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We present twelve new simulations of unequal mass neutron star mergers. The simulations were preformed with the SpEC code, and utilize nuclear-theory based equations of state and a two-moment gray neutrino transport scheme with an improved energy estimate based on evolving the number density. We model the neutron stars with the SFHo, LS220 and DD2 equations of state (EOS) and we study the neutrino and matter emission of all twelve models to search for robust trends between binary parameters and emission characteristics. We find that the total mass of the dynamical ejecta exceeds $0.01M_\odot$ only for SFHo with weak dependence on the mass-ratio across all models. We find that the ejecta have a broad electron fraction ($Y_e$) distribution ($\approx 0.06-0.48$), with mean $0.2$. $Y_e$ increases with neutrino irradiation over time, but decreases with increasing binary asymmetry. We also find that the models have ejecta with a broad asymptotic velocity distribution ($\approx 0.05-0.7c$). The average velocity lies in the range $0.2c - 0.3c$ and decreases with binary asymmetry. Furthermore, we find that disk mass increases with binary asymmetry and stiffness of the EOS. The $Y_e$ of the disk increases with softness of the EOS. The strongest neutrino emission occurs for the models with soft EOS. For (anti) electron neutrinos we find no significant dependence of the magnitude or angular distribution or neutrino luminosity with mass-ratio. The heavier neutrino species have a luminosity dependence on mass-ratio but an angular distribution which does not change with mass-ratio., 23 pages, 15 figures

Gravitational waves and electromagnetic signals from merging neutron star binaries provide valuable information about the the properties of dense matter, the formation of heavy elements, and high-energy astrophysics. To fully leverage observations of these systems, we need numerical simulations that provide reliable predictions for the properties of the matter unbound in these mergers. An important limitation of current simulations is the use of approximate methods for neutrino transport that do not converge to a solution of the transport equations as numerical resolution increases, and thus have errors that are impossible to quantify. Here, we report on a first simulation of a binary neutron star merger that uses Monte-Carlo techniques to directly solve the transport equations in low-density regions. In high-density regions, we use approximations inspired by implicit Monte-Carlo to greatly reduce the cost of simulations, while only introducing errors quantifiable through more expensive convergence studies. We simulate an unequal mass neutron star binary merger up to $5\,{\rm ms}$ past merger, and report on the properties of the matter and neutrino outflows. Finally, we compare our results to the output of our best approximate `M1' transport scheme, demonstrating that an M1 scheme that carefully approximates the neutrino energy spectrum only leads to $\sim 10\%$ uncertainty in the composition and velocity of the ejecta, and $\sim20\%$ uncertainty in the $\nu_e$ and $\bar\nu_e$ luminosities and energies. The most significant disagreement found between M1 and Monte-Carlo results is a factor of $\sim 2$ difference in the luminosity of heavy-lepton neutrinos., Comment: 9p, 4 figures, 1 table; version accepted by ApJL

The main problems of nonvacuum numerical relativity, compact binary mergers and stellar collapse, involve hydromagnetic instabilities and turbulent flows, so that kinetic energy at small scales have mean effects at large scale that drive the secular evolution. Notable among these effects is momentum transport. We investigate two models of this transport effect, a relativistic Navier-Stokes system and a turbulent mean stress model, that are similar to all of the prescriptions that have been attempted to date for treating subgrid effects on binary neutron star mergers and their aftermath. Our investigation involves both stability analysis and numerical experimentation on star and disk systems. We also begin the investigation of the effects of particle and heat transport on post-merger simulations. We find that correct handling of turbulent heating can be important for avoiding unphysical instabilities. Given such appropriate handling, the evolution of a differentially rotating star and the accretion rate of a disk are reassuringly insensitive to the choice of prescription. However, disk outflows can be sensitive to the choice of method, even for the same effective viscous strength. We also consider the effects of eddy diffusion in the evolution of an accretion disk and show that it can interestingly affect the composition of outflows., Comment: 15 pagers, 11 figures

High-accuracy numerical simulations of merging neutron stars play an important role in testing and calibrating the waveform models used by gravitational wave observatories. Obtaining high-accuracy waveforms at a reasonable computational cost, however, remains a significant challenge. One issue is that high-order convergence of the solution requires the use of smooth evolution variables, while many of the equations of state used to model the neutron star matter have discontinuities, typically in the first derivative of the pressure. Spectral formulations of the equation of state have been proposed as a potential solution to this problem. Here, we report on the numerical implementation of spectral equations of state in the Spectral Einstein Code. We show that, in our code, spectral equations of state allow for high-accuracy simulations at a lower computational cost than commonly used `piecewise polytrope' equations state. We also demonstrate that not all spectral equations of state are equally useful: different choices for the low-density part of the equation of state can significantly impact the cost and accuracy of simulations. As a result, simulations of neutron star mergers present us with a trade-off between the cost of simulations and the physical realism of the chosen equation of state., Submitted to PRD, 13p, 7 figures, 3 tables

Neutrino transport and neutrino-matter interactions are known to play an important role in the evolution of neutron star mergers, and of their post-merger remnants. Neutrinos cool remnants, drive post-merger winds, and deposit energy in the low-density polar regions where relativistic jets may eventually form. Neutrinos also modify the composition of the ejected material, impacting the outcome of nucleosynthesis in merger outflows and the properties of the optical/infrared transients that they power (kilonovae). So far, merger simulations have largely relied on approximate treatments of the neutrinos (leakage, moments) that simplify the equations of radiation transport in a way that makes simulations more affordable, but also introduces unquantifiable errors in the results. To improve on these methods, we recently published a first simulation of neutron star mergers using a low-cost Monte-Carlo algorithm for neutrino radiation transport. Our transport code limits costs in optically thick regions by placing a hard ceiling on the value of the absorption opacity of the fluid, yet all approximations made within the code are designed to vanish in the limit of infinite numerical resolution. We provide here an in-depth description of this algorithm, of its implementation in the SpEC merger code, and of the expected impact of our approximations in optically thick regions. We argue that the latter is a subdominant source of error at the accuracy reached by current simulations, and for the interactions currently included in our code. We also provide tests of the most important features of this code., 32p, 1 table and 14 figures; Accepted by ApJ

Simulations of neutron star--black hole (NSBH) binaries generally consider black holes with masses in the range $(5--10){M}_{\ensuremath{\bigodot}}$, where we expect to find most stellar mass black holes. The existence of lower mass black holes, however, cannot be theoretically ruled out. Low-mass black holes in binary systems with a neutron star companion could mimic neutron star--neutron star (NSNS) binaries, as they power similar gravitational waves and electromagnetic signals. To understand the differences and similarities between NSNS mergers and low-mass NSBH mergers, numerical simulations are required. Here, we perform a set of simulations of low-mass NSBH mergers, including systems compatible with GW170817. Our simulations use a composition and temperature dependent equation of state (DD2) and approximate neutrino transport, but no magnetic fields. We find that low-mass NSBH mergers produce remnant disks significantly less massive than previously expected, and consistent with the postmerger outflow mass inferred from GW170817 for a moderately asymmetric mass ratio. Whether postmerger disk outflows can also explain the inferred velocity and composition of that event's ejecta is an open question that our merger simulations cannot answer at this point. The dynamical ejecta produced by systems compatible with GW170817 are negligible except if the mass ratio and black hole spin are at the edge of the allowed parameter space. The dynamical ejecta are cold, neutron-rich, and surprisingly slow for ejecta produced during the tidal disruption of a neutron star: $v\ensuremath{\sim}(0.1--0.15)c$. We also find that the final mass of the remnant black hole is consistent with existing analytical predictions, while the final spin of that black hole is noticeably larger than expected---up to ${\ensuremath{\chi}}_{\mathrm{BH}}=0.84$ for our equal mass case.

We identify various contributors of systematic effects in the measurement of the neutron star (NS) tidal deformability and quantify their magnitude for several types of neutron star—black hole (NSBH) binaries. Gravitational waves from NSBH mergers contain information about the components’ masses and spins as well as the NS equation of state. Extracting this information requires comparison of the signal in noisy detector data with theoretical templates derived from some combination of post-Newtonian (PN) approximants, effective one-body (EOB) models, and numerical relativity (NR) simulations. The accuracy of these templates is limited by errors in the NR simulations, by the approximate nature of the PN/EOB waveforms, and by the hybridization procedure used to combine them. In this paper, we estimate the impact of these errors by constructing and comparing a set of PN-NR hybrid waveforms, for the first time with NR waveforms from two different codes, namely, SpEC and sacra, for such systems. We then attempt to recover the parameters of the binary using two non-precessing template approximants. As expected, these errors have negligible effect on detectability. Mass and spin estimates are moderately affected by systematic errors for near equal-mass binaries, while the recovered masses can be inaccurate at higher mass ratios. Large uncertainties are also found in the tidal deformability Λ , due to differences in PN base models used in hybridization, numerical relativity NR errors, and inherent limitations of the hybridization method. We find that systematic errors are too large for tidal effects to be accurately characterized for any realistic NS equation of state model. We conclude that NSBH waveform models must be significantly improved if they are to be useful for the extraction of NS equation of state information or even for distinguishing NSBH systems from binary black holes.

The discovery of GW170817 with gravitational waves (GWs) and electromagnetic (EM) radiation is prompting new questions in strong-gravity astrophysics. Importantly, it remains unknown whether the progenitor of the merger comprised two neutron stars (NSs), or a NS and a black hole (BH). Using new numerical-relativity simulations and incorporating modeling uncertainties we produce novel GW and EM observables for NS-BH mergers with similar masses. A joint analysis of GW and EM measurements reveals that if GW170817 is a NS-BH merger, 8 pages

We present a covariant ray tracing algorithm for computing high-resolution neutrino distributions in general relativistic numerical spacetimes with hydrodynamical sources. Our formulation treats the very important effect of elastic scattering of neutrinos off of nuclei and nucleons (changing the neutrino's direction but not energy) by incorporating estimates of the background neutrino fields. Background fields provide information about the spectra and intensities of the neutrinos scattered into each ray. These background fields may be taken from a low-order moment simulation or be ignored, in which case the method reduces to a standard state-of-the-art ray tracing formulation. The method handles radiation in regimes spanning optically thick to optically thin. We test the new code, highlight its strengths and weaknesses, and apply it to a simulation of a neutron star merger to compute neutrino fluxes and spectra, and to demonstrate a neutrino flavor oscillation calculation. In that environment, we find qualitatively different fluxes, spectra, and oscillation behaviors when elastic scattering is included., Comment: 25 pages, submitted to Physical Review D

Neutrino-matter interactions play an important role in the post-merger evolution of neutron star-neutron star and black hole-neutron star mergers. Most notably, they determine the properties of the bright optical/infrared transients observable after a merger. Unfortunately, Boltzmann's equations of radiation transport remain too costly to be evolved directly in merger simulations. Simulations rely instead on approximate transport algorithms with unquantified modeling errors. In this paper, we use for the first time a time-dependent general relativistic Monte-Carlo (MC) algorithm to solve Boltzmann's equations and estimate important properties of the neutrino distribution function ~10ms after a neutron star merger. We do not fully couple the MC algorithm to the fluid evolution, but use a short evolution of the merger remnant to critically assess errors in our approximate gray two-moment transport scheme. We demonstrate that the analytical closure used by the moment scheme is highly inaccurate in the polar regions, but performs well elsewhere. While the average energy of polar neutrinos is reasonably well captured by the two-moment scheme, estimates for the neutrino energy become less accurate at lower latitudes. The two-moment formalism also overestimates the density of neutrinos in the polar regions by ~50%, and underestimates the neutrino pair-annihilation rate at the poles by factors of 2-3. Although the latter is significantly more accurate than one might have expected before this study, our results indicate that predictions for the properties of polar outflows and for the creation of a baryon-free region at the poles are likely to be affected by errors in the two-moment scheme, thus limiting our ability to reliably model kilonovae and gamma-ray bursts., 15 pages, 10 figures

Each of the potential signals from a black hole-neutron star merger should contain an imprint of the neutron star equation of state: gravitational waves via its effect on tidal disruption, the kilonova via its effect on the ejecta, and the gamma ray burst via its effect on the remnant disk. These effects have been studied by numerical simulations and quantified by semi-analytic formulae. However, most of the simulations on which these formulae are based use equations of state without finite temperature and composition-dependent nuclear physics. In this paper, we simulate black hole-neutron star mergers varying both the neutron star mass and the equation of state, using three finite-temperature nuclear models of varying stiffness. Our simulations largely vindicate formulae for ejecta properties but do not find the expected dependence of disk mass on neutron star compaction. We track the early evolution of the accretion disk, largely driven by shocking and fallback inflow, and do find notable equation of state effects on the structure of this early-time, neutrino-bright disk., 10 pages, 11 figures, submitted to Phys. Rev. D

Black hole-torus systems from compact binary mergers are possible engines for gamma-ray bursts (GRBs). During the early evolution of the post-merger remnant, the state of the torus is determined by a combination of neutrino cooling and magnetically-driven heating processes, so realistic models must include both effects. In this paper, we study the post-merger evolution of a magnetized black hole-neutron star binary system using the Spectral Einstein Code (SpEC) from an initial post-merger state provided by previous numerical relativity simulations. We use a finite-temperature nuclear equation of state and incorporate neutrino effects in a leakage approximation. To achieve the needed accuracy, we introduce improvements to SpEC's implementation of general-relativistic magnetohydrodynamics (MHD), including the use of cubed-sphere multipatch grids and an improved method for dealing with supersonic accretion flows where primitive variable recovery is difficult. We find that a seed magnetic field triggers a sustained source of heating, but its thermal effects are largely cancelled by the accretion and spreading of the torus from MHD-related angular momentum transport. The neutrino luminosity peaks at the start of the simulation, and then drops significantly over the first 20\,ms but in roughly the same way for magnetized and nonmagnetized disks. The heating rate and disk's luminosity decrease much more slowly thereafter. These features of the evolution are insensitive to grid structure and resolution, formulation of the MHD equations, and seed field strength, although turbulent effects are not fully converged, Comment: 17 pages, 18 figures

Neutron star-black hole binaries are among the strongest sources of gravitational waves detectable by current observatories. They can also power bright electromagnetic signals (gamma-ray bursts, kilonovae), and may be a significant source of production of r-process nuclei. A misalignment of the black hole spin with respect to the orbital angular momentum leads to precession of that spin and of the orbital plane, and has a significant effect on the properties of the post-merger remnant and of the material ejected by the merger. We present a first set of simulations of precessing neutron star-black hole mergers using a hot, composition dependent, nuclear-theory based equation of state (DD2). We show that the mass of the remnant and of the dynamical ejecta are broadly consistent with the result of simulations using simpler equations of state, while differences arise when considering the dynamics of the merger and the velocity of the ejecta. We show that the latter can easily be understood from assumptions about the composition of low-density, cold material in the different equations of state, and propose an updated estimate for the ejecta velocity which takes those effects into account. We also present an updated mesh-refinement algorithm which allows us to improve the numerical resolution used to evolve neutron star-black hole mergers., 23 pages, 8 figures

We review the dramatic progress in the simulations of compact objects and compact-object binaries that has taken place in the first two decades of the twenty-first century. This includes simulations of the inspirals and violent mergers of binaries containing black holes and neutron stars, as well as simulations of black-hole formation through failed supernovae and high-mass neutron star--neutron star mergers. Modeling such events requires numerical integration of the field equations of general relativity in three spatial dimensions, coupled, in the case of neutron-star containing binaries, with increasingly sophisticated treatment of fluids, electromagnetic fields, and neutrino radiation. However, it was not until 2005 that accurate long-term evolutions of binaries containing black holes were even possible. Since then, there has been an explosion of new results and insights into the physics of strongly-gravitating system. Particular emphasis has been placed on understanding the gravitational wave and electromagnetic signatures from these extreme events. And with the recent dramatic discoveries of gravitational waves from merging black holes by the Laser Interferometric Gravitational Wave Observatory and Virgo, and the subsequent discovery of both electromagnetic and gravitational wave signals from a merging neutron star binary, numerical relativity became an indispensable tool for the new field of multimessenger astronomy., 52 pages, 21 figures, a review of numerical relativity, focusing on 21st century developments up to roughly 2017, Reports on Progress in Physics 2018

Extracting the unique information on ultradense nuclear matter from the gravitational waves emitted by merging, neutron-star binaries requires robust theoretical models of the signal. We develop a novel effective-one-body waveform model that includes, for the first time, dynamic (instead of only adiabatic) tides of the neutron star, as well as the merger signal for neutron-star--black-hole binaries. We demonstrate the importance of the dynamic tides by comparing our model against new numerical-relativity simulations of nonspinning neutron-star--black-hole binaries spanning more than 24 gravitational-wave cycles, and to other existing numerical simulations for double neutron-star systems. Furthermore, we derive an effective description that makes explicit the dependence of matter effects on two key parameters: tidal deformability and fundamental oscillation frequency.

During the merger of a black hole and a neutron star, baryonic mass can become unbound from the system. Because the ejected material is extremely neutron-rich, the r-process rapidly synthesizes heavy nuclides as the material expands and cools. In this work, we map general relativistic models of black hole-neutron star (BHNS) mergers into a Newtonian smoothed particle hydrodynamics (SPH) code and follow the evolution of the thermodynamics and morphology of the ejecta until the outflows become homologous. We investigate how the subsequent evolution depends on our mapping procedure and find that the results are robust. Using thermodynamic histories from the SPH particles, we then calculate the expected nucleosynthesis in these outflows while varying the level of neutrino irradiation coming from the postmerger accretion disk. We find that the ejected material robustly produces r-process nucleosynthesis even for unrealistically high neutrino luminosities, due to the rapid velocities of the outflow. Nonetheless, we find that neutrinos can have an impact on the detailed pat- tern of the r-process nucleosynthesis. Electron neutrinos are captured by neutrons to produce protons while neutron capture is occurring. The produced protons rapidly form low mass seed nuclei for the r-process. These low mass seeds are eventually incorporated into the first r-process peak at A~78, producing mainly Ge and Se. We consider the mechanism of this process in detail and discuss if it can impact galactic chemical evolution of the first peak r-process nuclei., Comment: 14 pages, 12 figures, accepted for publication in MNRAS

We present results on the inspiral, merger, and post-merger evolution of a neutron star - neutron star (NSNS) system. Our results are obtained using the hybrid pseudospectral-finite volume Spectral Einstein Code (SpEC). To test our numerical methods, we evolve an equal-mass system for $\approx 22$ orbits before merger. This waveform is the longest waveform obtained from fully general-relativistic simulations for NSNSs to date. Such long (and accurate) numerical waveforms are required to further improve semi-analytical models used in gravitational wave data analysis, for example the effective one body models. We discuss in detail the improvements to SpEC's ability to simulate NSNS mergers, in particular mesh refined grids to better resolve the merger and post-merger phases. We provide a set of consistency checks and compare our results to NSNS merger simulations with the independent BAM code. We find agreement between them, which increases confidence in results obtained with either code. This work paves the way for future studies using long waveforms and more complex microphysical descriptions of neutron star matter in SpEC., Comment: 23 pages, 15 figures, published version

Gravitational waves from binary neutron star (BNS) and black hole/neutron star (BHNS) inspirals are primary sources for detection by the Advanced Laser Interferometer Gravitational-Wave Observatory. The tidal forces acting on the neutron stars induce changes in the phase evolution of the gravitational waveform, and these changes can be used to constrain the nuclear equation of state. Current methods of generating BNS and BHNS waveforms rely on either computationally challenging full 3D hydrodynamical simulations or approximate analytic solutions. We introduce a new method for computing inspiral waveforms for BNS/BHNS systems by adding the post-Newtonian (PN) tidal effects to full numerical simulations of binary black holes (BBHs), effectively replacing the nontidal terms in the PN expansion with BBH results. Comparing a waveform generated with this method against a full hydrodynamical simulation of a BNS inspiral yields a phase difference of $, Comment: 7 pages, 3 figures; updated acknowledgements; published PRD version

Neutron star mergers are among the most promising sources of gravitational waves for advanced ground-based detectors. These mergers are also expected to power bright electromagnetic signals, in the form of short gamma-ray bursts, infrared/optical transients, and radio emission. Simulations of these mergers with fully general relativistic codes are critical to understand the merger and post-merger gravitational wave signals and their neutrinos and electromagnetic counterparts. In this paper, we employ the SpEC code to simulate the merger of low-mass neutron star binaries (two $1.2M_\odot$ neutron stars) for a set of three nuclear-theory based, finite temperature equations of state. We show that the frequency peaks of the post-merger gravitational wave signal are in good agreement with predictions obtained from simulations using a simpler treatment of gravity. We find, however, that only the fundamental mode of the remnant is excited for long periods of time: emission at the secondary peaks is damped on a millisecond timescale in the simulated binaries. For such low-mass systems, the remnant is a massive neutron star which, depending on the equation of state, is either permanently stable or long-lived. We observe strong excitations of l=2, m=2 modes, both in the massive neutron star and in the form of hot, shocked tidal arms in the surrounding accretion torus. We estimate the neutrino emission of the remnant using a neutrino leakage scheme and, in one case, compare these results with a gray two-moment neutrino transport scheme. We confirm the complex geometry of the neutrino emission, also observed in previous simulations with neutrino leakage, and show explicitly the presence of important differences in the neutrino luminosity, disk composition, and outflow properties between the neutrino leakage and transport schemes., Comment: Accepted by PRD; 23 pages; 24 figures; 4 tables

Dynamical instabilities in protoneutron stars may produce gravitational waves whose observation could shed light on the physics of core-collapse supernovae. When born with sufficient differential rotation, these stars are susceptible to a shear instability (the “low-T/|W| instability”), but such rotation can also amplify magnetic fields to strengths where they have a considerable impact on the dynamics of the stellar matter. Using a new magnetohydrodynamics module for the Spectral Einstein Code, we have simulated a differentially-rotating neutron star in full 3D to study the effects of magnetic fields on this instability. Though strong toroidal fields were predicted to suppress the low-T/|W| instability, we find that they do so only in a small range of field strengths. Below 4×10^(13) G, poloidal seed fields do not wind up fast enough to have an effect before the instability saturates, while above 5×10^(14) G, magnetic instabilities can actually amplify a global quadrupole mode (this threshold may be even lower in reality, as small-scale magnetic instabilities remain difficult to resolve numerically). Thus, the prospects for observing gravitational waves from such systems are not in fact diminished over most of the magnetic parameter space. Additionally, we report that the detailed development of the low-T/|W| instability, including its growth rate, depends strongly on the particular numerical methods used. The high-order methods we employ suggest that growth might be considerably slower than found in some previous simulations.

We present a first exploration of the results of neutron star-black hole mergers using black hole masses in the most likely range of $7M_\odot-10M_\odot$, a neutrino leakage scheme, and a modeling of the neutron star material through a finite-temperature nuclear-theory based equation of state. In the range of black hole spins in which the neutron star is tidally disrupted ($\chi_{\rm BH}\gtrsim 0.7$), we show that the merger consistently produces large amounts of cool ($T\lesssim 1\,{\rm MeV}$), unbound, neutron-rich material ($M_{\rm ej}\sim 0.05M_\odot-0.20M_\odot$). A comparable amount of bound matter is initially divided between a hot disk ($T_{\rm max}\sim 15\,{\rm MeV}$) with typical neutrino luminosity $L_\nu\sim 10^{53}\,{\rm erg/s}$, and a cooler tidal tail. After a short period of rapid protonization of the disk lasting $\sim 10\,{\rm ms}$, the accretion disk cools down under the combined effects of the fall-back of cool material from the tail, continued accretion of the hottest material onto the black hole, and neutrino emission. As the temperature decreases, the disk progressively becomes more neutron-rich, with dimmer neutrino emission. This cooling process should stop once the viscous heating in the disk (not included in our simulations) balances the cooling. These mergers of neutron star-black hole binaries with black hole masses $M_{\rm BH}\sim 7M_\odot-10M_\odot$ and black hole spins high enough for the neutron star to disrupt provide promising candidates for the production of short gamma-ray bursts, of bright infrared post-merger signals due to the radioactive decay of unbound material, and of large amounts of r-process nuclei., Comment: 20 pages, 19 figures

The merger of two neutron stars leaves behind a rapidly spinning hypermassive object whose survival is believed to depend on the maximum mass supported by the nuclear equation of state, angular momentum redistribution by (magneto-)rotational instabilities, and spindown by gravitational waves. The high temperatures (~5-40 MeV) prevailing in the merger remnant may provide thermal pressure support that could increase its maximum mass and, thus, its life on a neutrino-cooling timescale. We investigate the role of thermal pressure support in hypermassive merger remnants by computing sequences of spherically-symmetric and axisymmetric uniformly and differentially rotating equilibrium solutions to the general-relativistic stellar structure equations. Using a set of finite-temperature nuclear equations of state, we find that hot maximum-mass critically spinning configurations generally do not support larger baryonic masses than their cold counterparts. However, subcritically spinning configurations with mean density of less than a few times nuclear saturation density yield a significantly thermally enhanced mass. Even without decreasing the maximum mass, cooling and other forms of energy loss can drive the remnant to an unstable state. We infer secular instability by identifying approximate energy turning points in equilibrium sequences of constant baryonic mass parametrized by maximum density. Energy loss carries the remnant along the direction of decreasing gravitational mass and higher density until instability triggers collapse. Since configurations with more thermal pressure support are less compact and thus begin their evolution at a lower maximum density, they remain stable for longer periods after merger., 20 pages, 12 figures. Accepted for publication in ApJ

Neutrino emission significantly affects the evolution of the accretion tori formed in black hole-neutron star mergers. It removes energy from the disk, alters its composition, and provides a potential power source for a gamma-ray burst. To study these effects, simulations in general relativity with a hot microphysical equation of state and neutrino feedback are needed. We present the first such simulation, using a neutrino leakage scheme for cooling to capture the most essential effects and considering a moderate mass (1.4 M_{\odot} neutron star, 5.6 M_{\odot} black hole), high spin (black hole J/M^2=0.9) system with the K_0=220 MeV Lattimer-Swesty equation of state. We find that about 0.08 M_{\odot} of nuclear matter is ejected from the system, while another 0.3 M_{\odot} forms a hot, compact accretion disk. The primary effects of the escaping neutrinos are (i) to make the disk much denser and more compact, (ii) to cause the average electron fraction Y_e of the disk to rise to about 0.2 and then gradually decrease again, and (iii) to gradually cool the disk. The disk is initially hot (T~6 MeV) and luminous in neutrinos (L_{\nu}~10^{54} erg s^{-1}), but the neutrino luminosity decreases by an order of magnitude over 50 ms of post-merger evolution., Comment: Included erratum to the end of the article: affected average neutrino energy estimates

Black hole-neutron star mergers resulting in the disruption of the neutron star and the formation of an accretion disk and/or the ejection of unbound material are prime candidates for the joint detection of gravitational-wave and electromagnetic signals when the next generation of gravitational-wave detectors comes online. However, the disruption of the neutron star and the properties of the post-merger remnant are very sensitive to the parameters of the binary. In this paper, we study the impact of the radius of the neutron star and the alignment of the black hole spin for systems within the range of mass ratio currently deemed most likely for field binaries (M_BH ~ 7 M_NS) and for black hole spins large enough for the neutron star to disrupt (J/M^2=0.9). We find that: (i) In this regime, the merger is particularly sensitive to the radius of the neutron star, with remnant masses varying from 0.3M_NS to 0.1M_NS for changes of only 2 km in the NS radius; (ii) 0.01-0.05M_sun of unbound material can be ejected with kinetic energy >10^51 ergs, a significant increase compared to low mass ratio, low spin binaries. This ejecta could power detectable optical and radio afterglows. (iii) Only a small fraction (300 km/s) can be given to the final black hole as a result of a precessing BHNS merger, when the disruption of the neutron star occurs just outside or within the innermost stable spherical orbit., 25 pages, 16 Figures, updated to match published version

Black hole-neutron star (BHNS) binaries are important sources of gravitational waves for second-generation interferometers, and BHNS mergers are also a proposed engine for short, hard gamma-ray bursts. The behavior of both the spacetime (and thus the emitted gravitational waves) and the neutron star matter in a BHNS merger depend strongly and nonlinearly on the black hole's spin. While there is a significant possibility that astrophysical black holes could have spins that are nearly extremal (i.e. near the theoretical maximum), to date fully relativistic simulations of BHNS binaries have included black-hole spins only up to $S/M^2$=0.9, which corresponds to the black hole having approximately half as much rotational energy as possible, given the black hole's mass. In this paper, we present a new simulation of a BHNS binary with a mass ratio $q=3$ and black-hole spin $S/M^2$=0.97, the highest simulated to date. We find that the black hole's large spin leads to the most massive accretion disk and the largest tidal tail outflow of any fully relativistic BHNS simulations to date, even exceeding the results implied by extrapolating results from simulations with lower black-hole spin. The disk appears to be remarkably stable. We also find that the high black-hole spin persists until shortly before the time of merger; afterwards, both merger and accretion spin down the black hole., Comment: 20 pages, 10 figures, submitted to Classical and Quantum Gravity

The spin of black holes in black hole-neutron star (BHNS) binaries can have a strong influence on the merger dynamics and the postmerger state; a wide variety of spin magnitudes and orientations are expected to occur in nature. In this paper, we report the first simulations in full general relativity of BHNS mergers with misaligned black hole spin. We vary the spin magnitude from a/m=0 to a/m=0.9 for aligned cases, and we vary the misalignment angle from 0 to 80 degrees for a/m=0.5. We restrict our study to 3:1 mass ratio systems and use a simple Gamma-law equation of state. We find that the misalignment angle has a strong effect on the mass of the postmerger accretion disk, but only for angles greater than ~ 40 degrees. Although the disk mass varies significantly with spin magnitude and misalignment angle, we find that all disks have very similar lifetimes ~ 100ms. Their thermal and rotational profiles are also very similar. For a misaligned merger, the disk is tilted with respect to the final black hole's spin axis. This will cause the disk to precess, but on a timescale longer than the accretion time. In all cases, we find promising setups for gamma-ray burst production: the disks are hot, thick, and hyperaccreting, and a baryon-clear region exists above the black hole., Comment: 15 pages, 13 figures

We review the current status of attempts to numerically model the merger of neutron star-neutron star (NSNS) and black hole-neutron star (BHNS) binary systems, and we describe the understanding of such events that is emerging from these calculations. To accurately model the physics of NSNS and BHNS mergers is a difficult task. It requires solving Einstein's equations for dynamic spacetimes containing black holes. It also requires evolving the hot, supernuclear-density neutron star matter together with the magnetic and radiation fields that can influence the post-merger dynamics. Older studies concentrated on either one or the other of these challenges, but now efforts are being made to model both relativity and microphysics accurately together. These NSNS and BHNS simulations are then used to characterize the gravitational wave signals of such events and to address their potential for generating short-duration gamma ray bursts., 16 pages. Submitted to the Classical and Quantum Gravity special issue for NRDA2009

We present numerical simulations of orbiting black holes for around twelve cycles, using a high-order multipatch approach. Unlike some other approaches, the computational speed scales almost perfectly for thousands of processors. Multipatch methods are an alternative to AMR (adaptive mesh refinement), with benefits of simplicity and better scaling for improving the resolution in the wave zone. The results presented here pave the way for multipatch evolutions of black hole-neutron star and neutron star-neutron star binaries, where high resolution grids are needed to resolve details of the matter flow.

The merger dynamics of a black hole-neutron star (BHNS) binary is influenced by the neutron star equation of state (EoS) through the latter's effect on the neutron star's radius and on the character of the mass transfer onto the black hole. We study these effects by simulating a number of BHNS binaries in full general relativity using a mixed pseudospectral/finite difference code. We consider several models of the neutron star matter EoS, including Gamma=2 and Gamma=2.75 polytropes and the nuclear-theory based Shen EoS. For models using the Shen EoS, we consider two limits for the evolution of the composition: source-free advection and instantaneous beta-equilibrium. To focus on EoS effects, we fix the mass ratio to 3:1 and the initial aligned black hole spin to a/m=0.5 for all models. We confirm earlier studies which found that more compact stars create a stronger gravitational wave signal but a smaller postmerger accretion disk. We also vary the EoS while holding the compaction fixed. All mergers are qualitatively similar, but we find signatures of the EoS in the waveform and in the tail and disk structures., Comment: 11 pages, 3 figures. Submitted to the Classical and Quantum Gravity special issue for MICRA2009

The merger of two neutron stars usually produces a remnant with a mass significantly above the single (nonrotating) neutron star maximum mass. In some cases, the remnant will be stabilized against collapse by rapid, differential rotation. MHD-driven angular momentum transport eventually leads to the collapse of the remnant's core, resulting in a black hole surrounded by a massive accretion torus. Here we present simulations of this process. The plausibility of generating short duration gamma ray bursts through this scenario is discussed., 3 pages. To appear in the Proceedings of the Eleventh Marcel Grossmann Meeting, Berlin, Germany, 23-29 July 2006, World Scientific, Singapore (2007)

Hypermassive neutron stars (HMNSs) are equilibrium configurations supported against collapse by rapid differential rotation and likely form as transient remnants of binary neutron star mergers. Though HMNSs are dynamically stable, secular effects such as viscosity or magnetic fields tend to bring HMNSs into uniform rotation and thus lead to collapse. We simulate the evolution of magnetized HMNSs in axisymmetry using codes which solve the Einstein-Maxwell-MHD system of equations. We find that magnetic braking and the magnetorotational instability (MRI) both contribute to the eventual collapse of HMNSs to rotating black holes surrounded by massive, hot accretion tori and collimated magnetic fields. Such hot tori radiate strongly in neutrinos, and the resulting neutrino-antineutrino annihilation could power short-hard GRBs., Comment: 3 pages, 1 figure, submitted to the MG11 proceedings

The capacity to model magnetohydrodynamical (MHD) flows in dynamical, strongly curved spacetimes significantly extends the reach of numerical relativity in addressing many problems at the forefront of theoretical astrophysics. We have developed and tested an evolution code for the coupled Einstein-Maxwell-MHD equations which combines a BSSN solver with a high resolution shock capturing scheme. As one application, we evolve magnetized, differentially rotating neutron stars under the influence of a small seed magnetic field. Of particular significance is the behavior found for hypermassive neutron stars (HMNSs), which have rest masses greater the mass limit allowed by uniform rotation for a given equation of state. The remnant of a binary neutron star merger is likely to be a HMNS. We find that magnetic braking and the magnetorotational instability lead to the collapse of HMNSs and the formation of rotating black holes surrounded by massive, hot accretion tori and collimated magnetic field lines. Such tori radiate strongly in neutrinos, and the resulting neutrino-antineutrino annihilation (possibly in concert with energy extraction by MHD effects) could provide enough energy to power short-hard gamma-ray bursts. To explore the range of outcomes, we also evolve differentially rotating neutron stars with lower masses and angular momenta than the HMNS models. Instead of collapsing, the non-hypermassive models form nearly uniformly rotating central objects which, in cases with significant angular momentum, are surrounded by massive tori., Submitted to a special issue of Classical and Quantum Gravity based around the New Frontiers in Numerical Relativity meeting at the Albert Einstein Institute, Potsdam, July 17-21, 2006

We study the effects of magnetic fields on the evolution of differentially rotating neutron stars, which can form in stellar core collapse or binary neutron star coalescence. Magnetic braking and the magnetorotational instability (MRI) both redistribute angular momentum; the outcome of the evolution depends on the star's mass and spin. Simulations are carried out in axisymmetry using our recently developed codes which integrate the coupled Einstein-Maxwell-MHD equations. For initial data, we consider three categories of differentially rotating, equilibrium configurations, which we label normal, hypermassive and ultraspinning. Hypermassive stars have rest masses exceeding the mass limit for uniform rotation. Ultraspinning stars are not hypermassive, but have angular momentum exceeding the maximum for uniform rotation at the same rest mass. We show that a normal star will evolve to a uniformly rotating equilibrium configuration. An ultraspinning star evolves to an equilibrium state consisting of a nearly uniformly rotating central core, surrounded by a differentially rotating torus with constant angular velocity along magnetic field lines, so that differential rotation ceases to wind the magnetic field. In addition, the final state is stable against the MRI, although it has differential rotation. For a hypermassive neutron star, the MHD-driven angular momentum transport leads to catastrophic collapse of the core. The resulting rotating black hole is surrounded by a hot, massive, magnetized torus undergoing quasistationary accretion, and a magnetic field collimated along the spin axis--a promising candidate for the central engine of a short gamma-ray burst. (Abridged), 27 pages, 30 figures

Hypermassive neutron stars (HMNSs) -- equilibrium configurations supported against collapse by rapid differential rotation -- are possible transient remnants of binary neutron star mergers. Using newly developed codes for magnetohydrodynamic simulations in dynamical spacetimes, we are able to track the evolution of a magnetized HMNS in full general relativity for the first time. We find that secular angular momentum transport due to magnetic braking and the magnetorotational instability results in the collapse of an HMNS to a rotating black hole, accompanied by a gravitational wave burst. The nascent black hole is surrounded by a hot, massive torus undergoing quasistationary accretion and a collimated magnetic field. This scenario suggests that HMNS collapse is a possible candidate for the central engine of short gamma-ray bursts., Comment: Accepted for publication in Phys. Rev. Letters

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., Comment: 4 pages, 2 figures, submitted to Phys. Rev. Letter

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., Comment: 22 pages, 15 figures, accepted for publication in Phys. Rev. D

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, Comment: 5 pages, 4 figures. Minor comments and discussions added. Version accepted for publication in Phys. Rev. Letters

We model the adiabatic inspiral of relativistic binary neutron stars in a quasi-equilibrium (QE) approximation, and compute the gravitational wavetrain from the late phase of the inspiral. We compare corotational and irrotational sequences and find a significant difference in the inspiral rate, which is almost entirely caused by differences in the binding energy. We also compare our results with those of a point-mass post-Newtonian calculation. We illustrate how the late inspiral wavetrain computed with our QE numerical scheme can be matched to the subsequent plunge and merger waveform calculated with a fully relativistic hydrodynamics code., Comment: 9 pages, 5 figures, to be published in Physical Review D

We present a new method for generating the nonlinear gravitational wavetrain from the late inspiral (pre-coalescence) phase of a binary neutron star system by means of a numerical evolution calculation in full general relativity. In a prototype calculation, we produce 214 wave cycles from corotating polytropes, representing the final part of the inspiral phase prior to reaching the ISCO. Our method is based on the inequality that the orbital decay timescale due to gravitational radiation is much longer than an orbital period and the approximation that gravitational radiation has little effect on the structure of the stars. We employ quasi-equilibrium sequences of binaries in circular orbit for the matter source in our field evolution code. We compute the gravity-wave energy flux, and, from this, the inspiral rate, at a discrete set of binary separations. From these data, we construct the gravitational waveform as a continuous wavetrain. Finally, we discuss the limitations of our current calculation, planned improvements, and potential applications of our method to other inspiral scenarios., 4 pages, 4 figures

We improve and extend Shapiro's model of a relativistic, compact object which is stable in isolation but is driven dynamically unstable by the tidal field of a binary companion. Our compact object consists of a dense swarm of test particles moving in randomly-oriented, initially circular, relativistic orbits about a nonrotating black hole. The binary companion is a distant, slowly inspiraling point mass. The tidal field of the companion is treated as a small perturbation on the background Schwarzschild geometry near the hole; the resulting metric is determined by solving the perturbation equations of Regge and Wheeler and Zerilli in the quasi-static limit. The perturbed spacetime supports Bekenstein's conjecture that the horizon area of a near-equilibrium black hole is an adiabatic invariant. We follow the evolution of the system and confirm that gravitational collapse can be induced in a compact collisionless cluster by the tidal field of a binary companion., Comment: 9 Latex pages, 14 postscript figures