久徳 浩太郎

We perform high-resolution magnetohydrodynamics simulations of binary neutron star mergers in numerical relativity on the Japanese supercomputer K. The neutron stars and merger remnants are covered by a grid spacing of 70 m, which yields the highest-resolution results among those derived so far. By an in-depth resolution study, we clarify several amplification mechanisms of magnetic fields during the binary neutron star merger for the first time. First, the Kelvin-Helmholtz instability developed in the shear layer at the onset of the merger significantly amplifies the magnetic fields. A hypermassive neutron star (HMNS) formed after the merger is then subject to the nonaxisymmetric magnetorotational instability, which amplifies the magnetic field in the HMNS. These two amplification mechanisms cannot be found with insufficient-resolution runs. We also show that the HMNS eventually collapses to a black hole surrounded by an accretion torus which is strongly magnetized at birth.

Recent studies suggest that binary neutron star (NS-NS) mergers robustly produce heavy r-process nuclei above the atomic mass number A similar to 130 because their ejecta consist of almost pure neutrons (electron fraction of Y-e < 0.1). However, the production of a small amount of the lighter r-process nuclei (A approximate to 90-120) conflicts with the spectroscopic results of r-process-enhanced Galactic halo stars. We present, for the first time, the result of nucleosynthesis calculations based on the fully general relativistic simulation of a NS-NS merger with approximate neutrino transport. It is found that the bulk of the dynamical ejecta are appreciably shock-heated and neutrino processed, resulting in a wide range of Y-e (approximate to 0.09-0.45). The mass-averaged abundance distribution of calculated nucleosynthesis yields is in reasonable agreement with the full-mass range (A approximate to 90-240) of the solar r-process curve. This implies, if our model is representative of such events, that the dynamical ejecta of NS-NS mergers could be the origin of the Galactic r-process nuclei. Our result also shows that radioactive heating after similar to 1 day from the merging, which gives rise to r-process-powered transient emission, is dominated by the beta-decays of several species close to stability with precisely measured half-lives. This implies that the total radioactive heating rate for such an event can be well constrained within about a factor of two if the ejected material has a solar-like r-process pattern.

We study the possibility of pre-merger localization of eccentric compact binary coalescences by second-generation gravitational-wave detector networks. Gravitational waves from eccentric binaries can be regarded as a sequence of pulses, which are composed of various higher harmonic modes than ones with twice the orbital frequency. The higher harmonic modes from a very early inspiral phase will not only contribute to the signal-to-noise ratio, but also allow us to localize the gravitational-wave source before the merger sets in. This is due to the fact that high-frequency gravitational waves are essential for the source localization via triangulation by ground-based detector networks. We found that the single-detector signal-to-noise ratio exceeds 5 at 10 min before the merger for a 1.4-1.4 M-aS (TM) eccentric binary neutron stars at 100 Mpc in optimal cases, and it can be localized up to 10 deg(2) at half a minute before the merger by a four-detector network. We will even be able to achieve similar to 10 deg(2) at 10 min before the merger for a face-on eccentric compact binary by a five-detector network.

Astrophysical charge-free black holes are known to satisfy no-hair relations through which all multipole moments can be specified in terms of just their mass and spin angular momentum. We here investigate the possible existence of no-hair-like relations among multipole moments for neutron stars and quark stars that are independent of their equation of state. We calculate the multipole moments of these stars up to hexadecapole order by constructing uniformly rotating and unmagnetized stellar solutions to the Einstein equations. For slowly rotating stars, we construct stellar solutions to quartic order in spin in a slow-rotation expansion, while for rapidly rotating stars, we solve the Einstein equations numerically with the LORENE and RNS codes. We find that the multipole moments extracted from these numerical solutions are consistent with each other and agree with the quartic-order slow-rotation approximation for spin frequencies below roughly 500 Hz. We also confirm that the current dipole is related to the mass quadrupole in an approximately equation-of-state-independent fashion, which does not break for rapidly rotating neutron stars or quark stars. We further find that the current-octupole and the mass-hexadecapole moments are related to the mass quadrupole in an approximately equation-of-state-independent way to roughly O(10%), worsening in the hexadecapole case. All of our findings are in good agreement with previous work that considered stellar solutions to leading order in a weak-field, Newtonian expansion. In fact, the hexadecapole-quadrupole relation agrees with the Newtonian one quite well even in moderately relativistic regimes. The quartic in spin, slowly rotating solutions found here allows us to estimate the systematic errors in the measurement of the neutron star's mass and radius with future x-ray observations, such as Neutron star Interior Composition ExploreR (NICER) and Large Observatory for X-ray Timing (LOFT). We find that the effect of these quartic-in-spin terms on the quadrupole and hexadecapole moments and stellar eccentricity may dominate the error budget for very rapidly rotating neutron stars. The new universal relations found here should help to reduce such systematic errors.

We study high-energy emission from the mergers of neutron star binaries as electromagnetic counterparts to gravitational waves aside from short gamma-ray bursts. The mergers entail significant mass ejection, which interacts with the surrounding medium to produce similar but brighter remnants than supernova remnants in a few years. We show that electrons accelerated in the remnants can produce synchrotron radiation in x rays detectable at similar to 100 Mpc by current generation telescopes and inverse Compton emission in gamma rays detectable by the Fermi Large Area Telescopes and the Cherenkov Telescope Array under favorable conditions. Optical synchrotron radiation is also detectable by telescopes with good angular resolution. The remnants may have already appeared in high-energy surveys such as the Monitor of All-sky X-ray Image and the Fermi Large Area Telescope as unidentified sources. We also suggest that the merger remnants could be the origin of ultrahigh-energy cosmic rays beyond the knee energy, similar to 10(15) eV, in the cosmic ray spectrum.

Information about the neutron-star equation of state is encoded in the waveform of a black hole-neutron star system through tidal interactions and the possible tidal disruption of the neutron star. During the inspiral this information depends on the tidal deformability. of the neutron star, and we find that the best-measured parameter during the merger and ringdown is consistent with. as well. We performed 134 simulations where we systematically varied the equation of state as well as the mass ratio, neutron star mass, and aligned spin of the black hole. Using these simulations we develop an analytic representation of the full inspiral-merger-ringdown waveform calibrated to these numerical waveforms; we use this analytic waveform and a Fisher matrix analysis to estimate the accuracy to which. can be measured with gravitational-wave detectors. We find that although the inspiral tidal signal is small, coherently combining this signal with the merger-ringdown matter effect improves the measurability of. by a factor of similar to 3 over using just the merger-ringdown matter effect alone. However, incorporating correlations between all the waveform parameters then decreases the measurability of. by a factor of similar to 3. The uncertainty in. increases with the mass ratio, but decreases as the black hole spin increases. Overall, a single Advanced LIGO detector can only marginally measure. for mass ratios Q = 2-5, black hole spins J(BH)/M-BH(2) = -0.5-0.75, and neutron star masses M-NS = 1.2M(circle dot)-1.45M(circle dot) at an optimally oriented distance of 100 Mpc. For the proposed Einstein Telescope, however, the uncertainty in. is an order of magnitude smaller.

We propose a possibility of ultrarelativistic electromagnetic counterparts to gravitationalwaves from binary neutron star mergers at nearly all the viewing angles. Our proposed mechanism relies on the merger-shock propagation accelerating a smaller mass in the outer parts of the neutron star crust to a larger Lorentz factor Gamma with smaller energy similar to 10(47) Gamma(-1) erg. This mechanism is difficult to resolve by current 3D numerical simulations. The outflows emit synchrotron flares for seconds to days by shocking the ambient medium. Ultrarelativistic flares shine at an early time and in high-energy bands, potentially detectable by current X-ray to radio instruments, such as Swift XRT and Pan-STARRS, and even in low ambient density similar to 10(-2) cm(-3) by EVLA. The flares probe the merger position and time, and the merger types as black hole-neutron star outflows would be non-/mildly relativistic.

Detection of the electromagnetic counterparts of gravitational wave (GW) sources is important to unveil the nature of compact binary coalescences. We perform three-dimensional, time-dependent, multi-frequency radiative transfer simulations for radioactively powered emission from the ejecta of black hole (BH)-neutron star (NS) mergers. Depending on the BH to NS mass ratio, spin of the BH, and equations of state of dense matter, BH-NS mergers can eject more material than NS-NS mergers. In such cases, radioactively powered emission from the BH-NS merger ejecta can be more luminous than that from NS-NS mergers. We show that, in spite of the expected larger distances to BH-NS merger events, the observed brightness of BH-NS mergers can be comparable to or even higher than that of NS-NS mergers. We find that, when the tidally disrupted BH-NS merger ejecta are confined to a small solid angle, the emission from BH-NS merger ejecta tends to be bluer than that from NS-NS merger ejecta for a given total luminosity. Thanks to this property, we might be able to distinguish BH-NS merger events from NS-NS merger events by multi-band observations of the radioactively powered emission. In addition to the GW observations, such electromagnetic observations can potentially provide independent information on the progenitors of GW sources and the nature of compact binary coalescences.

An electromagnetic transient powered by the radioactive decay of r-process elements, a so-called kilonova/macronova, is one of the possible observable consequences of compact binary mergers including at least one neutron star. Recent observations strongly suggest the discovery of the first electromagnetic transient, which is associated with the short gamma ray burst 130603B. We explore a possible progenitor of this event by combining numerical-relativity simulations and radiative transfer simulations of the dynamical ejecta of binary neutron star and black hole-neutron star mergers. We show that the ejecta models within a realistic parameter range consistently reproduce the observed near-infrared excess. We also show that the soft equation-of-state models for binary neutron star mergers and the stiff equation-of-state models for black hole-neutron star mergers are suitable for reproducing the observed luminosity.

Black hole-neutron star binary mergers display a much richer phenomenology than black hole-black hole mergers, even in the relatively simple case-considered in this paper-in which both the black hole and the neutron star are nonspinning. When the neutron star is tidally disrupted, the gravitational wave emission is radically different from the black hole-black hole case and it can be broadly classified in two groups, depending on the spatial extent of the disrupted material. We present a phenomenological model for the gravitational waveform amplitude in the frequency domain that encompasses the three possible outcomes of the merger: no tidal disruption, "mild," and "strong" tidal disruption. The model is calibrated to general relativistic numerical simulations using piecewise polytropic neutron star equations of state. It should prove useful to extract information on the nuclear equation of state from future gravitational-wave observations, and also to obtain more accurate estimates of black hole-neutron star merger event rates in second-and third-generation interferometric gravitational-wave detectors. We plan to extend and improve the model as longer and more accurate gravitational waveforms become available, and we will make it publicly available online as a MATHEMATICA package. We also present in the Appendix analytical fits of the projected KAGRA noise spectral density, which should be useful in data analysis applications.

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. © 2013 American Physical Society.

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 parametrized 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 that two EOSs which vary in radius by 1.3 km are distinguishable in mergers at 100 Mpc. The second estimate relies on the construction of hybrid waveforms by matching to post-Newtonian inspiral and estimates that the same EOSs are distinguishable in mergers at 300 Mpc. 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.

The merger of black hole-neutron star binaries can eject substantial material with the mass similar to 0.01-0.1M(circle dot) when the neutron star is disrupted prior to the merger. The ejecta shows significant anisotropy, and travels in a particular direction with the bulk velocity similar to 0.2c. This is drastically different from the binary neutron star merger, for which ejecta is nearly isotropic. Anisotropic ejecta brings electromagnetic-counterpart diversity which is unique to black hole-neutron star binaries, such as viewing-angle dependence, polarization, and proper motion. The kick velocity of the black hole, gravitational-wave memory emission, and cosmic-ray acceleration are also discussed.

We study gravitational waves emitted in the late inspiral stage of binary neutron stars by analyzing the wave form obtained in numerical-relativity simulations. For deriving the physical gravitational wave forms from the numerical results, the resolution extrapolation plays an essential role for our simulations. The extrapolated gravitational-wave phases are compared with those calculated in the post-Newtonian (PN) and effective-one-body (EOB) formalisms including corrections of tidal effects. We show that the extrapolated gravitational-wave phases in numerical relativity agree well with those by the PN and EOB calculations for most of the inspiral stage except for a tidally dominated, final inspiral stage, in which the PN and EOB results underestimate the tidal effects. Nevertheless, the accumulated phase difference between our extrapolated results and the results by the PN/EOB calculations is at most 1-3 radian in the last 15 cycles. © 2013 American Physical Society.

Neutron Star equation of State can be measured through • tidal effects in the late inspiral stage and • fourier peak frequency of gws from HMNS. However, to succeed in measuring the EOS, higher order PN corrections and • longer and more accurate NR computation are needed. GRB130603B is a golden event • This could be direct evidence of compact binary merger hypothesis of short GRBs. • The time scale, brightness, and color of Kilonova are quite consistent with the NR prediction. For NS5NS merger models, soft EOSs are favored. For BH5NS merger models, stiff EOSs are favored.

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 similar to 0.15-0.25c and similar to 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(circle dot), 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) ergs. The numerical results suggest that for a binary of canonical total mass 2.7M(circle dot), the outflow could generate an electromagnetic signal observable by the planned telescopes through the production of heavy-element unstable nuclei via the r-process [6,20,21] or through the formation of blast waves during the interaction with the interstellar matter [7], if the EOS and mass of the binary are favorable ones. DOI: 10.1103/PhysRevD.87.024001

We construct a new three-dimensional general relativistic magnetohydrodynamics code, in which a fixed mesh refinement technique is implemented. To ensure the divergence-free condition as well as the magnetic flux conservation, we employ the method by Balsara [J. Comp. Physiol. 174, 614 (2001); J. Comp. Phys. 228, 5040 (2009)]. Using this new code, we evolve differentially rotating magnetized neutron stars, and find that a magnetically driven outflow is launched from the star exhibiting a kink instability. The matter ejection rate and Poynting flux are still consistent with our previous finding [M. Shibata, Y. Suwa, K. Kiuchi, and K. Ioka, Astrophys. J. 734, L36 (2011)] obtained in axisymmetric simulations.

The maximum likelihood method is often used for parameter estimation in gravitational wave astronomy. Recently, an interesting approach was proposed by Vallisneri to evaluate the distributions of parameter estimation errors expected for the method. This approach is to statistically analyze the local peaks of the likelihood surface, and works efficiently even for signals with low signal-to-noise ratios. Focusing special attention to geometric structure of the likelihood surface, we follow the proposed approach and derive formulas for a simplified model of data analysis where the target signal has only one intrinsic parameter, along with its overall amplitude. Then we apply our formulas to correlation analysis of stochastic gravitational wave background with a power-law spectrum. We report qualitative trends of the formulas using numerical results specifically obtained for correlation analysis with two Advanced-LIGO detectors.

Numerical simulations for the merger of binary neutron stars are performed in full general relativity incorporating both nucleonic and hyperonic finite-temperature equations of state (EOS) and neutrino cooling. It is found that for the nucleonic and hyperonic EOS, a hyper-massive neutron star (HMNS) with a long lifetime (t(life) greater than or similar to 10 ms) is the outcome for the total mass approximate to 2.7 M-circle dot. For the total mass approximate to 3 M-circle dot, a long-lived (short-lived with t(life) approximate to 3 ms) HMNS is the outcome for the nucleonic (hyperonic) EOS. It is shown that the typical total neutrino luminosity of the HMNS is similar to 3-6 x 10(53) erg s(-1) and the effective amplitude of gravitational waves from the HMNS is 1-4 x 10(-22) at f approximate to 2-3.2 kHz for a source of distance of 100 Mpc. During the HMNS phase, characteristic frequencies of gravitational waves shift to a higher frequency for the hyperonic EOS in contrast to the nucleonic EOS in which they remain constant approximately. Our finding suggests that the effects of hyperons are well imprinted in gravitational waves and their detection will give us a potential opportunity to explore the composition of the neutron star matter. We present the neutrino luminosity curve when a black hole is formed as well.

The late inspiral, merger, and ringdown of a black hole-neutron star (BHNS) system can provide information about the neutron-star equation of state (EOS). Candidate EOSs can be approximated by a parametrized piecewise-polytropic EOS above nuclear density, matched to a fixed low-density EOS; and we report results from a large set of BHNS inspiral simulations that systematically vary two parameters. To within the accuracy of the simulations, we find that, apart from the neutron-star mass, a single physical parameter Lambda, describing its deformability, can be extracted from the late inspiral, merger, and ringdown waveform. This parameter is related to the radius, mass, and l = 2 Love number, k(2), of the neutron star by Lambda = 2k(2)R(5)/3M(NS)(5), and it is the same parameter that determines the departure from point-particle dynamics during the early inspiral. Observations of gravitational waves from BHNS inspiral thus restrict the EOS to a surface of constant Lambda in the parameter space, thickened by the measurement error. Using various configurations of a single Advanced LIGO detector, we find that Lambda(1/5) or equivalently R can be extracted to 10-50% accuracy from single events for mass ratios of Q = 2 and 3 at a distance of 100 Mpc, while with the proposed Einstein Telescope, EOS parameters can be extracted to accuracy an order of magnitude better.

We describe the current status of our numerical simulations for the collapse of a massive stellar core to a black hole (BH) and the merger of binary neutron stars (BNS), performed in the framework of full general relativity incorporating finite-temperature equations of state (EOS) and neutrino cooling. For the stellar core collapse simulation, we present the latest numerical results. We employed a purely nucleonic EOS derived by Shen et al. [Nucl. Phys. A 637, 435 (1998)]. As an initial condition, we adopted a 100 M-circle dot presupernova model calculated by Umeda and Nomoto [Astrophys. J. 637, 1014 (2008)], which has a massive core (M approximate to 3M(circle dot)) with a high value of entropy per baryon (s approximate to 4k(B)). Changing the degree of rotation for the initial condition, we clarify the strong dependence of the outcome of the collapse on this. When the rotation is rapid enough, the shock wave formed at the core bounce is deformed to a torus-like shape. Then, the infalling matter accumulates in the central region due to the oblique shock at the torus surface, hitting the proto-neutron star and dissipating the kinetic energy there. As a result, outflows can be launched. The proto-neutron eventually collapses to a BH and an accretion torus is formed around it. We also found that the evolution of the BH and torus depends strongly on the rotation initially given. In the BNS merger simulations, we employ an EOS incorporating a degree of freedom for hyperons derived by Shen et al. [Astrophys. J. Suppl. 197, 20 (2011)], in addition to the purely nucleonic EOS. The numerical simulations show that for the purely nucleonic EOS, a hypermassive neutron star (HMNS) with a long lifetime (>> 10 ms) is the outcome for the total mass M less than or similar to 3.0M(circle dot). In contrast, the formed HMNS collapses to a BH in a shorter time scale with the hyperonic EOS for M greater than or similar to 2.7 M-circle dot. It is shown that the typical total neutrino luminosity of the HMNS is similar to(3-10) x 10(53) ergs/s and the effective amplitude of gravitational waves from the HMNS is (2-6) x 10(-22) at f approximate to 2-2.5 kHz for a source distance of 100 Mpc.

Numerical simulations for the merger of binary neutron stars are performed in full general relativity incorporating both nucleonic and hyperonic finite-temperature equations of state (EOS) and neutrino cooling. It is found that even for the hyperonic EOS, a hypermassive neutron star is first formed after the merger for the typical total mass approximate to 2: 7M(circle dot), and subsequently collapses to a black hole (BH). It is shown that hyperons play a substantial role in the postmerger dynamics, torus formation around the BH, and emission of gravitational waves (GWs). In particular, the existence of hyperons is imprinted in GWs. Therefore, GW observations will provide a potential opportunity to explore the composition of neutron star matter.

We study the merger of black hole-neutron star binaries with a variety of black hole spins aligned or antialigned with the orbital angular momentum, and with the mass ratio in the range M-BH/M-NS = 2-5, where M-BH and M-NS are the mass of the black hole and neutron star, respectively. We model neutron-star 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 black hole spin and assuming an irrotational velocity field for the fluid inside the neutron star. 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 neutron star is tidally disrupted irrespective of the mass ratio when the black hole has a moderately large prograde spin, whereas only binaries with low mass ratios, M-BH/M-NS less than or similar to 3, or small compactnesses of the neutron stars bring the tidal disruption when the black hole spin is zero or retrograde. The mass of the remnant disk is accordingly large as greater than or similar to 0.1M(circle dot), which is required by central engines of short gamma-ray bursts, if the black hole spin is prograde. Information of the tidal disruption is reflected in a clear relation between the compactness of the neutron star 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 neutron star and excitation of the quasinormal mode of the remnant black hole occur in a compatible manner in high mass-ratio binaries with the prograde black hole 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 black hole and an irrotational neutron star binary does not lead to the formation of an overspinning black hole.

Numerical simulations for the merger of binary neutron stars are performed in full general relativity incorporating a finite-temperature (Shen's) equation of state (EOS) and neutrino cooling for the first time. It is found that for this stiff EOS, a hypermassive neutron star (HMNS) with a long lifetime (>> 10 ms) is the outcome for the total mass less than or similar to 3.0M(circle dot). It is shown that the typical total neutrino luminosity of the HMNS is similar to 3-8 x 10(53) erg/s and the effective amplitude of gravitational waves from the HMNS is 4-6 x 10(-22) at f = 2.1-2.5 kHz for a source distance of 100 Mpc. We also present the neutrino luminosity curve when a black hole is formed for the first time.

We perform a numerical-relativity simulation for the merger of binary neutron stars with 6 nuclear-theory-based equations of states (EOSs) described by piecewise polytropes. Our purpose is to explore the dependence of the dynamical behavior of the binary neutron star merger and resulting gravitational waveforms on the EOS of the supernuclear-density matter. The numerical results show that the merger process and the first outcome are classified into three types: (i) a black hole is promptly formed, (ii) a short-lived hypermassive neutron star (HMNS) is formed, (iii) a long-lived HMNS is formed. The type of the merger depends strongly on the EOS and on the total mass of the binaries. For the EOS with which the maximum mass is larger than 2M(circle dot), the lifetime of the HMNS is longer than 10 ms for a total mass m(0) = 2.7M(circle dot). A recent radio observation suggests that the maximum mass of spherical neutron stars is Mmax >= 1.97 +/- 0.04M(circle dot) in one sigma level. This fact and our results support the possible existence of a HMNS soon after the onset of the merger for a typical binary neutron star with m(0) = 2.7M(circle dot). We also show that the torus mass surrounding the remnant black hole is correlated with the type of the merger process; the torus mass could be large, >= 0.1M(circle dot), in the case that a long-lived HMNS is formed. We also show that gravitational waves carry information of the merger process, the remnant, and the torus mass surrounding a black hole.

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., M-BH/M-NS = 2, where M-BH and M-NS 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.

The waveform of gravitational waves from the final stage of coalescing low-mass black hole-neutron star binaries depends sensitively on the equation of state of neutron star matter. We show that the observation of such gravitational waves can lead to constraining the nuclear-matter equations of state.

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 less than or similar to 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 greater than or similar to 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 non-negligible 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 similar to 2 smaller than those in quasiequilibrium given by other approaches.

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-BH/M-NS, is chosen in the range between 1.5 and 5. The compactness of the NS, defined by C=GM(NS)/c(2)R(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 less than or similar to 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 "cutoff" frequency above which the spectrum amplitude steeply decreases. When a 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 when the tidal disruption occurs, the kick velocity is significantly suppressed.