flow channel and a third plurality of pairs of spaced electrodes operatively connected to the third flow channel. A magnetic section and a control section are operatively connected to the spaced electrodes. The first substrate section, the second substrate section, the third substrate section, the first plurality of pairs of spaced electrodes, the second plurality of pairs of spaced electrodes, the third plurality of pairs of spaced electrodes, the magnetic section, and the control section are operated to move the first substance through the first flow channel, the second substance through the second flow channel, and both the first substance and the second substance into the third flow channel where they are mixed.
Magnetohydrodynamic Propulsion for the Classroom
Font, Gabriel I.; Dudley, Scott C.
2004-10-01
The cinema industry can sometimes prove to be an ally when searching for material with which to motivate students to learn physics. Consider, for example, the electromagnetic force on a current in the presence of a magnetic field. This phenomenon is at the heart of magnetohydrodynamic (MHD) propulsion systems. A submarine employing this type of propulsion was immortalized in the movie Hunt for Red October. While mentioning this to students certainly gets their attention, it often elicits comments that it is only fiction and not physically possible. Imagine their surprise when a working system is demonstrated! It is neither difficult nor expensive to construct a working system that can be demonstrated in the front of a classroom.2 In addition, all aspects of the engineering hurdles that must be surmounted and myths concerning this "silent propulsion" system are borne out in a simple apparatus. This paper details how to construct an inexpensive MHD propulsion boat that can be demonstrated for students in the classroom.
Magnetohydrodynamic Models of Molecular Tornadoes
Au, Kelvin; Fiege, Jason D.
2017-07-01
Recent observations near the Galactic Center (GC) have found several molecular filaments displaying striking helically wound morphology that are collectively known as molecular tornadoes. We investigate the equilibrium structure of these molecular tornadoes by formulating a magnetohydrodynamic model of a rotating, helically magnetized filament. A special analytical solution is derived where centrifugal forces balance exactly with toroidal magnetic stress. From the physics of torsional Alfvén waves we derive a constraint that links the toroidal flux-to-mass ratio and the pitch angle of the helical field to the rotation laws, which we find to be an important component in describing the molecular tornado structure. The models are compared to the Ostriker solution for isothermal, nonmagnetic, nonrotating filaments. We find that neither the analytic model nor the Alfvén wave model suffer from the unphysical density inversions noted by other authors. A Monte Carlo exploration of our parameter space is constrained by observational measurements of the Pigtail Molecular Cloud, the Double Helix Nebula, and the GC Molecular Tornado. Observable properties such as the velocity dispersion, filament radius, linear mass, and surface pressure can be used to derive three dimensionless constraints for our dimensionless models of these three objects. A virial analysis of these constrained models is studied for these three molecular tornadoes. We find that self-gravity is relatively unimportant, whereas magnetic fields and external pressure play a dominant role in the confinement and equilibrium radial structure of these objects.
Smoothed particle hydrodynamics and magnetohydrodynamics
Price, Daniel J.
2012-02-01
This paper presents an overview and introduction to smoothed particle hydrodynamics and magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, showing how the equations of motion and energy can be self-consistently derived from the density estimate. We then show how to interpret these equations using the basic SPH interpolation formulae and highlight the subtle difference in approach between SPH and other particle methods. In doing so, we also critique several 'urban myths' regarding SPH, in particular the idea that one can simply increase the 'neighbour number' more slowly than the total number of particles in order to obtain convergence. We also discuss the origin of numerical instabilities such as the pairing and tensile instabilities. Finally, we give practical advice on how to resolve three of the main issues with SPMHD: removing the tensile instability, formulating dissipative terms for MHD shocks and enforcing the divergence constraint on the particles, and we give the current status of developments in this area. Accompanying the paper is the first public release of the NDSPMHD SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD algorithms that can be used to test many of the ideas and used to run all of the numerical examples contained in the paper.
NDSPMHD Smoothed Particle Magnetohydrodynamics Code
Price, Daniel J.
2011-01-01
This paper presents an overview and introduction to Smoothed Particle Hydrodynamics and Magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, showing how the equations of motion and energy can be self-consistently derived from the density estimate. We then show how to interpret these equations using the basic SPH interpolation formulae and highlight the subtle difference in approach between SPH and other particle methods. In doing so, we also critique several 'urban myths' regarding SPH, in particular the idea that one can simply increase the 'neighbour number' more slowly than the total number of particles in order to obtain convergence. We also discuss the origin of numerical instabilities such as the pairing and tensile instabilities. Finally, we give practical advice on how to resolve three of the main issues with SPMHD: removing the tensile instability, formulating dissipative terms for MHD shocks and enforcing the divergence constraint on the particles, and we give the current status of developments in this area. Accompanying the paper is the first public release of the NDSPMHD SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD algorithms that can be used to test many of the ideas and used to run all of the numerical examples contained in the paper.
Gusakov, Mikhail
2016-01-01
The relativistic dynamic equations are derived for a superfluid-superconducting mixture coupled to the electromagnetic field. For definiteness and bearing in mind possible applications of our results to neutron stars, it is assumed that the mixture is composed of superfluid neutrons, superconducting protons, and normal electrons. Proton superconductivity of both I and II types is analysed, and possible presence of neutron and proton vortices (or magnetic domains in the case of type-I proton superconductivity) is allowed for. The derived equations neglect all dissipative effects except for the mutual friction dissipation and are valid for arbitrary temperatures (i.e. they do not imply that all nucleons are paired), which is especially important for magnetar conditions. It is demonstrated that these general equations can be substantially simplified for typical neutron stars, for which a kind of magnetohydrodynamic approximation is justified. Our results are compared to the nonrelativistic formulations existing ...
Tchekhovskoy, Alexander
2015-01-01
Active galactic nuclei jets are thought to form in the immediate vicinity of the event horizons of supermassive black holes. Therefore, jets could be excellent probes of general relativity. However, in practice, using jets to infer near-black hole physics is not straightforward since the cause of their most basic morphological features is not understood. For instance, there is no agreement on the cause of the well-known Fanaroff-Riley (FR) morphological dichotomy of jets, with FRI jets being shorter and wiggly and FRII jets being longer and more stable. Here, we carry out 3D relativistic magnetohydrodynamic (MHD) simulations of relativistic jets propagating through the ambient medium. Because in flat density cores of galaxies ($n \\propto r^{-\\alpha}$ with $\\alpha < 2$) the mass per unit distance ahead of the jets increases with distance, the jets slow down and collimate into smaller opening angles. This makes the jets more vulnerable to the 3D magnetic kink ("corkscrew") instability, which develops faster ...
Relativistic quantum mechanics; Mecanique quantique relativiste
Energy Technology Data Exchange (ETDEWEB)
Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.
SpECTRE: A Task-based Discontinuous Galerkin Code for Relativistic Astrophysics
Kidder, Lawrence E; Foucart, Francois; Schnetter, Erik; Teukolsky, Saul A; Bohn, Andy; Deppe, Nils; Diener, Peter; Hébert, François; Lippuner, Jonas; Miller, Jonah; Ott, Christian D; Scheel, Mark A; Vincent, Trevor
2016-01-01
We introduce a new relativistic astrophysics code, SpECTRE, that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more accurate solutions for challenging relativistic astrophysics problems such as core-collapse supernovae and binary neutron star mergers. The robustness of the discontinuous Galerkin method allows for the use of high-resolution shock capturing methods in regions where (relativistic) shocks are found, while exploiting high-order accuracy in smooth regions. A task-based parallelism model allows efficient use of the largest supercomputers for problems with a heterogeneous workload over disparate spatial and temporal scales. We argue that the locality and algorithmic structure of discontinuous Galerkin methods will exhibit good scalability within a task-based parallelism framework. We demonstrate the code on a wide variety of challenging benchmark problems in (non)-relativistic (magneto)-hydrodynamics. We demonstrate the code's scalability i...
Thermal-inertial effects on magnetic reconnection in relativistic pair plasmas.
Comisso, Luca; Asenjo, Felipe A
2014-07-25
The magnetic reconnection process is studied in relativistic pair plasmas when the thermal and inertial properties of the magnetohydrodynamical fluid are included. We find that in both Sweet-Parker and Petschek relativistic scenarios there is an increase of the reconnection rate owing to the thermal-inertial effects, both satisfying causality. To characterize the new effects we define a thermal-inertial number which is independent of the relativistic Lundquist number, implying that reconnection can be achieved even for vanishing resistivity as a result of only thermal-inertial effects. The current model has fundamental importance for relativistic collisionless reconnection, as it constitutes the simplest way to get reconnection rates faster than those accessible with the sole resistivity.
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Relativistic stars in bigravity theory
Aoki, Katsuki; Tanabe, Makoto
2016-01-01
Assuming static and spherically symmetric spacetimes in the ghost-free bigravity theory, we find a relativistic star solution, which is very close to that in general relativity. The coupling constants are classified into two classes: Class [I] and Class [II]. Although the Vainshtein screening mechanism is found in the weak gravitational field for both classes, we find that there is no regular solution beyond the critical value of the compactness in Class [I]. This implies that the maximum mass of a neutron star in Class [I] becomes much smaller than that in GR. On the other hand, for the solution in Class [II], the Vainshtein screening mechanism works well even in a relativistic star and the result in GR is recovered.
Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence.
Servidio, S; Matthaeus, W H; Shay, M A; Cassak, P A; Dmitruk, P
2009-03-20
Systematic analysis of numerical simulations of two-dimensional magnetohydrodynamic turbulence reveals the presence of a large number of X-type neutral points where magnetic reconnection occurs. We examine the statistical properties of this ensemble of reconnection events that are spontaneously generated by turbulence. The associated reconnection rates are distributed over a wide range of values and scales with the geometry of the diffusion region. Locally, these events can be described through a variant of the Sweet-Parker model, in which the parameters are externally controlled by turbulence. This new perspective on reconnection is relevant in space and astrophysical contexts, where plasma is generally in a fully turbulent regime.
CAFE: A NEW RELATIVISTIC MHD CODE
Energy Technology Data Exchange (ETDEWEB)
Lora-Clavijo, F. D.; Cruz-Osorio, A. [Instituto de Astronomía, Universidad Nacional Autónoma de México, AP 70-264, Distrito Federal 04510, México (Mexico); Guzmán, F. S., E-mail: fdlora@astro.unam.mx, E-mail: aosorio@astro.unam.mx, E-mail: guzman@ifm.umich.mx [Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo. Edificio C-3, Cd. Universitaria, 58040 Morelia, Michoacán, México (Mexico)
2015-06-22
We introduce CAFE, a new independent code designed to solve the equations of relativistic ideal magnetohydrodynamics (RMHD) in three dimensions. We present the standard tests for an RMHD code and for the relativistic hydrodynamics regime because we have not reported them before. The tests include the one-dimensional Riemann problems related to blast waves, head-on collisions of streams, and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the two-dimensional (2D) and 3D tests without magnetic field, we include the 2D Riemann problem, a one-dimensional shock tube along a diagonal, the high-speed Emery wind tunnel, the Kelvin–Helmholtz (KH) instability, a set of jets, and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin–Helmholtz instability, and a 3D magnetic field advection loop. The code uses high-resolution shock-capturing methods, and we present the error analysis for a combination that uses the Harten, Lax, van Leer, and Einfeldt (HLLE) flux formula combined with a linear, piecewise parabolic method and fifth-order weighted essentially nonoscillatory reconstructors. We use the flux-constrained transport and the divergence cleaning methods to control the divergence-free magnetic field constraint.
CAFE: A New Relativistic MHD Code
Lora-Clavijo, F D; Guzman, F S
2014-01-01
We present CAFE, a new independent code designed to solve the equations of Relativistic ideal Magnetohydrodynamics (RMHD) in 3D. We present the standard tests for a RMHD code and for the Relativistic Hydrodynamics (RMD) regime since we have not reported them before. The tests include the 1D Riemann problems related to blast waves, head-on collision of streams and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the 2D tests, without magnetic field we include the 2D Riemann problem, the high speed Emery wind tunnel, the Kelvin-Helmholtz instability test and a set of jets, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion and the Kelvin-Helmholtz instability. The code uses High Resolution Shock Capturing methods and as a standard set up we present the error analysis with a simple combination that uses the HLLE flux formula combined with linear, PPM ...
CAFE: A New Relativistic MHD Code
Lora-Clavijo, F. D.; Cruz-Osorio, A.; Guzmán, F. S.
2015-06-01
We introduce CAFE, a new independent code designed to solve the equations of relativistic ideal magnetohydrodynamics (RMHD) in three dimensions. We present the standard tests for an RMHD code and for the relativistic hydrodynamics regime because we have not reported them before. The tests include the one-dimensional Riemann problems related to blast waves, head-on collisions of streams, and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the two-dimensional (2D) and 3D tests without magnetic field, we include the 2D Riemann problem, a one-dimensional shock tube along a diagonal, the high-speed Emery wind tunnel, the Kelvin-Helmholtz (KH) instability, a set of jets, and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin-Helmholtz instability, and a 3D magnetic field advection loop. The code uses high-resolution shock-capturing methods, and we present the error analysis for a combination that uses the Harten, Lax, van Leer, and Einfeldt (HLLE) flux formula combined with a linear, piecewise parabolic method and fifth-order weighted essentially nonoscillatory reconstructors. We use the flux-constrained transport and the divergence cleaning methods to control the divergence-free magnetic field constraint.
Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory
Rogachevskii, Igor; Ruchayskiy, Oleg; Boyarsky, Alexey; Fröhlich, Jürg; Kleeorin, Nathan; Brandenburg, Axel; Schober, Jennifer
2017-09-01
The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (chiral magnetic effect). We present a self-consistent treatment of the chiral MHD equations, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfvén wave for incompressible flows, increases the frequencies of the Alfvén wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark–gluon plasma.
INVERSE CASCADE OF NONHELICAL MAGNETIC TURBULENCE IN A RELATIVISTIC FLUID
Energy Technology Data Exchange (ETDEWEB)
Zrake, Jonathan [Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Menlo Park, CA 94025 (United States)
2014-10-20
The free decay of nonhelical relativistic magnetohydrodynamic turbulence is studied numerically, and found to exhibit cascading of magnetic energy toward large scales. Evolution of the magnetic energy spectrum P{sub M} (k, t) is self-similar in time and well modeled by a broken power law with subinertial and inertial range indices very close to 7/2 and –2, respectively. The magnetic coherence scale is found to grow in time as t {sup 2/5}, much too slow to account for optical polarization of gamma-ray burst afterglow emission if magnetic energy is to be supplied only at microphysical length scales. No bursty or explosive energy loss is observed in relativistic MHD turbulence having modest magnetization, which constrains magnetic reconnection models for rapid time variability of GRB prompt emission, blazars, and the Crab nebula.
Probing Acceleration and Turbulence at Relativistic Shocks in Blazar Jets
Baring, Matthew G; Summerlin, Errol J
2016-01-01
Diffusive shock acceleration (DSA) at relativistic shocks is widely thought to be an important acceleration mechanism in various astrophysical jet sources, including radio-loud active galactic nuclei such as blazars. Such acceleration can produce the non-thermal particles that emit the broadband continuum radiation that is detected from extragalactic jets. An important recent development for blazar science is the ability of Fermi-LAT spectroscopy to pin down the shape of the distribution of the underlying non-thermal particle population. This paper highlights how multi-wavelength spectra spanning optical to X-ray to gamma-ray bands can be used to probe diffusive acceleration in relativistic, oblique, magnetohydrodynamic (MHD) shocks in blazar jets. Diagnostics on the MHD turbulence near such shocks are obtained using thermal and non-thermal particle distributions resulting from detailed Monte Carlo simulations of DSA. These probes are afforded by the characteristic property that the synchrotron $\
The Influence of Helical Magnetic Fields in the Dynamics and Emission of Relativistic Jets
Roca-Sogorb, M; Gómez, J L; Martí, J M; Antón, L; Aloy, M A; Agudo, I
2008-01-01
We present numerical relativistic magnetohydrodynamic and emission simulations aimed to study the role played by the magnetic field in the dynamics and emission of relativistic jets in Active Galactic Nuclei. We focus our analysis on the study of the emission from recollimation shocks since they may provide an interpretation for the stationary components seen at parsec-scales in multiple sources. We show that the relative brightness of the knots associated with the recollimation shocks decreases with increasing jet magnetization, suggesting that jets presenting stationary components may have a relatively weak magnetization, with magnetic fields of the order of equipartition or below.
Einstein Toolkit for Relativistic Astrophysics
Collaborative Effort
2011-02-01
The Einstein Toolkit is a collection of software components and tools for simulating and analyzing general relativistic astrophysical systems. Such systems include gravitational wave space-times, collisions of compact objects such as black holes or neutron stars, accretion onto compact objects, core collapse supernovae and Gamma-Ray Bursts. The Einstein Toolkit builds on numerous software efforts in the numerical relativity community including CactusEinstein, Whisky, and Carpet. The Einstein Toolkit currently uses the Cactus Framework as the underlying computational infrastructure that provides large-scale parallelization, general computational components, and a model for collaborative, portable code development.
Density perturbations with relativistic thermodynamics
Maartens, R
1997-01-01
We investigate cosmological density perturbations in a covariant and gauge- invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description. The gradient of density inhomogeneities splits covariantly into a scalar part, a rotational vector part that is determined by the vorticity, and a tensor part that describes the shape. We give the evolution equations for these parts in the general dissipative case. Causal thermodynamics gives evolution equations for viswcous stress and heat flux, which are coupled to the density perturbation equation and to the entropy and temperature perturbation equations. We give the full coupled system in the general dissipative case, and simplify the system in certain cases.
Relativistic and Non-relativistic Equations of Motion
Mangiarotti, L
1998-01-01
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.
Accurate, meshless methods for magnetohydrodynamics
Hopkins, Philip F.; Raives, Matthias J.
2016-01-01
Recently, we explored new meshless finite-volume Lagrangian methods for hydrodynamics: the `meshless finite mass' (MFM) and `meshless finite volume' (MFV) methods; these capture advantages of both smoothed particle hydrodynamics (SPH) and adaptive mesh refinement (AMR) schemes. We extend these to include ideal magnetohydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains nabla \\cdot B≈ 0. We implement these in the code GIZMO, together with state-of-the-art SPH MHD. We consider a large test suite, and show that on all problems the new methods are competitive with AMR using constrained transport (CT) to ensure nabla \\cdot B=0. They correctly capture the growth/structure of the magnetorotational instability, MHD turbulence, and launching of magnetic jets, in some cases converging more rapidly than state-of-the-art AMR. Compared to SPH, the MFM/MFV methods exhibit convergence at fixed neighbour number, sharp shock-capturing, and dramatically reduced noise, divergence errors, and diffusion. Still, `modern' SPH can handle most test problems, at the cost of larger kernels and `by hand' adjustment of artificial diffusion. Compared to non-moving meshes, the new methods exhibit enhanced `grid noise' but reduced advection errors and diffusion, easily include self-gravity, and feature velocity-independent errors and superior angular momentum conservation. They converge more slowly on some problems (smooth, slow-moving flows), but more rapidly on others (involving advection/rotation). In all cases, we show divergence control beyond the Powell 8-wave approach is necessary, or all methods can converge to unphysical answers even at high resolution.
From the Einstein-Szilard Patent to Modern Magnetohydrodynamics.
Povh, I. L.; Barinberg, A. D.
1979-01-01
Examines present-day and future prospects of the applications of modern magnetohydrodynamics in a number of countries. Explains how the electromagnetic pump, which was invented by Einstein and Leo Szilard, led to the development of applied magnetohydrodynamics. (HM)
Nakajima, Yuya; Seino, Junji; Nakai, Hiromi
2016-05-10
An analytical energy gradient for the spin-dependent general Hartree-Fock method based on the infinite-order Douglas-Kroll-Hess (IODKH) method was developed. To treat realistic systems, the local unitary transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth- and sixth-period elements and to examine the efficiency in one-, two-, and three-dimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of fac-tris(2-phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavy-element atoms.
Rubin, Jacques
2014-01-01
Relativistic stereometric coordinates supplied by relativistic auto-locating positioning systems made up of four satellites supplemented by a fifth one are defined in addition to the well-known emission and reception coordinates. Such a constellation of five satellites defines a so-called relativistic localizing system. The determination of such systems is motivated by the need to not only locate (within a grid) users utilizing receivers but, more generally, to localize any spacetime event. The angles measured on the celestial spheres of the five satellites enter into the definition. Therefore, there are, up to scalings, intrinsic physical coordinates related to the underlying conformal structure of spacetime. Moreover, they indicate that spacetime must be endowed everywhere with a local projective geometry characteristic of a so-called generalized Cartan space locally modeled on four-dimensional, real projective space. The particular process of localization providing the relativistic stereometric coordinates...
Convexity and symmetrization in relativistic theories
Ruggeri, T.
1990-09-01
There is a strong motivation for the desire to have symmetric hyperbolic field equations in thermodynamics, because they guarantee well-posedness of Cauchy problems. A generic quasi-linear first order system of balance laws — in the non-relativistic case — can be shown to be symmetric hyperbolic, if the entropy density is concave with respect to the variables. In relativistic thermodynamics this is not so. This paper shows that there exists a scalar quantity in relativistic thermodynamics whose concavity guarantees a symmetric hyperbolic system. But that quantity — we call it —bar h — is not the entropy, although it is closely related to it. It is formed by contracting the entropy flux vector — ha with a privileged time-like congruencebar ξ _α . It is also shown that the convexity of h plus the requirement that all speeds be smaller than the speed of light c provide symmetric hyperbolic field equations for all choices of the direction of time. At this level of generality the physical meaning of —h is unknown. However, in many circumstances it is equal to the entropy. This is so, of course, in the non-relativistic limit but also in the non-dissipative relativistic fluid and even in relativistic extended thermodynamics for a non-degenerate gas.
The relativistic geoid: redshift and acceleration potential
Philipp, Dennis; Lämmerzahl, Claus; Puetzfeld, Dirk; Hackmann, Eva; Perlick, Volker
2017-04-01
We construct a relativistic geoid based on a time-independent redshift potential, which foliates the spacetime into isochronometric surfaces. This relativistic potential coincides with the acceleration potential for isometric congruences. We show that the a- and u- geoid, defined in a post-Newtonian framework, coincide also in a more general setup. Known Newtonian and post-Newtonian results are recovered in the respective limits. Our approach offers a relativistic definition of the Earth's geoid as well as a description of the Earth itself (or observers on its surface) in terms of an isometric congruence. Being fully relativistic, this notion of a geoid can also be applied to other compact objects such as neutron stars. By definition, this relativistic geoid can be determined by a congruence of Killing observers equipped with standard clocks by comparing their frequencies as well as by measuring accelerations of objects that follow the congruence. The redshift potential gives the correct result also for frequency comparison through optical fiber links as long as the fiber is at rest w.r.t. the congruence. We give explicit expressions for the relativistic geoid in the Kerr spacetime and the Weyl class of spacetimes. To investigate the influence of higher order mass multipole moments we compare the results for the Schwarzschild case to those obtained for the Erez-Rosen and q-metric spacetimes.
Three-Dimensional Magnetohydrodynamic Simulations of the Crab Nebula
Porth, Oliver; Keppens, Rony
2013-01-01
In this paper we give a detailed account of the first 3D relativistic magnetohydrodynamic (MHD) simulations of Pulsar Wind Nebulae (PWN), with parameters most suitable for the Crab Nebula. In order to clarify the new features specific to 3D models, reference 2D simulations have been carried out as well. Compared to the previous 2D simulations, we considered pulsar winds with much stronger magnetisation, up to \\sigma=3, and accounted more accurately for the anticipated magnetic dissipation in the striped zone of these winds. While the 3D models preserve the separation of the post termination shock flow into the equatorial and polar components, their relative strength and significance differ. Whereas the highly magnetised 2D models produce highly coherent and well collimated polar jets capable of efficient "drilling" through the supernova shell, in the corresponding 3D models the jets are disrupted by the kink mode current driven instability and "dissolve" into the main body of PWN after propagation of several ...
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Gomis, Joaquim; Not, Daniel
2017-02-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Not, Daniel
2016-01-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Unification of Relativistic and Quantum Mechanics from Elementary Cycles Theory
Dolce, Donatello
2016-01-01
In Elementary Cycles theory elementary quantum particles are consistently described as the manifestation of ultra-fast relativistic spacetime cyclic dynamics, classical in the essence. The peculiar relativistic geometrodynamics of Elementary Cycles theory yields de facto a unification of ordinary relativistic and quantum physics. In particular its classical-relativistic cyclic dynamics reproduce exactly from classical physics first principles all the fundamental aspects of Quantum Mechanics, such as all its axioms, the Feynman path integral, the Dirac quantisation prescription (second quantisation), quantum dynamics of statistical systems, non-relativistic quantum mechanics, atomic physics, superconductivity, graphene physics and so on. Furthermore the theory allows for the explicit derivation of gauge interactions, without postulating gauge invariance, directly from relativistic geometrodynamical transformations, in close analogy with the description of gravitational interaction in general relativity. In thi...
Magnetohydrodynamically generated velocities in confined plasma
Morales, Jorge A.; Bos, Wouter J. T.; Schneider, Kai; Montgomery, David C.
2015-04-01
We investigate by numerical simulation the rotational flows in a toroid confining a conducting magnetofluid in which a current is driven by the application of externally supported electric and magnetic fields. The computation involves no microscopic instabilities and is purely magnetohydrodynamic (MHD). We show how the properties and intensity of the rotations are regulated by dimensionless numbers (Lundquist and viscous Lundquist) that contain the resistivity and viscosity of the magnetofluid. At the magnetohydrodynamic level (uniform mass density and incompressible magnetofluids), rotational flows appear in toroidal, driven MHD. The evolution of these flows with the transport coefficients, geometry, and safety factor are described.
Continuous magnetohydrodynamic spectra of two-dimensional coronal magnetostatic flux tubes
Belien, A. J. C.; Poedts, S.; Goedbloed, J. P.
1997-01-01
In this paper we derive the equations for the continuous ideal magnetohydrodynamic (MHD) spectrum of two-dimensional coronal loops, including gravity and expansion, in general curvilinear coordinates. The equations clearly show the coupling between Alfven and slow magnetosonic continuum waves when b
Thermodynamics of Relativistic Fermions with Chern-Simons Coupling
Bralic, N; Schaposnik, F A
1994-01-01
We study the thermodynamics of the relativistic Quantum Field Theory of massive fermions in three space-time dimensions coupled to an Abelian Maxwell-Chern-Simons gauge field. We evaluate the specific heat at finite temperature and density and find that the variation with the statistical angle is consistent with the non-relativistic ideas on generalized statistics.
Meson-Meson Scattering in Relativistic Constraint Dynamics
Crater, H W; Crater, Horace W.
2004-01-01
Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. We use this formalism to describe a microscopic theory of meson-meson scattering as a relativistic generalization of the nonrelativistic quark-interchange model developed by Barnes and Swanson.
Relativistic spherical plasma waves
Bulanov, S. S.; Maksimchuk, A.; Schroeder, C. B.; Zhidkov, A. G.; Esarey, E.; Leemans, W. P.
2012-02-01
Tightly focused laser pulses that diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we study theoretically and numerically relativistic spherical wake waves and their properties, including wave breaking.
Bliokh, Konstantin Y
2011-01-01
We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the correct Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices, mechanical flywheel, and discuss various fundamental aspects of the phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales: from elementary spinning particles, through classical light, to rotating black-holes.
Gusakov, M. E.; Dommes, V. A.
2016-10-01
The relativistic dynamic equations are derived for a superfluid-superconducting mixture coupled to an electromagnetic field. For definiteness, and bearing in mind possible applications of our results to neutron stars, it is assumed that the mixture is composed of superfluid neutrons, superconducting protons, and normal electrons. We analyze the proton superconductivity of both types I and II and allow for the possible presence of neutron and proton vortices (or magnetic domains in the case of type-I proton superconductivity). The derived equations neglect all dissipative effects except for the mutual friction dissipation and are valid for arbitrary temperatures (i.e., they do not imply that all nucleons are paired), which is especially important for magnetar conditions. It is demonstrated that these general equations can be substantially simplified for typical neutron stars, for which a kind of magnetohydrodynamic approximation is justified. Our results are compared to the nonrelativistic formulations existing in the literature, and a number of discrepancies are found. In particular, it is shown that, generally, the electric displacement D does not coincide with the electric field E , contrary to what is stated in previous works. The relativistic framework developed here is easily extendable to account for more sophisticated microphysics models, and it provides the necessary basis for realistic modeling of neutron stars.
Exact Relativistic 'Antigravity' Propulsion
Felber, F S
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3^-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Newton-Cartan (super)gravity as a non-relativistic limit
Bergshoeff, Eric; Rosseel, Jan; Zojer, Thomas
2015-01-01
We define a procedure that, starting from a relativistic theory of supergravity, leads to a consistent, non-relativistic version thereof. As a first application we use this limiting procedure to show how the Newton-Cartan formulation of non-relativistic gravity can be obtained from general relativit
On energy conservation in extended magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Kimura, Keiji [Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan); Morrison, P. J. [Department of Physics and Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712-1060 (United States)
2014-08-15
A systematic study of energy conservation for extended magnetohydrodynamic models that include Hall terms and electron inertia is performed. It is observed that commonly used models do not conserve energy in the ideal limit, i.e., when viscosity and resistivity are neglected. In particular, a term in the momentum equation that is often neglected is seen to be needed for conservation of energy.
Dynamic grid adaptation for computational magnetohydrodynamics
Keppens, R.; Nool, M.; Zegeling, P. A.; Goedbloed, J. P.; Bubak, M.; Williams, R.; Afsarmanesh, H.; Hertzberger, B.
2000-01-01
In many plasma physical and astrophysical problems, both linear and nonlinear effects can lead to global dynamics that induce, or occur simultaneously with, local phenomena. For example, a magnetically confined plasma column can potentially posses global magnetohydrodynamic (MHD) eigenmodes with an
Potential vorticity formulation of compressible magnetohydrodynamics.
Arter, Wayne
2013-01-04
Compressible ideal magnetohydrodynamics is formulated in terms of the time evolution of potential vorticity and magnetic flux per unit mass using a compact Lie bracket notation. It is demonstrated that this simplifies analytic solution in at least one very important situation relevant to magnetic fusion experiments. Potentially important implications for analytic and numerical modelling of both laboratory and astrophysical plasmas are also discussed.
Using high performance Fortran for magnetohydrodynamic simulations
Keppens, R.; Toth, G.
2000-01-01
Two scientific application programs, the Versatile Advection Code (VAC) and the HEating by Resonant Absorption (HERA) code are adapted to parallel computer platforms. Both programs can solve the time-dependent nonlinear partial differential equations of magnetohydrodynamics (MHD) with different nume
On the relativistic anisotropic configurations
Energy Technology Data Exchange (ETDEWEB)
Shojai, F. [University of Tehran, Department of Physics, Tehran (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), Foundations of Physics Group, School of Physics, Tehran (Iran, Islamic Republic of); Kohandel, M. [Alzahra University, Department of Physics and Chemistry, Tehran (Iran, Islamic Republic of); Stepanian, A. [University of Tehran, Department of Physics, Tehran (Iran, Islamic Republic of)
2016-06-15
In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov equations, we explore the relativistic anisotropic Lane-Emden equations. We find how the anisotropic pressure affects the boundary conditions of these equations. Also we argue that the behavior of physical quantities near the center of star changes in the presence of anisotropy. For constant density, a class of exact solution is derived with the aid of a new ansatz and its physical properties are discussed. (orig.)
Validation of Magnetospheric Magnetohydrodynamic Models
Curtis, Brian
Magnetospheric magnetohydrodynamic (MHD) models are commonly used for both prediction and modeling of Earth's magnetosphere. To date, very little validation has been performed to determine their limits, uncertainties, and differences. In this work, we performed a comprehensive analysis using several commonly used validation techniques in the atmospheric sciences to MHD-based models of Earth's magnetosphere for the first time. The validation techniques of parameter variability/sensitivity analysis and comparison to other models were used on the OpenGGCM, BATS-R-US, and SWMF magnetospheric MHD models to answer several questions about how these models compare. The questions include: (1) the difference between the model's predictions prior to and following to a reversal of Bz in the upstream interplanetary field (IMF) from positive to negative, (2) the influence of the preconditioning duration, and (3) the differences between models under extreme solar wind conditions. A differencing visualization tool was developed and used to address these three questions. We find: (1) For a reversal in IMF Bz from positive to negative, the OpenGGCM magnetopause is closest to Earth as it has the weakest magnetic pressure near-Earth. The differences in magnetopause positions between BATS-R-US and SWMF are explained by the influence of the ring current, which is included in SWMF. Densities are highest for SWMF and lowest for OpenGGCM. The OpenGGCM tail currents differ significantly from BATS-R-US and SWMF; (2) A longer preconditioning time allowed the magnetosphere to relax more, giving different positions for the magnetopause with all three models before the IMF Bz reversal. There were differences greater than 100% for all three models before the IMF Bz reversal. The differences in the current sheet region for the OpenGGCM were small after the IMF Bz reversal. The BATS-R-US and SWMF differences decreased after the IMF Bz reversal to near zero; (3) For extreme conditions in the solar
Center for Extended Magnetohydrodynamic Modeling Cooperative Agreement
Energy Technology Data Exchange (ETDEWEB)
Carl R. Sovinec
2008-02-15
nonlinear simulations, which has been publicized as a success story of SciDAC-fostered collaboration. Furthermore, the SuperLU software does not assume any mathematical symmetry, and its generality provides an important capability for extending the physical model beyond magnetohydrodynamics (MHD). With respect to algorithmic and model development, our most significant accomplishment is the development of a new method for solving plasma models that treat electrons as an independent plasma component. These ‘two-fluid’ models encompass MHD and add temporal and spatial scales that are beyond the response of the ion species. Implementation and testing of a previously published algorithm did not prove successful for NIMROD, and the new algorithm has since been devised, analyzed, and implemented. Two-fluid modeling, an important objective of the original NIMROD project, is now routine in 2D applications. Algorithmic components for 3D modeling are in place and tested; though, further computational work is still needed for efficiency. Other algorithmic work extends the ion-fluid stress tensor to include models for parallel and gyroviscous stresses. In addition, our hot-particle simulation capability received important refinements that permitted completion of a benchmark with the M3D code. A highlight of our applications work is the edge-localized mode (ELM) modeling, which was part of the first-ever computational Performance Target for the DOE Office of Fusion Energy Science, see http://www.science.doe.gov/ofes/performancetargets.shtml. Our efforts allowed MHD simulations to progress late into the nonlinear stage, where energy is conducted to the wall location. They also produced a two-fluid ELM simulation starting from experimental information and demonstrating critical drift effects that are characteristic of two-fluid physics. Another important application is the internal kink mode in a tokamak. Here, the primary purpose of the study has been to benchmark the two main code
GRay: A Massively Parallel GPU-based Code for Ray Tracing in Relativistic Spacetimes
Chan, Chi-kwan; Psaltis, Dimitrios; Özel, Feryal
2013-11-01
We introduce GRay, a massively parallel integrator designed to trace the trajectories of billions of photons in a curved spacetime. This graphics-processing-unit (GPU)-based integrator employs the stream processing paradigm, is implemented in CUDA C/C++, and runs on nVidia graphics cards. The peak performance of GRay using single-precision floating-point arithmetic on a single GPU exceeds 300 GFLOP (or 1 ns per photon per time step). For a realistic problem, where the peak performance cannot be reached, GRay is two orders of magnitude faster than existing central-processing-unit-based ray-tracing codes. This performance enhancement allows more effective searches of large parameter spaces when comparing theoretical predictions of images, spectra, and light curves from the vicinities of compact objects to observations. GRay can also perform on-the-fly ray tracing within general relativistic magnetohydrodynamic algorithms that simulate accretion flows around compact objects. Making use of this algorithm, we calculate the properties of the shadows of Kerr black holes and the photon rings that surround them. We also provide accurate fitting formulae of their dependencies on black hole spin and observer inclination, which can be used to interpret upcoming observations of the black holes at the center of the Milky Way, as well as M87, with the Event Horizon Telescope.
Stream instabilities in relativistically hot plasma
Shaisultanov, Rashid; Eichler, David
2011-01-01
The instabilities of relativistic ion beams in a relativistically hot electron background are derived for general propagation angles. It is shown that the Weibel instability in the direction perpendicular to the streaming direction is the fastest growing mode, and probably the first to appear, consistent with the aligned filaments that are seen in PIC simulations. Oblique, quasiperpendicular modes grow almost as fast, as the growth rate varies only moderately with angle, and they may distort or corrugate the filaments after the perpendicular mode saturates.
Relativistic Celestial Mechanics of the Solar System
Kopeikin, Sergei; Kaplan, George
2011-01-01
This authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic r
Correspondence between constrained transport and vector potential methods for magnetohydrodynamics
Mocz, Philip
2017-01-01
We show that one can formulate second-order field- and flux-interpolated constrained transport/central difference (CT/CD) type methods as cell-centered magnetic vector potential schemes. We introduce four vector potential CTA/CDA schemes - three of which correspond to CT/CD methods of Tóth (2000) [1] and one of which is a new simple flux-CT-like scheme - where the centroidal vector potential is the primal update variable. These algorithms conserve a discretization of the ∇ ṡ B = 0 condition to machine precision and may be combined with shock-capturing Godunov type base schemes for magnetohydrodynamics. Recasting CT in terms of a centroidal vector potential allows for some simple generalizations of divergence-preserving methods to unstructured meshes, and potentially new directions to generalize CT schemes to higher-order.
Viscous, resistive magnetohydrodynamic stability computed by spectral techniques.
Dahlburg, R B; Zang, T A; Montgomery, D; Hussaini, M Y
1983-09-01
Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydrodynamic quasiequilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfvén speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.
Viscous, resistive magnetohydrodynamic stability computed by spectral techniques
Dahlburg, R. B.; Zang, T. A.; Montgomery, D.; Hussaini, M. Y.
1983-01-01
Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydrodynamic quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.