arXiv subjects

Stuart L. Shapiro

Publications and source records attributed to Stuart L. Shapiro.

At least 109 records · Page 6Linked to original sources

arXiv2012

Relativistic MHD in dynamical spacetimes: Improved EM gauge condition for AMR grids

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 eigenvalue analysis and a numerical study that zero-speed modes in the algebraic gauge, coupled with the frequency filtering that occurs on refinement level boundaries, are responsible for the creation of spurious magnetic fields. We show that the EM Lorenz gauge exhibits no zero-speed modes, and as a consequence, spurious magnetic effects are quickly propagated away, allowing for long-term, stable magnetized BHNS evolutions. Our study demonstrates how the EM gauge degree of freedom can be chosen to one's advantage, and that for magnetized BHNS simulations the Lorenz gauge constitutes a major improvement over the algebraic gauge.

astro-ph.HE↗

arXiv2011

Oppenheimer-Snyder Collapse in Moving-Puncture Coordinates

Moving-puncture coordinates are commonly used in numerical simulations of black holes. Their properties for vacuum Schwarzschild black holes have been analyzed in a number of studies. The behavior of moving-puncture coordinates in spacetimes containing matter, however, is less well understood. In this paper we explore the behavior of these coordinates for Oppenheimer-Snyder collapse, i.e., the collapse of a uniform density, pressureless sphere of dust initially at rest to a black hole. Oppenheimer-Snyder collapse provides a stringent test of the singularity-avoiding properties of moving-puncture coordinates, since the singularity can form more quickly than it would for matter with pressure. Our results include analytical expressions for the matter density, lapse function, and mean curvature at early times, as well as interesting limits for later times. We also carry out numerical simulations to obtain the full solution and these show that, even in the absence of pressure, moving-puncture coordinates are able to avoid the singularity. At late times the geometry settles down to a trumpet slice of a vacuum black hole.

gr-qc↗

arXiv2011

Binary black hole mergers in gaseous disks: Simulations in general relativity

Simultaneous gravitational and electromagnetic wave observations of merging black hole binaries (BHBHs) can provide unique opportunities to study gravitation physics, accretion and cosmology. Here we perform fully general relativistic, hydrodynamic simulations of equal-mass, nonspinning BHBHs coalescing in a circumbinary disk. We evolve the metric using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of Einstein's field equations with standard moving puncture gauge conditions. We handle the hydrodynamics via a high-resolution shock-capturing (HRSC) scheme. We track the inspiral starting from a binary separation of 10M, where M is the total binary mass. We take the disks to have an inner radius at R_in~15M to account for the hollow created by the binary torques. Our disks extend to R=65M and have an initial scale height of H/R=0.03-0.11. The gas is governed by a Gamma-law EOS, with Gamma equal to 5/3, 4/3, and 1.1. Disks are allowed to relax in the "early inspiral" epoch to provide quasistationary realistic initial data. We then evolve the metric and matter during the "late inspiral and merger" epoch. The later simulations are designed to track BHBH inspiral following disk-binary decoupling, through merger and ringdown, terminating before viscosity has time to fill the hollow about the remnant. We compute the gas flow and accretion rate and estimate the electromagnetic luminosity due to bremsstrahlung and synchrotron emission as a perturbation for optically thin disks. The synchrotron component of the luminosity peaks in the infrared band and should be detectable by WFIRST and possibly the LSST for a 10^8 M_sun binary embedded in a disk with a density n~10^12/cm^3 at z=1, beginning with a maximum value of $L~10^46 n_12^2 M_8^3 erg/s at decoupling, and decreasing steadily over a timescale of ~100 M_8 hours to a value of L~10^45 n_12^2 M_8^3 erg/s at merger.

astro-ph.HE↗

arXiv2011

Constraint propagation equations of the 3+1 decomposition of f(R) gravity

Theories of gravity other than general relativity (GR) can explain the observed cosmic acceleration without a cosmological constant. One such class of theories of gravity is f(R). Metric f(R) theories have been proven to be equivalent to Brans-Dicke (BD) scalar-tensor gravity without a kinetic term. Using this equivalence and a 3+1 decomposition of the theory it has been shown that metric f(R) gravity admits a well-posed initial value problem. However, it has not been proven that the 3+1 evolution equations of metric f(R) gravity preserve the (hamiltonian and momentum) constraints. In this paper we show that this is indeed the case. In addition, we show that the mathematical form of the constraint propagation equations in BD-equilavent f(R) gravity and in f(R) gravity in both the Jordan and Einstein frames, is exactly the same as in the standard ADM 3+1 decomposition of GR. Finally, we point out that current numerical relativity codes can incorporate the 3+1 evolution equations of metric f(R) gravity by modifying the stress-energy tensor and adding an additional scalar field evolution equation. We hope that this work will serve as a starting point for relativists to develop fully dynamical codes for valid f(R) models.

gr-qc↗

arXiv2011

Head-on collisions of binary white dwarf--neutron stars: Simulations in full general relativity

We simulate head-on collisions from rest at large separation of binary white dwarf -- neutron stars (WDNSs) in full general relativity. Our study serves as a prelude to our analysis of the circular binary WDNS problem. We focus on compact binaries whose total mass exceeds the maximum mass that a cold degenerate star can support, and our goal is to determine the fate of such systems. A fully general relativistic hydrodynamic computation of a realistic WDNS head-on collision is prohibitive due to the large range of dynamical time scales and length scales involved. For this reason, we construct an equation of state (EOS) which captures the main physical features of NSs while, at the same time, scales down the size of WDs. We call these scaled-down WD models "pseudo-WDs (pWDs)". Using pWDs, we can study these systems via a sequence of simulations where the size of the pWD gradually increases toward the realistic case. We perform two sets of simulations; One set studies the effects of the NS mass on the final outcome, when the pWD is kept fixed. The other set studies the effect of the pWD compaction on the final outcome, when the pWD mass and the NS are kept fixed. All simulations show that 14%-18% of the initial total rest mass escapes to infinity. All remnant masses still exceed the maximum rest mass that our cold EOS can support (1.92 solar masses), but no case leads to prompt collapse to a black hole. This outcome arises because the final configurations are hot. All cases settle into spherical, quasiequilibrium configurations consisting of a cold NS core surrounded by a hot mantle, resembling Thorne-Zytkow objects. Extrapolating our results to realistic WD compactions, we predict that the likely outcome of a head-on collision of a realistic, massive WDNS system will be the formation of a quasiequilibrium Thorne-Zytkow-like object.

astro-ph.HE↗

arXiv2010

Relativistic magnetohydrodynamics in dynamical spacetimes: A new AMR implementation

We have written and tested a new general relativistic magnetohydrodynamics (GRMHD) code, capable of evolving MHD fluids in dynamical spacetimes with adaptive-mesh refinement (AMR). Our code solves the Einstein-Maxwell-MHD system of coupled equations in full 3+1 dimensions, evolving the metric via the Baumgarte-Shapiro Shibata-Nakamura (BSSN) formalism and the MHD and magnetic induction equations via a conservative, high-resolution shock-capturing scheme. The induction equations are recast as an evolution equation for the magnetic vector potential, which exists on a grid that is staggered with respect to the hydrodynamic and metric variables. The divergenceless constraint div(B)=0 is enforced by the curl of the vector potential. Our MHD scheme is fully compatible with AMR, so that fluids at AMR refinement boundaries maintain div(B)=0. In simulations with uniform grid spacing, our MHD scheme is numerically equivalent to a commonly used, staggered-mesh constrained-transport scheme. We present code validation test results, both in Minkowski and curved spacetimes. They include magnetized shocks, nonlinear Alfvén waves, cylindrical explosions, cylindrical rotating disks, magnetized Bondi tests, and the collapse of a magnetized rotating star. Some of the more stringent tests involve black holes. We find good agreement between analytic and numerical solutions in these tests, and achieve convergence at the expected order.

astro-ph.HE↗

arXiv2010

Evolution of near-extremal-spin black holes using the moving puncture technique

We propose a new radial coordinate to write the Kerr metric in puncture form. Unlike the quasi-radial coordinate introduced previously, the horizon radius remains finite in our radial coordinate in the extreme Kerr limit a/M -> 1. This significantly improves the accuracy of the evolution of black holes with spins close to the extreme Kerr limit. We are able to evolve accurately both stationary and boosted black holes with spins as high as a/M=0.99 using initial data constructed in these new puncture coordinates. Initial data of compact binaries with rapidly spinning black holes can be constructed using our proposed new puncture metric for the background conformal metric. Our simulations for single black holes suggest that such initial data can be evolved successfully by the moving puncture technique.

gr-qc↗

arXiv2009

Binary Black Hole Mergers in Gaseous Environments: "Binary Bondi" and "Binary Bondi-Hoyle-Lyttleton" Accretion

Merging supermassive black hole-black hole (BHBH) binaries produced in galaxy mergers are promising sources of detectable gravitational waves. If such a merger takes place in a gaseous environment, there is a possibility of a simultaneous detection of electromagnetic and gravitational radiation, as the stirring, shock heating and accretion of the gas may produce variability and enhancements in the electromagnetic flux. Such a simultaneous detection can provide a wealth of opportunities to study gravitational physics, accretion physics, and cosmology. We investigate this scenario by performing fully general relativistic, hydrodynamic simulations of merging, equal-mass, nonspinning BHBH binaries embedded in gas clouds. We evolve the metric using the BSSN formulation with standard moving puncture gauge conditions and handle the hydrodynamics via a high-resolution shock-capturing (HRSC) scheme. We consider both "binary Bondi accretion" in which the binary is at rest relative to the ambient gas cloud, as well as "binary Bondi-Hoyle-Lyttleton accretion" in which the binary moves relative to the gas cloud. The gas cloud is assumed to be homogeneous far from the binary and governed by a Γ-law equation of state. We vary Γbetween 4/3 and 5/3. For each simulation, we compute the gas flow and accretion rate and estimate the electromagnetic luminosity due to bremsstrahlung and synchrotron emission. We find evidence for significant enhancements in both the accretion rate and luminosity over values for a single black hole of the same mass as the binary. We estimate that this luminosity enhancement should be detectable by LSST for a 10^6 M_sun binary in a hot gas cloud of density n~10/cm^3 and temperature T~10^6 K at z=1, reaching a maximum of L~3x10^43 erg/s, with the emission peaking in the visible band.

astro-ph.HE↗

arXiv2009

Filling the disk hollow following binary black hole merger: The transient accretion afterglow

Tidal torques from a binary black hole (BHBH) empty out the central regions in any circumbinary gaseous accretion disk. The balance between tidal torques and viscosity maintain the inner edge of the disk at a radius r ~ 1.5a -- 2a, where a is the binary semimajor axis. Eventually, the inspiraling binary decouples from disk and merges, leaving behind a central hollow ("donut hole") in the disk orbiting the remnant black hole. We present a simple, time-dependent, Newtonian calculation that follows the secular (viscous) evolution of the disk as it fills up the hollow down to the black hole innermost stable circular orbit and then relaxes to stationary equilibrium. We use our model to calculate the electromagnetic radiation ("afterglow") spectrum emitted during this transient accretion epoch. Observing the temporal increase in the total electromagnetic flux and the hardening of the spectrum as the donut hole fills may help confirm a BHBH merger detected by a gravitational wave interferometer. We show how the very existence of the initial hollow can lead to super-Eddington accretion during this secular phase if the rate is not very far below Eddington prior to decoupling. Our model, though highly idealized, may be useful in establishing some of the key parameters, thermal emission features and scalings that characterize this transient. It can serve as a guide in the design and calibration of future radiation-magnetohydrodynamic simulations in general relativity.

astro-ph.HE↗

arXiv2009

Merger of white dwarf-neutron star binaries: Prelude to hydrodynamic simulations in general relativity

White dwarf-neutron star binaries generate detectable gravitational radiation. We construct Newtonian equilibrium models of corotational white dwarf-neutron star (WDNS) binaries in circular orbit and find that these models terminate at the Roche limit. At this point the binary will undergo either stable mass transfer (SMT) and evolve on a secular time scale, or unstable mass transfer (UMT), which results in the tidal disruption of the WD. The path a given binary will follow depends primarily on its mass ratio. We analyze the fate of known WDNS binaries and use population synthesis results to estimate the number of LISA-resolved galactic binaries that will undergo either SMT or UMT. We model the quasistationary SMT epoch by solving a set of simple ordinary differential equations and compute the corresponding gravitational waveforms. Finally, we discuss in general terms the possible fate of binaries that undergo UMT and construct approximate Newtonian equilibrium configurations of merged WDNS remnants. We use these configurations to assess plausible outcomes of our future, fully relativistic simulations of these systems. If sufficient WD debris lands on the NS, the remnant may collapse, whereby the gravitational waves from the inspiral, merger, and collapse phases will sweep from LISA through LIGO frequency bands. If the debris forms a disk about the NS, it may fragment and form planets.

astro-ph.HE↗

arXiv2009

A formalism for the construction of binary neutron stars with arbitrary circulation

Most numerical models of binary stars - in particular neutron stars in compact binaries - assume the companions to be either corotational or irrotational. Either one of these assumptions leads to a significant simplification in the hydrodynamic equations of stationary equilibrium. In this paper we develop a new formalism for the construction of binary stars with circulation intermediate between corotational and irrotational. Generalizing the equations for irrotational flow we cast the Euler equation, which is an algebraic equation in the case of corotational or irrotational fluid flow, as an elliptic equation for a new auxiliary quantity. We also suggest a parameterized decomposition of the fluid flow that allows for a variation of the stellar circulation.

gr-qc↗

arXiv2009

Testing gravitational-wave searches with numerical relativity waveforms: Results from the first Numerical INJection Analysis (NINJA) project

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the Initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter-estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.

gr-qc↗

arXiv2009

Status of NINJA: the Numerical INJection Analysis project

The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new collaborative effort between the numerical relativity community and the data analysis community. NINJA focuses on modeling and searching for gravitational wave signatures from the coalescence of binary system of compact objects. We review the scope of this collaboration and the components of the first NINJA project, where numerical relativity groups shared waveforms and data analysis teams applied various techniques to detect them when embedded in colored Gaussian noise.

gr-qc↗

arXiv2009

Relativistic Simulations of Black Hole-Neutron Star Mergers: Effects of black-hole spin

Black hole-neutron star (BHNS) binary mergers are candidate engines for generating both short-hard gamma-ray bursts (SGRBs) and detectable gravitational waves. Using our most recent conformal thin-sandwich BHNS initial data and our fully general relativistic hydrodynamics code, which is now AMR-capable, we are able to efficiently and accurately simulate these binaries from large separations through inspiral, merger, and ringdown. We evolve the metric using the BSSN formulation with the standard moving puncture gauge conditions and handle the hydrodynamics with a high-resolution shock-capturing scheme. We explore the effects of BH spin (aligned and anti-aligned with the orbital angular momentum) by evolving three sets of initial data with BH:NS mass ratio q=3: the data sets are nearly identical, except the BH spin is varied between a/M = -0.5 (anti-aligned), 0.0, and 0.75. The number of orbits before merger increases with a/M, as expected. We also study the nonspinning BH case in more detail, varying q between 1, 3, and 5. We calculate gravitational waveforms for the cases we simulate and compare them to binary black-hole waveforms. Only a small disk (< 0.01 M_sun) forms for the anti-aligned spin case (a/M = -0.5) and for the most extreme mass ratio case (q=5). By contrast, a massive (M_disk is about 0.2 M_sun), hot disk forms in the rapidly spinning (a/M = 0.75) aligned BH case. Such a disk could drive a SGRB,possibly by, e.g., producing a copious flux of neutrino-antineutino pairs.

astro-ph↗

arXiv2008

Fully General Relativistic Simulations of Black Hole-Neutron Star Mergers

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 the 2:1 mass ratio case. These ambient disks reach temperatures suitable for triggering SGRBs, but their masses may be too small to produce the required total energy output. We measure gravitational waveforms and compute the effective strain in frequency space, finding measurable differences between our waveforms and those produced by binary black hole mergers within the advanced LIGO band. These differences appear at frequencies corresponding to the emission that occurs when the NS is tidally disrupted and accreted by the black hole. The resulting information about the radius of the neutron star may be used to constrain the neutron star equation of state.

astro-ph↗

arXiv2008

General relativistic simulations of magnetized binary neutron star mergers

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 the initial configurations and study the subsequent evolution. For cases in which the remnant is a hypermassive neutron star, we see measurable differences in both the amplitude and phase of the gravitational waveforms following the merger. For cases in which the remnant is a black hole surrounded by a disk, the disk mass and the gravitational waveforms are about the same as the unmagnetized cases. Magnetic fields substantially affect the long-term, secular evolution of a hypermassive neutron star (driving `delayed collapse') and an accretion disk around a nascent black hole.

astro-ph↗

arXiv2008

Relativistic Radiation Magnetohydrodynamics in Dynamical Spacetimes: Numerical Methods and Tests

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, we have developed a general relativistic code capable of evolving MHD fluids and radiation in dynamical spacetimes. Our code solves the coupled Einstein-Maxwell-MHD-Radiation system of equations both in axisymmetry and in full 3+1 dimensions. We evolve the metric by integrating the BSSN equations, and use a conservative, high-resolution shock-capturing scheme to evolve both the MHD and radiation moment equations. In this paper, we implement our scheme for optically thick gases and grey-body opacities. Our code gives accurate results in a suite of tests involving radiating shocks and nonlinear waves propagating in Minkowski spacetime. In addition, to test our code's ability to evolve the relativistic radiation-MHD equations in strong-field dynamical spacetimes, we study "thermal Oppenheimer-Snyder collapse" to a black hole, and find good agreement between analytic and numerical solutions.

astro-ph↗

arXiv2008

Collapse of magnetized hypermassive neutron stars in general relativity: Disk evolution and outflows

We study the evolution in axisymmetry of accretion disks formed self-consistently through collapse of magnetized hypermassive neutron stars to black holes. Such stars can arise following the merger of binary neutron stars. They are differentially rotating, dynamically stable, and have rest masses exceeding the mass limit for uniform rotation. However, hypermassive neutron stars are secularly unstable to collapse due to MHD-driven angular momentum transport. The rotating black hole which forms in this process is surrounded by a hot, massive, magnetized torus and a magnetic field collimated along the spin axis. This system is a candidate for the central engine of a short-hard gamma-ray burst (GRB). Our code integrates the coupled Einstein-Maxwell-MHD equations and is used to follow the collapse of magnetized hypermassive neutron star models in full general relativity until the spacetime settles down to a quasi-stationary state. We then employ the Cowling approximation, in which the spacetime is frozen, to track the subsequent evolution of the disk. This approximation allows us to greatly extend the disk evolutions and study the resulting outflows, which may be relevant to the generation of a GRB. We find that outflows are suppressed when a stiff equation of state is assumed for low density disk material and are sensitive to the initial magnetic field configuration.

astro-ph↗