arXiv subjects

Stuart L. Shapiro

Publications and source records attributed to Stuart L. Shapiro.

At least 145 records · Page 8Linked to original sources

arXiv2005

Magnetized hypermassive neutron star collapse: a central engine for short gamma-ray bursts

A hypermassive neutron star (HMNS) is a possible transient formed after the merger of a neutron star binary. In the latest magnetohydrodynamic simulations in full general relativity, we find that a magnetized HMNS undergoes `delayed' collapse to a rotating black hole (BH) as a result of angular momentum transport via magnetic braking and the magnetorotational instability. The outcome is a BH surrounded by a massive, hot torus with a collimated magnetic field. The torus accretes onto the BH at a quasi-steady accretion rate ~10 solar mass/s; the lifetime of the torus is ~10 ms. The torus has a temperature \sim 10^{12} K, leading to copious neutrino-antineutrino thermal radiation. Therefore, the collapse of an HMNS is a promising scenario for generating short-duration gamma-ray bursts and an accompanying burst of gravitational waves and neutrinos.

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arXiv2005

Numerical Relativity at the Frontier

Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve these nonlinear equations in 3+1 dimensions has enabled us to tackle many long-standing problems of astrophysical interest, leading to an explosion of important new results. Numerical relativity has been used to simulate the evolution of a diverse array of physical systems, including coalescing black hole and neutron star binaries, rotating and collapsing compact objects (stars, collisionless clusters, and scalar fields), and magnetic and viscous stars, to name a few. Numerical relativity has been exploited to address fundamental points of principle, including critical phenomena and cosmic censorship. It holds great promise as a guide for interpreting observations of gravitational waves and gamma-ray bursts and identifying the sources of such radiation. Highlights of a few recent developments in numerical relativity are sketched in this brief overview.

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arXiv2005

Relativistic Magnetohydrodynamics In Dynamical Spacetimes: Numerical Methods And Tests

Many problems at the forefront of theoretical astrophysics require the treatment of magnetized fluids in dynamical, strongly curved spacetimes. Such problems include the origin of gamma-ray bursts, magnetic braking of differential rotation in nascent neutron stars arising from stellar core collapse or binary neutron star merger, the formation of jets and magnetized disks around newborn black holes, etc. To model these phenomena, all of which involve both general relativity (GR) and magnetohydrodynamics (MHD), we have developed a GRMHD code capable of evolving MHD fluids in dynamical spacetimes. Our code solves the Einstein-Maxwell-MHD system of coupled equations in axisymmetry and in full 3+1 dimensions. We evolve the metric by integrating the BSSN equations, and use a conservative, shock-capturing scheme to evolve the MHD equations. Our code gives accurate results in standard MHD code-test problems, including magnetized shocks and magnetized Bondi flow. To test our code's ability to evolve the MHD equations in a dynamical spacetime, we study the perturbations of a homogeneous, magnetized fluid excited by a gravitational plane wave, and we find good agreement between the analytic and numerical solutions.

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arXiv2005

Excitation Of MHD Modes With Gravitational Waves: A Testbed For Numerical Codes

We consider a gravitational wave oscillating in an initially homogeneous, magnetized fluid. The fluid is perfectly conducting and isentropic, and the magnetic field is initially uniform. We find analytic solutions for the case in which the gravitational wave is linear and unaffected by the background fluid and field. Our solutions show how gravitational waves can excite three magnetohydrodynamic (MHD) modes in the fluid: Alfven waves, and both fast and slow magnetosonic waves. Our analytic solutions are particularly useful for testing numerical codes designed to treat general relativistic MHD in dynamical spacetimes, as we demonstrate in a companion paper.

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arXiv2004

Spin, Accretion and the Cosmological Growth of Supermassive Black Holes

If supermassive black holes (SMBHs) are the energy sources that power quasars and active galactic nuclei, then QSO SDSS 1148+5251, the quasar with the highest redshift (z_QSO=6.43), hosts a supermassive black hole formed within 0.9 Gyr after the Big Bang. This requirement places constraints on the cosmological formation of SMBHs, believed to grow from smaller initial seeds by a combination of accretion and mergers. We focus on gas accretion onto seeds produced by the collapse of Pop III stars at high redshift. We incorporate the results of recent relativistic, MHD simulations of disk accretion onto Kerr black holes to track the coupled evolution of the masses and spins of the holes. We allow for an additional amplification of ~10^4 in the mass of a typical seed due to mergers, consistent with recent Monte Carlo simulations of hierarchical mergers of cold, dark matter halos containing black hole seeds. We find that the growth of Pop III black hole seeds to ~10^9 M_sun by z_QSO = 6.43 favors MHD accretion disks over standard thin disks. MHD disks tend to drive the holes to a submaximal equilibrium spin rate a/M ~ 0.95 and radiation efficiency epsilon_M ~ 0.2, while standard thin disks drive them to maximal spin (a/M = 1) and efficiency (epsilon_M = 0.42). This small difference in efficiency results in a huge difference in mass amplification by accretion at the Eddington limit. The MHD equilibrium efficiency is consistent with the observed ratio of the QSO plus AGN luminosity density to the local SMBH mass density. Our prototype analysis is designed to stimulate the incorporation of results from relativistic stellar collapse and MHD accretion simulations in future Monte Carlo simulations of hierarchical structure formation to better determine the cosmological role of SMBHs and their mass and spin distributions.

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arXiv2004

Quasi-equilibrium Binary Black Hole Initial Data for Dynamical Evolutions

We present a formalism for constructing quasi-equilibrium binary black hole initial data suitable for numerical evolution. We construct quasi-equilibrium models by imposing an approximate helical Killing symmetry appropriate for quasi-circular orbits. We use the sum of two Kerr-Schild metrics as our background metric, thereby improving on conformally flat backgrounds that do not accommodate rotating black holes and providing a horizon-penetrating lapse, convenient for implementing black hole excision. We set inner boundary conditions at an excision radius well inside the apparent horizon and construct these boundary conditions to incorporate the quasi-equilibrium condition and recover the solution for isolated black holes in the limit of large separation. We use our formalism both to generate initial data for binary black hole evolutions and to construct a crude quasi-equilibrium, inspiral sequence for binary black holes of fixed irreducible mass.

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arXiv2004

The Secular Bar-Mode Instability in Rapidly Rotating Stars Revisited

Uniformly rotating, homogeneous, incompressible Maclaurin spheroids that spin sufficiently rapidly are secularly unstable to nonaxisymmetric, bar-mode perturbations when viscosity is present. The intuitive explanation is that energy dissipation by viscosity can drive an unstable spheroid to a stable, triaxial configuration of lower energy - a Jacobi ellipsoid. But what about rapidly rotating compressible stars? Unlike incompressible stars, which contain no internal energy and therefore immediately liberate all the energy dissipated by viscosity, compressible stars have internal energy and can retain the dissipated energy as internal heat. Now compressible stars that rotate sufficiently rapidly and also manage to liberate this dissipated energy very quickly are known to be unstable to bar-mode perturbations, like their incompressible counterparts. But what is the situation for rapidly rotating compressible stars that have very long cooling timescales, so that all the energy dissipated by viscosity is retained as heat, whereby the total energy of the star remains constant on a secular (viscous) evolution timescale? Are such stars also unstable to the nonlinear growth of bar modes, or is the viscous heating sufficient to cause them to expand, drive down the ratio of rotational kinetic to gravitational potential energy T/|W| ~ 1/R, where R is the equatorial radius, and turn off the instability before it gets underway? If the instability still arises in such stars, at what rotation rate do they become unstable, and to what final state do they evolve? We provide answers to these questions in the context of the compressible ellipsoid model for rotating stars. The results should serve as useful guides for numerical simulations in 3+1 dimensions for rotating stars containing viscosity.

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arXiv2004

Black Hole-Neutron Star Binaries in General Relativity: Quasiequilibrium Formulation

We present a new numerical method for the construction of quasiequilibrium models of black hole-neutron star binaries. We solve the constraint equations of general relativity, decomposed in the conformal thin-sandwich formalism, together with the Euler equation for the neutron star matter. We take the system to be stationary in a corotating frame and thereby assume the presence of a helical Killing vector. We solve these coupled equations in the background metric of a Kerr-Schild black hole, which accounts for the neutron star's black hole companion. In this paper we adopt a polytropic equation of state for the neutron star matter and assume large black hole--to--neutron star mass ratios. These simplifications allow us to focus on the construction of quasiequilibrium neutron star models in the presence of strong-field, black hole companions. We summarize the results of several code tests, compare with Newtonian models, and locate the onset of tidal disruption in a fully relativistic framework.

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arXiv2004

Collapse of Uniformly Rotating Stars to Black Holes and the Formation of Disks

Simulations in general relativity show that the outcome of collapse of a marginally unstable, uniformly rotating star spinning at the mass-shedding limit depends critically on the equation of state. For a very stiff equation of state, which is likely to characterize a neutron star, essentially all of the mass and angular momentum of the progenitor are swallowed by the Kerr black hole formed during the collapse, leaving nearly no residual gas to form a disk. For a soft equation of state with an adiabatic index Γ- 4/3 << 1, which characterizes a very massive or supermassive star supported predominantly by thermal radiation pressure, as much as 10% of the mass of the progenitor avoids capture and goes into a disk about the central hole. We present a semi-analytic calculation that corroborates these numerical findings and shows how the final outcome of such a collapse may be determined from simple physical considerations. In particular, we employ a simple energy variational principle with an approximate, post-Newtonian energy functional to determine the structure of a uniformly rotating, polytropic star at the onset of collapse as a function of polytropic index n, where Γ= 1+1/n. We then use this data to calculate the mass and spin of the final black hole and ambient disk. We show that the fraction of the total mass that remains in the disk falls off sharply as 3-n (equivalently, Γ- 4/3) increases.

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arXiv2004

General relativistic hydrodynamics with viscosity: contraction, catastrophic collapse, and disk formation in hypermassive neutron stars

Viscosity and magnetic fields drive differentially rotating stars toward uniform rotation, which has important consequences in many astrophysical contexts. For example, merging binary neutron stars can form a "hypermassive" remnant, i.e. a differentially rotating star with a mass greater than the maximum allowed by uniform rotation. The removal of the centrifugal support provided by differential rotation can lead to delayed collapse of the remnant to a black hole, accompanied by a burst of gravitational radiation. Both magnetic fields and viscosity alter the structure of differentially rotating stars on secular timescales, making numerical tracking of the evolution difficult. Here, we present the first simulations of rapidly rotating stars with shear viscosity in full general relativity. We self-consistently include viscosity in our relativistic hydrodynamic code to solve the relativistic Navier-Stokes equations both in axisymmetry and in full 3+1 dimensions. In axisymmetry, we follow secular evolution with high resolution over dozens of rotation periods (thousands of M). We find that viscosity operating in a hypermassive star generically leads to the formation of a compact, uniformly rotating core surrounded by a low-density disk. These uniformly rotating cores are often, but not always, unstable to gravitational collapse. In the unstable cases, we follow the collapse and determine the mass and the spin of the final black hole and ambient disk. In all cases studied, the rest mass of the resulting disk is found to be 10-20% of the original star, whether surrounding a uniformly rotating core or a rotating black hole. This study foreshadows more detailed, future simulations of secular processes, including magnetic effects, in relativistic stars.

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arXiv2004

Dynamical Determination of the Innermost Stable Circular Orbit of Binary Neutron Stars

We determine the innermost stable circular orbit (ISCO) of binary neutron stars (BNSs) by performing dynamical simulations in full general relativity. Evolving quasiequilibrium (QE) binaries that begin at different separations, we bracket the location of the ISCO by distinguishing stable circular orbits from unstable plunges. We study Gamma=2 polytropes of varying compactions in both corotational and irrotational equal-mass binaries. For corotatonal binaries we find an ISCO orbital angular frequency somewhat smaller than that determined by applying turning-point methods to QE initial data. For the irrotational binaries the initial data sequences terminate before reaching a turning point, but we find that the ISCO frequency is reached prior to the termination point. Our findings suggest that the ISCO frequency varies with compaction but does not depend strongly on the stellar spin. Since the observed gravitational wave signal undergoes a transition from a nearly periodic ``chirp'' to a burst at roughly twice the ISCO frequency, the measurement of its value by laser interferometers (e.g LIGO) will be important for determining some of the physical properites of the underlying stars

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arXiv2004

Effect of Differential Rotation on the Maximum Mass of Neutron Stars: Realistic Nuclear Equations of State

The merger of binary neutron stars is likely to lead to differentially rotating remnants. In this paper, we survey several cold nuclear equations of state (EOSs) and numerically construct models of differentially rotating neutron stars in general relativity. For each EOS we tabulate maximum allowed masses as a function of the degree of differential rotation. We also determine effective polytropic indices, and compare the maximum allowed masses with those for the corresponding polytropes. We consistently find larger mass increases for the polytropes, but even for the nuclear EOSs we typically find maximum masses 50% higher than the corresponding values for nonrotating (TOV) stars. We evaluate our findings for the six observed binary neutron star (pulsar) systems, including the recently discovered binary pulsar J0737-3039. For each EOS we determine whether their merger will automatically lead to prompt collapse to a black hole, or whether the remnant can be supported against collapse by uniform rotation (possibly as a supramassive star) or differential rotation (possibly as a hypermassive star). For hypermassive stars, delayed collapse to a black hole is likely. For the most recent EOSs we survey the merger remnants can all be supported by rotation against prompt collapse, but their actual fate will depend on the nonequilibrium dynamics of the coalescence event. Gravitational wave observations of coalescing binary neutron stars may be able to distinguish these outcomes -- no, delayed or prompt collapse -- and thereby constrain possible EOSs.

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arXiv2004

Relativistic Hydrodynamic Evolutions with Black Hole Excision

We present a numerical code designed to study astrophysical phenomena involving dynamical spacetimes containing black holes in the presence of relativistic hydrodynamic matter. We present evolutions of the collapse of a fluid star from the onset of collapse to the settling of the resulting black hole to a final stationary state. In order to evolve stably after the black hole forms, we excise a region inside the hole before a singularity is encountered. This excision region is introduced after the appearance of an apparent horizon, but while a significant amount of matter remains outside the hole. We test our code by evolving accurately a vacuum Schwarzschild black hole, a relativistic Bondi accretion flow onto a black hole, Oppenheimer-Snyder dust collapse, and the collapse of nonrotating and rotating stars. These systems are tracked reliably for hundreds of M following excision, where M is the mass of the black hole. We perform these tests both in axisymmetry and in full 3+1 dimensions. We then apply our code to study the effect of the stellar spin parameter J/M^2 on the final outcome of gravitational collapse of rapidly rotating n = 1 polytropes. We find that a black hole forms only if J/M^2<1, in agreement with previous simulations. When J/M^2>1, the collapsing star forms a torus which fragments into nonaxisymmetric clumps, capable of generating appreciable ``splash'' gravitational radiation.

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arXiv2003

Magnetic Braking in Differentially Rotating, Relativistic Stars

We study the magnetic braking and viscous damping of differential rotation in incompressible, uniform density stars in general relativity. Differentially rotating stars can support significantly more mass in equilibrium than nonrotating or uniformly rotating stars. The remnant of a binary neutron star merger or supernova core collapse may produce such a "hypermassive" neutron star. Although a hypermassive neutron star may be stable on a dynamical timescale, magnetic braking and viscous damping of differential rotation will ultimately alter the equilibrium structure, possibly leading to delayed catastrophic collapse. Here we consider the slow-rotation, weak-magnetic field limit in which E_rot << E_mag << W, where E_rot is the rotational kinetic energy, E_mag is the magnetic energy, and W is the gravitational binding energy of the star. We assume the system to be axisymmetric and solve the MHD equations in both Newtonian gravitation and general relativity. Toroidal magnetic fields are generated whenever the angular velocity varies along the initial poloidal field lines. We find that the toroidal fields and angular velocities oscillate independently along each poloidal field line, which enables us to transform the original 2+1 equations into 1+1 form and solve them along each field line independently. The incoherent oscillations on different field lines stir up turbulent-like motion in tens of Alfven timescales ("phase mixing"). In the presence of viscosity, the stars eventually are driven to uniform rotation, with the energy contained in the initial differential rotation going into heat. Our evolution calculations serve as qualitative guides and benchmarks for future, more realistic MHD simulations in full 3+1 general relativity.

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arXiv2003

Black Hole Spin Evolution

We consider a subset of the physical processes that determine the spin j = a/M of astrophysical black holes. These include: (1) Initial conditions. Recent models suggest that the collapse of supermassive stars are likely to produce black holes with j ~ 0.7. (2) Major mergers. The outcome of a nearly equal mass black hole-black hole merger is not yet known, but we review the current best guesses and analytic bounds. (3) Minor mergers. We recover the result of Blandford & Hughes that accretion of small companions with isotropically distributed orbital angular momenta results in spindown, with j ~ M^{-7/3}. (4) Accretion. We present new results from fully relativistic magnetohydrodynamic accretion simulations. These show that, at least for one sequence of flow models, spin equilibrium (dj/dt = 0) is reached for j ~ 0.9, far less than the canonical value 0.998 of Thorne that was derived in the absence of MHD effects. This equilibrium value may not apply to all accretion flows, particularly thin disks. Nevertheless, it opens the possibility that black holes that have grown primarily through accretion are not maximally rotating.

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arXiv2003

Magnetic Braking and Viscous Damping of Differential Rotation in Cylindrical Stars

Differential rotation in stars generates toroidal magnetic fields whenever an initial seed poloidal field is present. The resulting magnetic stresses, along with viscosity, drive the star toward uniform rotation. This magnetic braking has important dynamical consequences in many astrophysical contexts. For example, merging binary neutron stars can form "hypermassive" remnants supported against collapse by differential rotation. The removal of this support by magnetic braking induces radial fluid motion, which can lead to delayed collapse of the remnant to a black hole. We explore the effects of magnetic braking and viscosity on the structure of a differentially rotating, compressible star, generalizing our earlier calculations for incompressible configurations. The star is idealized as a differentially rotating, infinite cylinder supported initially by a polytropic equation of state. The gas is assumed to be infinitely conducting and our calculations are performed in Newtonian gravitation. Though highly idealized, our model allows for the incorporation of magnetic fields, viscosity, compressibility, and shocks with minimal computational resources in a 1+1 dimensional Lagrangian MHD code. Our evolution calculations show that magnetic braking can lead to significant structural changes in a star, including quasistatic contraction of the core and ejection of matter in the outermost regions to form a wind or an ambient disk. These calculations serve as a prelude and a guide to more realistic MHD simulations in full 3+1 general relativity.

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arXiv2003

Relativistic Collapse of Rotating Supermassive Stars to Supermassive Black Holes

There is compelling evidence that supermassive black holes (SMBHs) exist. Yet the origin of these objects, or their seeds, is still unknown. We are performing general relativistic simulations of gravitational collapse to black holes in different scenarios to help reveal how SMBH seeds might arise in the universe. SMBHs with ~ 10^9 solar masses must have formed by z > 6, or within 10^9 yrs after the Big Bang, to power quasars. It may be difficult for gas accretion to build up such a SMBH by this time unless the initial seed black hole already has a substantial mass. One plausible progenitor of a massive seed black hole is a supermassive star (SMS). We have followed the collapse of a SMS to a SMBH by means of 3D hydrodynamic simulations in post-Newtonian gravity and axisymmetric simulations in full general relativity. The initial SMS of arbitrary mass M in these simulations rotates uniformly at the mass--shedding limit and is marginally unstable to radial collapse. The final black hole mass and spin are determined to be M_h/M ~ 0.9 and J_h/M_h^2 ~ 0.75. The remaining mass goes into a disk of mass M_{disk}/M ~ 0.1. This disk arises even though the total spin of the progenitor star, J/M^2 = 0.97, is safely below the Kerr limit. The collapse generates a mild burst of gravitational radiation. Nonaxisymmetric bars or one-armed spirals may arise during the quasi-stationary evolution of a SMS, during its collapse, or in the ambient disk about the hole, and are potential sources of quasi-periodic waves, detectable by LISA.

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arXiv2003

Relativistic Models for Binary Neutron Stars with Arbitrary Spins

We introduce a new numerical scheme for solving the initial value problem for quasiequilibrium binary neutron stars allowing for arbitrary spins. The coupled Einstein field equations and equations of relativistic hydrodynamics are solved in the Wilson-Mathews conformal thin sandwich formalism. We construct sequences of circular-orbit binaries of varying separation, keeping the rest mass and circulation constant along each sequence. Solutions are presented for configurations obeying an n=1 polytropic equation of state and spinning parallel and antiparallel to the orbital angular momentum. We treat stars with moderate compaction ((m/R) = 0.14) and high compaction ((m/R) = 0.19). For all but the highest circulation sequences, the spins of the neutron stars increase as the binary separation decreases. Our zero-circulation cases approximate irrotational sequences, for which the spin angular frequencies of the stars increases by 13% (11%) of the orbital frequency for (m/R) = 0.14 ((m/R) = 0.19) by the time the innermost circular orbit is reached. In addition to leaving an imprint on the inspiral gravitational waveform, this spin effect is measurable in the electromagnetic signal if one of the stars is a pulsar visible from Earth.

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