General relativistic hydrodynamics near equilibrium
General relativistic hydrodynamics near equilibrium, discussing velocity and kinetic energy increase spherically symmetric large masses as function of radius change
Bardeen, J. M.↗
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A Numerical Gamma-Ray Burst Simulation Using Three-Dimensional Relativistic Hydrodynamics: The Transition from Spherical to Jet-like Expansion
Utilizing 3D relativistic hydrodynamical calculations, we have examined the evolution of an expanding relativistic blob of gas intended to be representative of a jet associated with ejecta from an extremely energetic event such as a hypernova, that produces a gamma-ray burst (Aloy et al. 2000; Tan, Matzner, & McKee 2001; MacFadyen, Woosley, & Heger 2001, Zhang, Woosley, & Heger 2003, Zhang, Woosley, & MacFadyen 2003). Since these are the first such calculations applied to the blob during the time in which the afterglow radiation is produced, we have purposely kept them simple in an effort to concentrate on the most fundamental aspects of the physics. We restrict our attention to the transition from spherical to jetlike expansion that occurs during the time that the Lorentz factor becomes less than the reciprocal of the jet spreading angle. We have not yet attached specific numbers to our results. From the SRHD equations, one sees that the relevant quantities are the ratios of pressure to density, and of distance to time. If we specify either one of these two sets of numbers, the other one is also determined.
Cannizzo, John K.↗
Observer-time as a coordinate in relativistic spherical hydrodynamics.
Relativistic supernova model, discussing Einstein equation solution with two part stress- energy tensor
Misner, C. W.↗
Computational Relativistic Astrophysics Using the Flow Field-Dependent Variation Theory
We present our method for solving general relativistic nonideal hydrodynamics. Relativistic effects become pronounced in such cases as jet formation from black hole magnetized accretion disks which may lead to the study of gamma-ray bursts. Nonideal flows are present where radiation, magnetic forces, viscosities, and turbulence play an important role. Our concern in this paper is to reexamine existing numerical simulation tools as to the accuracy and efficiency of computations and introduce a new approach known as the flow field-dependent variation (FDV) method. The main feature of the FDV method consists of accommodating discontinuities of shock waves and high gradients of flow variables such as occur in turbulence and unstable motions. In this paper, the physics involved in the solution of relativistic hydrodynamics and solution strategies of the FDV theory are elaborated. The general relativistic astrophysical flow and shock solver (GRAFSS) is introduced, and some simple example problems for computational relativistic astrophysics (CRA) are demonstrated.
Richardson, G. A.↗
Observer time as a coordinate in relativistic spherical hydrodynamics.
Retarded observer time as coordinate in relativistic spherical hydrodynamic equations prevents Schwarzschild surface formation
SPACE-TIME METRIC↗
Cosmic-ray hydrodynamics at relativistic shocks
A test particle description of first-order Fermi acceleration of cosmic rays at plane-parallel relativistic shocks is presented in which the pitch angle distribution is obtained explicitly and used to determine the pressure anisotropy or variable Eddington factor as a function of position. The Eddington factor is in turn used to find the hydrodynamical cosmic-ray sound speed, taking the anisotropy into account. For upstream flows speeds above c/sq rt 3, it is shown that the cosmic-ray sound speed exceeds the shock speed in a region just upstream of the shock and decreases montonically with distance further upstream, reaching the value c/sq rt 3 far from the shock. Thus, the shock succeeds in maintaining an anisotropy in the cosmic-ray distribution which is sufficient to keep the flow subsonic with respect to the cosmic-ray sound speed both downstream and in a finite region upstream. The astrophysical implications of these findings are discussed.
Kirk, J. G.↗
Hydrodynamics of Relativistic Fireballs
Many models of gamma-ray bursts involve a fireball, which is an optically thick concentration of radiation energy with a high ratio of energy density to rest mass. We examine analytically and numerically the evolution of a relativistic fireball. We show that, after an early rearrangement phase, most of the matter and energy in the fireball is concentrated within a narrow shell. The shell propagates at nearly the speed of light, with a frozen radial profile, and according to a simple set of scaling laws. The spectrum of the escaping radiation is harder at early times and softer later on. Depending on the initial energy-to-mass ratio, the final outcome of a fireball is either photons with roughly the initial temperature or ultrarelativistic baryons. In the latter case, the energy could be converted back to gamma-rays via interaction with surrounding material.
Piran, Tsvi↗
Gamma-Ray Bursts and Relativistic MHD around Coalescing Neutron Stars
In this proposal we performed the first relativistic hydrodynamic simulations of the binary neutron stars near coalescence. Calculations were performed in three spatial dimensions and were supplemented with magnetohydrodynamic simulations of the magnetic reconnection as the neutron star fluid responds to the relativistic forces of the binary. The ultimate goal of the proposed work was to develop a theoretical model for the temporal and spectral evolution of cosmological gamma-ray bursts produced during the magnetic reconnection. This is the first time such hydrodynamic calculations were performed and some surprising results were obtained. The neutrons stars were observed to compress and heat in the simulations. They could even collapse to black holes many orbits before coalescence. The question then arose as to whether this strange phenomenon could power a gamma-ray burst. The bulk of computing effort in this proposal was therefore devoted to an analysis of the implications of this possible new gamma-ray burst paradigm. The initial focus of the work performed under this proposal was therefore to utilize (3+1) dimensional and spherical numerical general relativistic hydrodynamics to study the origin, evolution, and parametric sensitivity of the collapse instability. We derived modified conditions of hydrostatic equilibrium for stars in the curved space of quasi-static orbits. We followed the magnetic field evolution for approximately one orbit (10 msec). The magnetic field energy was observed to exponentiate with an e-folding time of about 1 msec. Thus, the field should build up very quickly to a magnitude such that reconnection and back reaction of the fluid inhibits further growth.
Mathews, Grant J.↗
Computational Relativistic Astrophysics Using the Flowfield-Dependent Variation Theory
Theoretical models, observations and measurements have preoccupied astrophysicists for many centuries. Only in recent years, has the theory of relativity as applied to astrophysical flows met the challenges of how the governing equations can be solved numerically with accuracy and efficiency. Even without the effects of relativity, the physics of magnetohydrodynamic flow instability, turbulence, radiation, and enhanced transport in accretion disks has not been completely resolved. Relativistic effects become pronounced in such cases as jet formation from black hole magnetized accretion disks and also in the study of Gamma-Ray bursts (GRB). Thus, our concern in this paper is to reexamine existing numerical simulation tools as to the accuracy and efficiency of computations and introduce a new approach known as the flowfield-dependent variation (FDV) method. The main feature of the FDV method consists of accommodating discontinuities of shock waves and high gradients of flow variables such as occur in turbulence and unstable motions. In this paper, the physics involved in the solution of relativistic hydrodynamics and solution strategies of the FDV theory are elaborated. The general relativistic astrophysical flow and shock solver (GRAFSS) is introduced, and some simple example problems for Computational Relativistic Astrophysics (CRA) are demonstrated.
Richardson, G. A.↗
Tidal Disruptions of Main-sequence Stars. IV. Relativistic Effects and Dependence on Black Hole Mass
Using a suite of fully relativistic hydrodynamic simulations applied to main-sequence stars with realistic internal density profiles, we examine full and partial tidal disruptions across a wide range of black hole mass( MM105 105BH7)and stellar mass (MM0.33) as larger MBH leads to stronger relativistic effects. For fixed Må, as MBH increases, the ratio of the maximum pericenter distance yielding full disruptions (t) to its Newtonian prediction rises rapidly, becoming triple the Newtonian value for= ́MM510BH7, while the ratio of the energy width of the stellar debris for full disruptions to the Newtonian prediction decreases steeply, resulting in a factor of 2 correction at= ́MM510BH7. We provide approximate formulae that express the relativistic corrections of both t and the energy width relative to their Newtonian approximate estimates. For partial disruptions, we find that the fractional remnant mass for a given ratio of the pericenter to t is higher for larger MBH. These results have several implications. As MBH increases above~M107, the cross section for complete disruptions is suppressed by competition with direct capture. However, the cross-section ratio for partial to complete disruptions depends only weakly on MBH. The relativistic correction to the debris energy width delays the time of peak mass-return rate and diminishes the magnitude of the peak return rate. ForMM10BH7, the MBH-dependence of the full disruption cross section and the peak mass-return rate and time is influenced more by relativistic effects than by Newtonian dynamics.
Taeho Ryu↗
Tidal Disruptions of Main-sequence Stars. IV. Relativistic Effects and Dependence on Black Hole Mass
Using a suite of fully relativistic hydrodynamic simulations applied to main-sequence stars with realistic internal density profiles, we examine full and partial tidal disruptions across a wide range of black hole mass (10(exp 5)≤M(BH)/M(ʘ)≤5 x 10(exp 7) and stellar mass (0.3≤M(*)/M(ʘ)≤3) as larger M(BH) leads to stronger relativistic effects. For fixed M( ), as M(BH) increases, the ratio of the maximum pericenter distance yielding full disruptions ( ) to its Newtonian prediction rises rapidly, becoming triple the Newtonian value for M(BH)=5 x 10(exp 7)M(ʘ), while the ratio of the energy width of the stellar debris for full disruptions to the Newtonian prediction decreases steeply, resulting in a factor of 2 correction at M(BH)=5 x 10(exp 7)M(ʘ). We provide approximate formulae that express the relativistic corrections of both R(t) and the energy width relative to their Newtonian approximate estimates. For partial disruptions, we find that the fractional remnant mass for a given ratio of the pericenter to R(t) is higher for larger M(BH). These results have several implications. As M(BH) increases above ~10(exp 7)M(ʘ), the cross section for complete disruptions is suppressed by competition with direct capture. However, the cross-section ratio for partial to complete disruptions depends only weakly on M(BH). The relativistic correction to the debris energy width delays the time of peak mass-return rate and diminishes the magnitude of the peak return rate. For M(BH)≳10(exp 7)M(ʘ), the M(BH)-dependence of the full disruption cross section and the peak mass-return rate and time is influenced more by relativistic effects than by Newtonian dynamics.
Taeho Ryu↗
Time-dependent, optically thick accretion onto a black hole
A fully relativistic hydrodynamics code which incorporates diffusive radiation transport is used to study time-dependent, spherically symmetric, optically thick accretion onto a black hole. It is found that matter free-falls into the hole regardless of whether the diffusion time scale is longer or shorter than the dynamical time. Nonadiabatic heating due to magnetic field reconnection is included. The internal energy thus generated affects the flow in a purely relativistic way, again ensuring free-fall collapse of the inflowing matter. Any matter enveloping a black hole will thus be swallowed on a dynamical time scale with relatively small net release of energy. The inclusion of angular momentum will not necessarily affect this conclusion.
Gilden, D. L.↗
Tidal Disruptions of Main Sequence Stars - I. Observable Quantities and their Dependence on Stellar and Black Hole Mass
This paper introduces a series of papers presenting a quantitative theory for the tidal disruption of main-sequence stars by supermassive black holes. Using fully general relativistic hydrodynamics simulations and MESA-model initial conditions, we explore the pericenter-dependence of tidal disruption properties for eight stellar masses(MM0.1510)and six black hole masses( MM105 105BH7). We present here the results most relevant to observations. The effects of internal stellar structure and relativity decouple for both the disruption cross section and the characteristic energy width of the debris. Moreover, the full disruption cross section is almost independent of Må for Må/Me3. Independent of Må, relativistic effects increase the critical pericenter distance for full disruption events by up to a factor of∼3 relative to the Newtonian prediction. The probability of a direct capture is also independent of Må; at MBH/Me;5×106 this probability is equal to the probability of a complete disruption. The breadth of the debris energy distribution ΔE can differ from the standard estimate by factors of0.35−2, depending on Må and MBH, implying a corresponding change(∝(ΔE)−3/2)in the characteristic mass-return timescale. We provide analytic forms, suitable for use in both event rate estimates and parameter inference, to describe all these trends. For partial disruptions, we find a nearly universal relation between the star’s angular momentum and the fraction of Må remaining. Within the “empty loss-cone” regime, partial disruptions must precede full disruptions. These partial disruptions can drastically affect the rate and appearance of subsequent total disruptions.
Taeho Ryu↗
Tidal Disruptions of Main Sequence Stars - II. Simulation Methodology and Stellar Mass Dependence of the Character of Full Tidal Disruptions
This paper introduces a series of papers presenting a quantitative theory for the tidal disruption of main-sequence stars by supermassive black holes. Using fully general relativistic hydrodynamics simulations and MESA-model initial conditions, we explore the pericenter-dependence of tidal disruption properties for eight stellar masses (0.15 < M_/M<10)and six black hole masses( ́10<MM105 105BH7). We present here the results most relevant to observations. The effects of internal stellar structure and relativity decouple for both the disruption cross section and the characteristic energy width of the debris. Moreover, the full disruption cross section is almost independent of Må for Må/Me3. Independent of Må, relativistic effects increase the critical pericenter distance for full disruption events by up to a factor of ∼3 relative to the Newtonian prediction. The probability of a direct capture is also independent of Må; at MBH/Me5×106this probability is equal to the probability of a complete disruption. The breadth of the debris energy distribution ΔE can differ from the standard estimate by factors of 0.35−2, depending on Må and MBH, implying a corresponding change(∝(ΔE)−3/2)in the characteristic mass-return timescale. We provide analytic forms, suitable for use in both event rate estimates and parameter inference, to describe all these trends. For partial disruptions, we find a nearly universal relation between the star’s angular momentum and the fraction of Må remaining. Within the “empty loss-cone” regime, partial disruptions must precede full disruptions. These partial disruptions can drastically affect the rate and appearance of subsequent total disruptions
Taeho Ryu↗
Gravitational collapse, neutrinos and supernovae.
Supernova explosion and collapse theory using relativistic hydrodynamics
STELLAR EVOLUTION↗
The cosmic-ray shock structure problem for relativistic shocks
The time asymptotic behaviour of a relativistic (parallel) shock wave significantly modified by the diffusive acceleration of cosmic-rays is investigated by means of relativistic hydrodynamical equations for both the cosmic-rays and thermal gas. The form of the shock structure equation and the dispersion relation for both long and short wavelength waves in the system are obtained. The dependence of the shock acceleration efficiency on the upstream fluid spped, long wavelength Mach number and the ratio N = P sub co/cP sub co+P sub go)(Psub co and P sub go are the upstream cosmic-ray and thermal gas pressures respectively) are studied.
Webb, G. M.↗
Collapse of 9 solar mass stars
General relativistic hydrodynamical calculations of the collapse of O + Ne + Mg cores of a 9 solar mass star are reported. Collapse is induced by rapid electron captures as the O + Ne + Mg is burned to nuclear statistical equilibrium. The high entropy in the core after burning leads to a large abundance of free protons which readily capture electrons. This leads to large neutrino losses and a correspondingly small infalling homologous core. The hydrodynamic shock thus forms at a small mass point. The shock stalls before reaching the edge of the O + Ne + Mg core and thereby fails to produce a successful supernova explosion by the direct mechanism. No enhancement in the shock energy due to nuclear burning is found.
Baron, E.↗
On the Maximum Stellar Rotation to Form a Black Hole without an Accompanying Luminous Transient
The collapse of a massive star with low angular momentum content is commonly argued to result in the formation of a black hole without an accompanying bright transient. Our goal in this Letter is to understand the flow in and around a newly-formed black hole, involving accretion and rotation, via general relativistic hydrodynamics simulations aimed at studying the conditions under which infalling material can accrete without forming a centrifugally supported structure and, as a result, generate no effective feedback. If the feedback from the black hole is, on the other hand, significant, the collapse would be halted and we suggest that the event is likely to be followed by a bright transient. We find that feedback is only efficient if the specific angular momentum of the infalling material at the innermost stable circular orbit exceeds that of geodesic circular flow at that radius by at least≈20%. We use the results of our simulations to constrain the maximal stellar rotation rates of the disappearing massive progenitors PHL293B-LBV and N6946-BH1, and to provide an estimate of the overall rate of disappearing massive stars. We find that about a few percent of single O-type stars with measured rotational velocities are expected to spin below the critical value before collapse and are thus predicted to vanish without a trace.
Scott C Noble↗