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We present numerical solutions for stationary and axisymmetric equilibriums of compact stars associated with extremely strong magnetic fields. The interior of the compact stars is assumed to satisfy ideal magnetohydrodynamic (MHD) conditions, while in the region of negligible mass density the force-free conditions or electromagnetic vacuum are assumed. Solving all components of Einstein's equations, Maxwell's equations, ideal MHD equations, and force-free conditions, equilibriums of rotating compact stars associated with mixed poloidal and toroidal magnetic fields are obtained. It is found that in the extreme cases the strong mixed magnetic fields concentrating in a toroidal region near the equatorial surface expel the matter and form a force-free toroidal magnetotunnel. We also introduce a new differential rotation law for computing solutions associated with force-free magnetosphere, and present other extreme models without the magnetotunnel., Comment: 13 pages, 4 figures

We review the current status of general relativistic studies for coalescences of black hole--neutron star binaries. First, high-precision computations of black hole--neutron star binaries in quasiequilibrium circular orbits are summarized, focusing on the quasiequilibrium sequences and the mass-shedding limit. Next, the current status of numerical-relativity simulations for the merger of black hole--neutron star binaries is described. We summarize our understanding for the merger process, tidal disruption and its criterion, properties of the merger remnant and ejected material, gravitational waveforms, and gravitational-wave spectra. We also discuss expected electromagnetic counterparts to black hole--neutron star coalescences., Comment: 178 pages, 54 figures, Invited review article for Living Reviews in Relativity, accepted version

We develop a method to compute low-eccentricity initial data of black hole--neutron star binaries in the puncture framework extending previous work on other types of compact binaries. In addition to adjusting the orbital angular velocity of the binary, the approaching velocity of a neutron star is incorporated by modifying the helical Killing vector used to derive equations of the hydrostationary equilibrium. The approaching velocity of the black hole is then induced by requiring the vanishing of the total linear momentum of the system, differently from the case of binary black holes in the puncture framework where the linear momentum of each black hole is specified explicitly. We successfully reduce the orbital eccentricity to <~0.001 by modifying the parameters iteratively using simulations of ~3 orbits both for nonprecessing and precessing configurations. We find that empirical formulas for binary black holes derived in the excision framework do not reduce the orbital eccentricity to ~0.001 for black hole--neutron star binaries in the puncture framework, although they work for binary neutron stars., Comment: 15 pages, 9 figures

Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is the future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could be produced during the inflationary period right after the birth of the universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in the heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1,000 km. Three clusters of DECIGO will be placed far from each other, and the fourth cluster will be placed in the same position as one of the three clusters to obtain the correlation signals for the detection of the primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder of DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand the multi-messenger astronomy., Comment: 10 pages, 3 figures

A new code for computing fully general relativistic solutions of strongly magnetized rapidly rotating compact stars is developed as a part of the COCAL (Compact Object CALculator) code. The full set of Einstein's equations, Maxwell's equations and magnetohydrodynamic equations are consistently solved assuming perfect conductivity, stationarity, and axisymmetry, and strongly magnetized solutions associated with mixed poloidal and toroidal components of magnetic fields are successfully obtained in generic (non-circular) spacetimes. We introduce the formulation of the problem and the numerical method in detail, then present examples of extremely magnetized compact star solutions and their convergence tests. It is found that, in extremely magnetized stars, the stellar matter can be expelled from the region of strongest toroidal fields. Hence we conjecture that a toroidal electro-vacuum region may appear inside of the extremely magnetized compact stars, which may seem like the neutron star becoming the strongest toroidal solenoid coil in the universe., Comment: 30 pages, 4 figures

We revisit the lower bound on binary tidal deformability tilde{Lambda} imposed by a luminous kilonova/macronova, AT 2017gfo, by numerical-relativity simulations of models that are consistent with gravitational waves from the binary neutron star merger GW170817. Contrary to the claim made in the literature, we find that binaries with tilde{Lambda}<~400 can explain the luminosity of AT 2017gfo, as long as moderate mass ejection from the remnant is assumed as had been done in previous work. The reason is that the maximum mass of a neutron star is not strongly correlated with the tidal deformability of neutron stars with a typical mass of ~1.4M_sun. If the maximum mass is so large that the binary does not collapse into a black hole immediately after merger, the mass of the ejecta can be sufficiently large irrespective of the binary tidal deformability. We present models of binary mergers with tilde{Lambda} down to 242 that satisfy the requirement on the mass of the ejecta from the luminosity of AT 2017gfo. We further find that the luminosity of AT 2017gfo could be explained by models that do not experience bounce after merger. We conclude that the luminosity of AT 2017gfo is not very useful for constraining the binary tidal deformability. Accurate estimation of the mass ratio will be necessary to establish a lower bound using electromagnetic counterparts in the future. We also caution that merger simulations that employ a limited class of tabulated equations of state could be severely biased due to the lack of generality., Comment: 6 pages, 3 figures

We develop a model for frequency-domain gravitational waveforms from inspiraling binary neutron stars. Our waveform model is calibrated by comparison with hybrid waveforms constructed from our latest high-precision numerical-relativity waveforms and the SEOBNRv2T waveforms in the frequency range of $10$--$1000\,{\rm Hz}$. We show that the phase difference between our waveform model and the hybrid waveforms is always smaller than $0.1\, {\rm rad}$ for the binary tidal deformability, ${\tilde \Lambda}$, in the range $300\lesssim{\tilde \Lambda}\lesssim1900$ and for the mass ratio between 0.73 and 1. We show that, for $10$--$1000\,{\rm Hz}$, the distinguishability for the signal-to-noise ratio $\lesssim50$ and the mismatch between our waveform model and the hybrid waveforms are always smaller than 0.25 and $1.1\times10^{-5}$, respectively. The systematic error of our waveform model in the measurement of ${\tilde \Lambda}$ is always smaller than $20$ with respect to the hybrid waveforms for $300\lesssim{\tilde \Lambda}\lesssim1900$. The statistical error in the measurement of binary parameters is computed employing our waveform model, and we obtain results consistent with the previous studies. We show that the systematic error of our waveform model is always smaller than $20\%$ (typically smaller than $10\%$) of the statistical error for events with the signal-to-noise ratio of $50$., Comment: 22 pages, 16 figures, accepted for publication in PRD

We study the merger of black hole-neutron star binaries by fully general-relativistic neutrino-radiation-hydrodynamics simulations throughout the coalescence, particularly focusing on the role of neutrino irradiation in dynamical mass ejection. Neutrino transport is incorporated by an approximate transfer scheme based on the truncated moment formalism. While we fix the mass ratio of the black hole to the neutron star to be 4 and the dimensionless spin parameter of the black hole to be 0.75, the equations of state for finite-temperature neutron-star matter are varied. The hot accretion disk formed after tidal disruption of the neutron star emits a copious amount of neutrinos with the peak total luminosity ~1--3x10^53 erg s^(-1) via thermal pair production and subsequent electron/positron captures on free nucleons. Nevertheless, the neutrino irradiation does not modify significantly the electron fraction of the dynamical ejecta from the neutrinoless beta-equilibrium value at zero temperature of initial neutron stars. The mass of the wind component driven by neutrinos from the remnant disk is negligible compared to the very neutron-rich dynamical component, throughout our simulations performed until a few tens milliseconds after the onset of merger, for the models considered in this study. These facts suggest that the ejecta from black hole-neutron star binaries are very neutron rich and are expected to accommodate strong r-process nucleosynthesis, unless magnetic or viscous processes contribute substantially to the mass ejection from the disk. We also find that the peak neutrino luminosity does not necessarily increase as the disk mass increases, because tidal disruption of a compact neutron star can result in a remnant disk with a small mass but high temperature., Comment: 17 pages, 16 figures, matched to the published version

Outcomes of numerical relativity simulations of massive core collapses or binary neutron star mergers with moderate masses suggest formations of rapidly and differentially rotating neutron stars. Subsequent fall back accretion may also amplify the degree of differential rotations. We propose new formulations for modeling differential rotations of those compact stars, and present selected solutions of differentially rotating, stationary, and axisymmetric compact stars in equilibriums. For the cases when rotating stars reach break-up velocities, the maximum masses of such rotating models are obtained., Comment: 7 pages, 4 figures

Extending our previous studies, we perform high-resolution simulations of inspiraling binary neutron stars in numerical relativity. We thoroughly carry through a convergence study in our currently available computational resources with the smallest grid spacing of $\approx 63$--86~meter for the neutron-star radius 10.9--13.7\,km. The estimated total error in the gravitational-wave phase is of order 0.1~rad for the total phase of $\gtrsim 210$\,rad in the last $\sim 15$--16 inspiral orbits. We then compare the waveforms (without resolution extrapolation) with those calculated by the latest effective-one-body formalism (tidal SEOBv2 model referred to as TEOB model). We find that for any of our models of binary neutron stars, the waveforms calculated by the TEOB formalism agree with the numerical-relativity waveforms up to $\approx 3$\,ms before the peak of the gravitational-wave amplitude is reached: For this late inspiral stage, the total phase error is $\lesssim 0.1$\,rad. Although the gravitational waveforms have an inspiral-type feature for the last $\sim 3$\,ms, this stage cannot be well reproduced by the current TEOB formalism, in particular, for neutron stars with large tidal deformability (i.e., lager radius). The reason for this is described., Comment: 13 pages, 11 figures, submitted to PRD

We study quasiequilibrium solutions of triaxially deformed rotating compact stars -- a generalization of Jacobi ellipsoids under relativistic gravity and compressible equations of state (EOS). For relatively stiff (piecewise) polytropic EOSs, we find supramassive triaxial solutions whose masses exceed the maximum mass of the spherical solution, but are always lower than those of axisymmetric equilibriums. The difference in the maximum masses of triaxial and axisymmetric solutions depends sensitively on the EOS. If the difference turns out to be only about 10%, it will be strong evidence that the EOS of high density matter becomes substantially softer in the core of neutron stars. This finding opens a novel way to probe phase transitions of high density nuclear matter using detections of gravitational waves from new born neutron stars or magnetars under fallback accretion., Comment: 5 pages, 3 figures. Revised version to appear in PRD rapid communication

We perform neutrino radiation-hydrodynamics simulations for the merger of asymmetric binary neutron stars in numerical relativity. Neutron stars are modeled by soft and moderately stiff finite-temperature equations of state (EOS). We find that the properties of the dynamical ejecta such as the total mass, neutron richness profile, and specific entropy profile depend on the mass ratio of the binary systems for a given EOS in a unique manner. For the soft EOS (SFHo), the total ejecta mass depends weakly on the mass ratio, but the average of electron number per baryon ($Y_e$) and specific entropy ($s$) of the ejecta decreases significantly with the increase of the degree of mass asymmetry. For the stiff EOS (DD2), with the increase of the mass asymmetry degree, the total ejecta mass significantly increases while the average of $Y_e$ and $s$ moderately decreases. We find again that only for the soft EOS (SFHo), the total ejecta mass exceeds $0.01M_\odot$ irrespective of the mass ratio chosen in this paper. The ejecta have a variety of electron number per baryon with its average approximately between $Y_e \sim 0.2$ and $\sim 0.3$ irrespective of the EOS employed, which is well-suited for the production of the r-process heavy elements (second and third peaks), although its averaged value decreases with the increase of the degree of mass asymmetry., Comment: 12 pages, 5 figures, submitted to PRD

We report results of a high-resolution numerical-relativity simulation for the merger of black hole-magnetized neutron star binaries on Japanese supercomputer "K". We focus on a binary that is subject to tidal disruption and subsequent formation of a massive accretion torus. We find the launch of thermally driven torus wind, subsequent formation of a funnel wall above the torus and a magnetosphere with collimated poloidal magnetic field, and high Blandford-Znajek luminosity. We show for the first time this picture in a self-consistent simulation. The turbulence-like motion induced by the non-axisymmetric magnetorotational instability as well as the Kelvin-Helmholtz instability inside the accretion torus works as an agent to drive the mass accretion and converts the accretion energy to thermal energy, which results in the generation of a strong wind. By an in-depth resolution study, we reveal that high resolution is essential to draw such a picture. We also discuss the implication for the r-process nucleosynthesis, the radioactively-powered transient emission, and short gamma-ray bursts., Comment: 8 pages, 8 figures, to be appeared in PRD

We systematically performed numerical-relativity simulations for black hole (BH) - neutron star (NS) binary mergers with a variety of the BH spin orientation and equations of state (EOS) of the NS. The initial misalignment angles of the BH spin are chosen in the range of i_tilt,0 = 30--90[deg.]. We employed four models of NS EOS with which the compactness of the NS is in the range of C = M_NS/R_NS = 0.138--0.180, where M_NS and R_NS are the mass and the radius of the NS, respectively. The mass ratio of the BH to the NS, Q = M_BH/M_NS, and the dimensionless spin parameter of the BH, chi, are chosen to be Q = 5 and chi = 0.75, together with M_NS = 1.35 M_sun. We obtain the following results: (i) The inclination angle of i_tilt,0 < 70[deg.] and i_tilt,0 < 50[deg.] are required for the formation of a remnant disk with its mass larger than 0.1 M_sun for the case C = 0.140 and C = 0.160, respectively, while the disk mass is always smaller than 0.1M_sun for C = 0.175. The ejecta with its mass larger than 0.01 M_sun is obtained for i_tilt,0 < 85[deg.] with C = 0.140, for i_tilt,0 < 65[deg.] with C = 0.160, and for i_tilt,0 < 30[deg.] with C = 0.175. (ii) The rotational axis of the dense part of the remnant disk is approximately aligned with the remnant BH spin for i_tilt,0 = 30[deg.]. On the other hand, the disk axis is misaligned initially with ~ 30[deg.] for i_tilt,0 = 60[deg.], and the alignment with the remnant BH spin is achieved at ~ 50--60 ms after the onset of merger. The accretion time scale of the remnant disk is typically ~ 100 ms and depends only weakly on the misalignment angle and the EOS. (iii) The ejecta velocity is typically ~ 0.2--0.3c and depends only weakly on i_tilt,0 and the EOS of the NS, while the morphology of the ejecta depends on its mass. (iv) The gravitational-wave spectra contains the information of the NS compactness in the cutoff frequency for i_tilt,0 < 60[deg.]., Comment: 26 pages, 19 figures

We investigate properties of material ejected dynamically in the merger of black hole-neutron star binaries by numerical-relativity simulations. We systematically study the dependence of ejecta properties on the mass ratio of the binary, spin of the black hole, and equation of state of the neutron-star matter. Dynamical mass ejection is driven primarily by tidal torque, and the ejecta is much more anisotropic than that from binary neutron star mergers. In particular, the dynamical ejecta is concentrated around the orbital plane with a half opening angle of 10--20deg and often sweeps out only a half of the plane. The ejecta mass can be as large as ~0.1M_sun, and the velocity is subrelativistic with ~0.2--0.3c for typical cases. The ratio of the ejecta mass to the bound mass (disk and fallback components) is larger, and the ejecta velocity is larger, for larger values of the binary mass ratio, i.e., for larger values of the black-hole mass. The remnant black hole-disk system receives a kick velocity of O(100)km/s due to the ejecta linear momentum, and this easily dominates the kick velocity due to gravitational radiation. Structures of postmerger material, velocity distribution of the dynamical ejecta, fallback rates, and gravitational waves are also investigated. We also discuss the effect of ejecta anisotropy on electromagnetic counterparts, specifically a macronova/kilonova and synchrotron radio emission, developing analytic models., Comment: 37 pages, 22 figures, matched to the published version

We calculate quasiequilibrium sequences of equal-mass, irrotational binary neutron stars (BNSs) in a scalar-tensor (ST) theory of gravity that admits dynamical scalarization. We model neutron stars with realistic equations of state (notably through piecewise polytropic equations of state). Using these quasiequilibrium sequences we compute the binary's scalar charge and binding energy versus orbital angular frequency. We find that the absolute value of the binding energy is smaller than in general relativity (GR), differing at most by ~14% at high frequencies for the cases considered. We use the newly computed binding energy and the balance equation to estimate the number of gravitational-wave (GW) cycles during the adiabatic, quasicircular inspiral stage up to the end of the sequence, which is the last stable orbit or the mass-shedding point, depending on which comes first. We find that, depending on the ST parameters, the number of GW cycles can be substantially smaller than in GR. In particular, we obtain that when dynamical scalarization sets in around a GW frequency of ~130 Hz, the sole inclusion of the ST binding energy causes a reduction of GW cycles from ~120 Hz up to the end of the sequence (~1200 Hz) of ~11% with respect to the GR case. We estimate that when the ST energy flux is also included the reduction in GW cycles becomes of ~24%. Quite interestingly, dynamical scalarization can produce a difference in the number of GW cycles with respect to the GR point-particle case that is much larger than the effect due to tidal interactions, which is on the order of only a few GW cycles. These results further clarify and confirm recent studies that have evolved BNSs either in full numerical relativity or in post-Newtonian theory, and point out the importance of developing accurate ST-theory waveforms for systems composed of strongly self-gravitating objects, such as BNSs., Comment: 16 pages, 14 figures, 2 tables, updated to match the published version

We develop a method to compute low-eccentricity initial data of binary neutron stars required to perform realistic simulations in numerical relativity. The orbital eccentricity is controlled by adjusting the orbital angular velocity of a binary and incorporating an approaching relative velocity of the neutron stars. These modifications improve the solution primarily through the hydrostatic equilibrium equation for the binary initial data. The orbital angular velocity and approaching velocity of initial data are updated iteratively by performing time evolutions over ~3 orbits. We find that the eccentricity can be reduced by an order of magnitude compared to standard quasicircular initial data, specifically from ~0.01 to <~0.001, by three successive iterations for equal-mass binaries leaving ~10 orbits before the merger., Comment: 20 pages, 12 figures, matched to the published version

We carry out numerical-relativity simulations of coalescing binary neutron stars in a scalar-tensor theory that admits spontaneous scalarization. We model neutron stars with realistic equations of state. We choose the free parameters of the theory taking into account the constraints imposed by the latest observations of neutron-star-- white-dwarf binaries with pulsar timing. We show that even within those severe constraints, scalarization can still affect the evolution of the binary neutron stars not only during the late inspiral, but also during the merger stage. We also confirm that even when both neutron stars have quite small scalar charge at large separations, they can be strongly scalarized dynamically during the final stages of the inspiral. In particular, we identify the binary parameters for which scalarization occurs either during the late inspiral or only after the onset of the merger when a remnant, supramassive or hypermassive neutron star is formed. We also discuss how those results can impact the extraction of physical information on gravitational waves once they are detected., Comment: 17 pages, 12 figures

Massive (hypermassive and supramassive) neutron stars are likely to be often formed after the merger of binary neutron stars. We explore the evolution process of the remnant massive neutron stars and gravitational waves emitted by them, based on numerical-relativity simulations for binary neutron star mergers employing a variety of equations of state and choosing a plausible range of the neutron-star mass of binaries. We show that the lifetime of remnant hypermassive neutron stars depends strongly on the total binary mass and also on the equations of state. Gravitational waves emitted by the remnant massive neutron stars universally have a quasiperiodic nature of an approximately constant frequency although the frequency varies with time. We also show that the frequency and time-variation feature of gravitational waves depend strongly on the equations of state. We derive a fitting formula for the quasiperiodic gravitational waveforms, which may be used for the data analysis of a gravitational-wave signal., Comment: 33 pages, 18 figures. Accepted for publication in Physical Review D

Using an extended set of equations of state and a multiple-group multiple-code collaborative effort to generate waveforms, we improve numerical-relativity-based data-analysis estimates of the measurability of matter effects in neutron-star binaries. We vary two parameters of a parameterized piecewise-polytropic equation of state (EOS) to analyze the measurability of EOS properties, via a parameter {\Lambda} that characterizes the quadrupole deformability of an isolated neutron star. We find that, to within the accuracy of the simulations, the departure of the waveform from point-particle (or spinless double black-hole binary) inspiral increases monotonically with {\Lambda}, and changes in the EOS that did not change {\Lambda} are not measurable. We estimate with two methods the minimal and expected measurability of {\Lambda} in second- and third- generation gravitational-wave detectors. The first estimate, using numerical waveforms alone, shows two EOS which vary in radius by 1.3km are distinguishable in mergers at 100Mpc. The second estimate relies on the construction of hybrid waveforms by matching to post-Newtonian inspiral, and estimates that the same EOS are distinguishable in mergers at 300Mpc. We calculate systematic errors arising from numerical uncertainties and hybrid construction, and we estimate the frequency at which such effects would interfere with template-based searches., Comment: 21 pages, 13 figures

Numerical-relativity simulations for the merger of binary neutron stars are performed for a variety of equations of state (EOSs) and for a plausible range of the neutron-star mass, focusing primarily on the properties of the material ejected from the system. We find that a fraction of the material is ejected as a mildly relativistic and mildly anisotropic outflow with the typical and maximum velocities $\sim 0.15$ -- $0.25c$ and $\sim 0.5$ -- $0.8c$ (where $c$ is the speed of light), respectively, and that the total ejected rest mass is in a wide range $10^{-4}$ -- $10^{-2}M_{\odot}$, which depends strongly on the EOS, the total mass, and the mass ratio. The total kinetic energy ejected is also in a wide range between $10^{49}$ and $10^{51} {\rm ergs}$. The numerical results suggest that for a binary of canonical total mass $2.7M_{\odot}$, the outflow could generate an electromagnetic signal observable by the planned telescopes through the production of heavy-element unstable nuclei via the $r$-process or through the formation of blast waves during the interaction with the interstellar matter, if the EOS and mass of the binary are favorable ones., Comment: 28 pages, 19 figures, accepted to Physical Review D

We study the merger of black hole (BH)-neutron star (NS) binaries with a variety of BH spins aligned or anti-aligned with the orbital angular momentum, and with the mass ratio in the range MBH/MNS = 2--5, where MBH and MNS are the mass of the BH and NS, respectively. We model NS matter by systematically parametrized piecewise polytropic equations of state. The initial condition is computed in the puncture framework adopting an isolated horizon framework to estimate the BH spin and assuming an irrotational velocity field for the fluid inside the NS. Dynamical simulations are performed in full general relativity by an adaptive mesh refinement code, SACRA. The treatment of hydrodynamic equations and estimation of the disk mass are improved. We find that the NS is tidally disrupted irrespective of the mass ratio when the BH has a moderately large prograde spin, whereas only binaries with low mass ratios, MBH/MNS <~ 3 or small compactnesses of the NSs, bring the tidal disruption when the BH spin is zero or retrograde. The mass of the remnant disk is accordingly large as >~ 0.1 Msun, which is required by central engines of short gamma-ray bursts, if the BH spin is prograde. Information of the tidal disruption is reflected in a clear relation between the compactness of the NS and an appropriately defined "cutoff frequency" in the gravitational-wave spectrum, above which the spectrum damps exponentially. We find that the tidal disruption of the NS and excitation of the quasinormal mode of the remnant BH occur in a compatible manner in high mass-ratio binaries with the prograde BH spin. The correlation between the compactness and the cutoff frequency still holds for such cases. It is also suggested by extrapolation that the merger of an extremely spinning BH and an irrotational NS binary does not lead to formation of an overspinning BH., Comment: 33 pages, 26 figures, minor revision according to the published version and reference added

We report results of a numerical-relativity simulation for the merger of a black hole-neutron star binary with a variety of equations of state (EOSs) modeled by piecewise polytropes. We focus in particular on the dependence of the gravitational waveform at the merger stage on the EOSs. The initial conditions are computed in the moving-puncture framework, assuming that the black hole is nonspinning and the neutron star has an irrotational velocity field. For a small mass ratio of the binaries (e.g., MBH/MNS = 2 where MBH and MNS are the masses of the black hole and neutron star, respectively), the neutron star is tidally disrupted before it is swallowed by the black hole irrespective of the EOS. Especially for less-compact neutron stars, the tidal disruption occurs at a more distant orbit. The tidal disruption is reflected in a cutoff frequency of the gravitational-wave spectrum, above which the spectrum amplitude exponentially decreases. A clear relation is found between the cutoff frequency of the gravitational-wave spectrum and the compactness of the neutron star. This relation also depends weakly on the stiffness of the EOS in the core region of the neutron star, suggesting that not only the compactness but also the EOS at high density is reflected in gravitational waveforms. The mass of the disk formed after the merger shows a similar correlation with the EOS, whereas the spin of the remnant black hole depends primarily on the mass ratio of the binary, and only weakly on the EOS. Properties of the remnant disks are also analyzed., Comment: 27pages, 21 figures; erratum is added on Aug 5. 2011

Quasi-equilibrium sequences of binary neutron stars are constructed for a variety of equations of state in general relativity. Einstein's constraint equations in the Isenberg-Wilson-Mathews approximation are solved together with the relativistic equations of hydrostationary equilibrium under the assumption of irrotational flow. We focus on unequal-mass sequences as well as equal-mass sequences, and compare those results. We investigate the behavior of the binding energy and total angular momentum along a quasi-equilibrium sequence, the endpoint of sequences, and the orbital angular velocity as a function of time, changing the mass ratio, the total mass of the binary system, and the equation of state of a neutron star. It is found that the orbital angular velocity at the mass-shedding limit can be determined by an empirical formula derived from an analytic estimation. We also provide tables for 160 sequences which will be useful as a guideline of numerical simulations for the inspiral and merger performed in the near future., Comment: 66 pages, 26 figures, 6 tables, aastex

We elucidate the feature of gravitational waves (GWs) from binary neutron star merger collapsing to a black hole by general relativistic simulation. We show that GW spectrum imprints the coalescence dynamics, formation process of disk, equation of state for neutron stars, total masses, and mass ratio. A formation mechanism of the central engine of short $\gamma$-ray bursts, which are likely to be composed of a black hole and surrounding disk, therefore could be constrained by GW observation., Comment: Accepted to PRL

General relativistic quasiequilibrium states of black hole-neutron star binaries are computed in the moving-puncture framework. We propose three conditions for determining the quasiequilibrium states and compare the numerical results with those obtained in the excision framework. We find that the results obtained in the moving-puncture framework agree with those in the excision framework and with those in the third post-Newtonian approximation for the cases that (i) the mass ratio of the binary is close to unity irrespective of the orbital separation, and (ii) the orbital separation is large enough ($m_0\Omega \alt 0.02$ where $m_0$ and $\Omega$ are the total mass and the orbital angular velocity, respectively) irrespective of the mass ratio. For $m_0 \Omega \agt 0.03$, both of the results in the moving-puncture and excision frameworks deviate, more or less, from those in the third post-Newtonian approximation. Thus the numerical results do not provide a quasicircular state, rather they seem to have a nonnegligible eccentricity of order 0.01--0.1. We show by numerical simulation that a method in the moving-puncture framework can provide approximately quasicircular states in which the eccentricity is by a factor of $\sim 2$ smaller than those in quasiequilibrium given by other approaches., Comment: 14 pages, 5 figures; minor revision

General relativistic simulations for the merger of binary neutron stars are performed as an extension of a previous work\cite{Shibata:2006nm}. We prepare binary neutron stars with a large initial orbital separation and employ the moving-puncture formulation, which enables to follow merger and ringdown phases for a long time, even after black hole formation. For modeling inspiraling neutron stars, which should be composed of cold neutron stars, the Akmal-Pandhalipande-Ravenhall (APR) equation of state (EOS) is adopted. After the onset of the merger, the hybrid-type EOS is used; i.e., the cold and thermal parts are given by the APR and $\Gamma$-law EOSs, respectively. Three equal-mass binaries each with mass $1.4M_\odot,1.45M_\odot,1.5M_\odot$ and two unequal-mass binaries with mass 1.3--$1.6M_\odot$, 1.35--$1.65M_\odot$ are prepared. We focus primarily on the black hole formation case, and explore mass and spin of the black hole, mass of disks which surround the black hole, and gravitational waves emitted during the black hole formation. We find that (i) for the systems of $m_0=2.9$--$3.0M_\odot$ and of mass ratio $\approx 0.8$, the mass of disks which surround the formed black hole is 0.006--$0.02M_{\odot}$; (ii) the spin of the formed black hole is $0.78 \pm 0.02$ when a black hole is formed after the merger in the dynamical time scale. This value depends weakly on the total mass and mass ratio, and is about 0.1 larger than that of a black hole formed from nonspinning binary black holes; (iii) for the black-hole formation case, Fourier spectrum shape of gravitational waves emitted in the merger and ringdown phases has a universal qualitative feature irrespective of the total mass and mass ratio, but quantitatively, the spectrum reflects the parameters of the binary neutron stars., Comment: 35 pages, 20 figures, accepted to PRD

Using our new numerical-relativity code SACRA, long-term simulations for inspiral and merger of black hole (BH)-neutron star (NS) binaries are performed, focusing particularly on gravitational waveforms. As the initial conditions, BH-NS binaries in a quasiequilibrium state are prepared in a modified version of the moving-puncture approach. The BH is modeled by a nonspinning moving puncture and for the NS, a polytropic equation of state with $\Gamma=2$ and the irrotational velocity field are employed. The mass ratio of the BH to the NS, $Q=M_{\rm BH}/M_{\rm NS}$, is chosen in the range between 1.5 and 5. The compactness of the NS, defined by ${\cal C}=GM_{\rm NS}/c^2R_{\rm NS}$, is chosen to be between 0.145 and 0.178. For a large value of $Q$ for which the NS is not tidally disrupted and is simply swallowed by the BH, gravitational waves are characterized by inspiral, merger, and ringdown waveforms. In this case, the waveforms are qualitatively the same as that from BH-BH binaries. For a sufficiently small value of $Q \alt 2$, the NS may be tidally disrupted before it is swallowed by the BH. In this case, the amplitude of the merger and ringdown waveforms is very low, and thus, gravitational waves are characterized by the inspiral waveform and subsequent quick damping. The difference in the merger and ringdown waveforms is clearly reflected in the spectrum shape and in the "cut-off" frequency above which the spectrum amplitude steeply decreases. When an NS is not tidally disrupted (e.g., for Q=5), kick velocity, induced by asymmetric gravitational wave emission, agrees approximately with that derived for the merger of BH-BH binaries, whereas for the case that the tidal disruption occurs, the kick velocity is significantly suppressed., Comment: 25 pages, 3 jpg figures, accepted for publication in PRD; erratum is added on Jul 23. 2012

We report our new code (named SACRA) for numerical relativity simulations in which an adaptive mesh refinement algorithm is implemented. In this code, the Einstein equations are solved in the BSSN formalism with a fourth-order finite differencing, and the hydrodynamic equations are solved by a third-order high-resolution central scheme. The fourth-order Runge-Kutta scheme is adopted for integration in time. To test the code, simulations for coalescence of black hole-black hole (BH-BH), neutron star-neutron star (NS-NS), and black hole-neutron star (BH-NS) binaries are performed, and also, properties of BHs formed after the merger and gravitational waveforms are compared among those three cases. For the simulations of BH-BH binaries, we adopt the same initial conditions as those by Buonanno et al. and compare numerical results. We find reasonable agreement except for a slight disagreement possibly associated with the difference in choice of gauge conditions and numerical schemes. For an NS-NS binary, we performed simulations employing both SACRA and Shibata's previous code, and find reasonable agreement. For a BH-NS binary, we compare numerical results with our previous ones, and find that gravitational waveforms and properties of the BH formed after the merger agree well with those of our previous ones, although the disk mass formed after the merger is less than 0.1% of the total rest mass, which disagrees with the previous result. We also report numerical results of a longterm simulation (with $\sim 4$ orbits) for a BH-NS binary for the first time. All these numerical results show behavior of convergence, and extrapolated numerical results for time spent in the inspiral phase agree with post-Newtonian predictions in a reasonable accuracy., Comment: PRD in press. Typos are corrected, and references are added

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., Comment: 19 pages, 23 figures, replaced with the published version

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., Comment: 22 pages, 14 figures, fixed a few typos

We systematically perform the merger simulation of black hole-neutron star (BH-NS) binaries in full general relativity, focusing on the case that the NS is tidally disrupted. We prepare BH-NS binaries in a quasicircular orbit as the initial condition in which the BH is modeled by a nonspinning moving puncture. For modeling the NS, we adopt the $\Gamma$-law equation of state with $\Gamma=2$ and the irrotational velocity field. We change the BH mass in the range $M_{\rm BH} \approx 3.3$--$4.6M_{\odot}$, while the rest mass of the NS is fixed to be $M_{*}=1.4 M_{\odot}$ (i.e., the NS mass $M_{\rm NS} \approx 1.3M_{\odot}$). The radius of the corresponding spherical NS is set in the range $R_{\rm NS} \approx 12$--15 km (i.e., the compactness $GM_{\rm NS}/R_{\rm NS}c^2 \approx 0.13$--0.16). We find for all the chosen initial conditions that the NS is tidally disrupted near the innermost stable circular orbit. For the model of $R_{\rm NS}=12$ km, more than 97 % of the rest mass is quickly swallowed into the BH and the resultant torus mass surrounding the BH is less than $0.04M_{\odot}$. For the model of $R_{\rm NS} \approx 14.7$ km, by contrast, the torus mass is about $0.16M_{\odot}$ for the BH mass $\approx 4M_{\odot}$. The thermal energy of the material in the torus increases by the shock heating occurred in the collision between the spiral arms, resulting in the temperature $10^{10}$--$10^{11}$ K. (.. omission ..) We also present gravitational waveforms during the inspiral, tidal disruption of the NS, and subsequent evolution of the disrupted material. (.. omission ..), Comment: 20 pages

We construct new models of black hole-neutron star binaries in quasiequilibrium circular orbits by solving Einstein's constraint equations in the conformal thin-sandwich decomposition together with the relativistic equations of hydrostationary equilibrium. We adopt maximal slicing, assume spatial conformal flatness, and impose equilibrium boundary conditions on an excision surface (i.e., the apparent horizon) to model the black hole. In our previous treatment we adopted a "leading-order" approximation for a parameter related to the black-hole spin in these boundary conditions to construct approximately nonspinning black holes. Here we improve on the models by computing the black hole's quasilocal spin angular momentum and setting it to zero. As before, we adopt a polytropic equation of state with adiabatic index Gamma=2 and assume the neutron star to be irrotational. In addition to recomputing several sequences for comparison with our earlier results, we study a wider range of neutron star masses and binary mass ratios. To locate the innermost stable circular orbit we search for turning points along both the binding energy and total angular momentum curves for these sequences. Unlike for our previous approximate boundary condition, these two minima now coincide. We also identify the formation of cusps on the neutron star surface, indicating the onset of tidal disruption. Comparing these two critical binary separations for different mass ratios and neutron star compactions we distinguish those regions that will lead to a tidal disruption of the neutron star from those that will result in the plunge into the black hole of a neutron star more or less intact, albeit distorted by tidal forces., Comment: Minor corrections, Fig.8 revised, 15 pages, 15 figures, published in Phys. Rev. D

Many of the recent numerical simulations of binary black holes in vacuum adopt the moving puncture approach. This successful approach avoids the need to impose numerical excision of the black hole interior and is easy to implement. Here we wish to explore how well the same approach can be applied to moving black hole punctures in the presence of relativistic hydrodynamic matter. First, we evolve single black hole punctures in vacuum to calibrate our BSSN (Baumgarte-Shapiro-Shibata-Nakamura) implementation and to confirm that the numerical solution for the exterior spacetime is invariant to any ``junk'' (i.e., constraint-violating) initial data employed in the black hole interior. Then we focus on relativistic Bondi accretion onto a moving puncture Schwarzschild black hole as a numerical testbed for our high-resolution shock-capturing relativistic hydrodynamics scheme. We find that the hydrodynamical equations can be evolved successfully in the interior without imposing numerical excision. These results help motivate the adoption of the moving puncture approach to treat the binary black hole-neutron star problem using conformal thin-sandwich initial data., Comment: 21 pages, 21 figures, RevTex, accepted by PRD; minor updates

We construct quasiequilibrium sequences of black hole-neutron star binaries in general relativity. We solve Einstein's constraint equations in the conformal thin-sandwich formalism, subject to black hole boundary conditions imposed on the surface of an excised sphere, together with the relativistic equations of hydrostatic equilibrium. In contrast to our previous calculations we adopt a flat spatial background geometry and do not assume extreme mass ratios. We adopt a Gamma=2 polytropic equation of state and focus on irrotational neutron star configurations as well as approximately nonspinning black holes. We present numerical results for ratios of the black hole's irreducible mass to the neutron star's ADM mass in isolation of M_{irr}^{BH}/M_{ADM,0}^{NS} = 1, 2, 3, 5, and 10. We consider neutron stars of baryon rest mass M_B^{NS}/M_B^{max} = 83% and 56%, where M_B^{max} is the maximum allowed rest mass of a spherical star in isolation for our equation of state. For these sequences, we locate the onset of tidal disruption and, in cases with sufficiently large mass ratios and neutron star compactions, the innermost stable circular orbit. We compare with previous results for black hole-neutron star binaries and find excellent agreement with third-order post-Newtonian results, especially for large binary separations. We also use our results to estimate the energy spectrum of the outgoing gravitational radiation emitted during the inspiral phase for these binaries., Comment: 17 pages, 15 figures, published in Phys. Rev. D

We construct quasiequilibrium sequences of black hole-neutron star binaries for arbitrary mass ratios by solving the constraint equations of general relativity in the conformal thin-sandwich decomposition. We model the neutron star as a stationary polytrope satisfying the relativistic equations of hydrodynamics, and account for the black hole by imposing equilibrium boundary conditions on the surface of an excised sphere (the apparent horizon). In this paper we focus on irrotational configurations, meaning that both the neutron star and the black hole are approximately nonspinning in an inertial frame. We present results for a binary with polytropic index n=1, mass ratio M_{irr}^{BH}/M_{B}^{NS}=5 and neutron star compaction M_{ADM,0}^{NS}/R_0=0.0879, where M_{irr}^{BH} is the irreducible mass of the black hole, M_{B}^{NS} the neutron star baryon rest-mass, and M_{ADM,0}^{NS} and R_0 the neutron star Arnowitt-Deser-Misner mass and areal radius in isolation, respectively. Our models represent valid solutions to Einstein's constraint equations and may therefore be employed as initial data for dynamical simulations of black hole-neutron star binaries., Comment: 5 pages, 1 figure, revtex4, published in Phys.Rev.D

We have calculated the first dynamical evolutions of merging black hole-neutron star binaries that treat the combined spacetime in a nonperturbative general relativistic framework. Using the conformal flatness approximation, we have studied how the location of the tidal disruption radius with respect to the the black hole horizon and innermost stable circular orbit (ISCO) affects the qualitative evolution of the system. Based on simple arguments, we show that for a binary mass ratio q>~0.24, tidal disruption occurs outside the ISCO, while the opposite is true for q<~0.24. When tidal disruption occurs sufficiently far outside the ISCO, mass is transferred unstably from the neutron star to the black hole, resulting in the complete disruption of the neutron star. When tidal disruption occurs slightly within the ISCO, we find that some of the mass forms an extremely hot disk around the black hole. The resulting configurations in this case are excellent candidates for the progenitors of short-hard gamma ray bursts., Comment: 8 pages, 5 figures, in Proceedings of the Albert Einstein Century International Conference, Paris, France, 2005, edited by Jean-Michel Alimi and Andre Fuzfa