We present numerical results of three-dimensional simulations for the merger of binary neutron stars in full general relativity. Hybrid equations of state are adopted to mimic realistic nuclear equations of state. In this approach, we divide the equations of state into two parts as P = P cold + P th . P cold is the cold part for which we assign a fitting formula for realistic equations of state of cold nuclear matter slightly modifying the formula developed by Haensel and Potekhin. We adopt the SLy and FPS equations of state for which the maximum allowed ADM mass of cold and spherical neutron stars is ≈ 2.04M⊙ and 1.80M⊙, respectively. P th denotes the thermal part which is written as P th = (Γ th − 1)ρ(ε − ε cold ), where ρ, ε, ε cold , and Γ th are the baryon rest-mass density, total specific internal energy, specific internal energy of the cold part, and the adiabatic constant, respectively. Simulations are performed for binary neutron stars of the total ADM mass in the range between 2.4M⊙ and 2.8M⊙ with the rest-mass ratio QM to be in the range 0.9 < ∼ QM ≤ 1. It is found that if the total ADM mass of the system is larger than a threshold M thr , a black hole is promptly formed in the merger irrespective of the mass ratios. In the other case, the outcome is a hypermassive neutron star of a large ellipticity, which results from the large adiabatic index of the realistic equations of state adopted. The value of M thr depends on the equation of state: M thr ∼ 2.7M⊙ and ∼ 2.5M⊙ for the SLy and FPS equations of state, respectively. Gravitational waves are computed in terms of a gauge-invariant wave extraction technique. In the formation of the hypermassive neutron star, quasiperiodic gravitational waves of a large amplitude and of frequency between 3 and 4 kHz are emitted. The estimated emission time scale is < ∼ 100 ms, after which the hypermassive neutron star collapses to a black hole. Because of the long emission time, the effective amplitude may be large enough to be detected by advanced laser interferometric gravitational wave detectors if the distance to the source is smaller than ∼ 100 Mpc. Thermal properties of the outcome formed after the merger are also analyzed to approximately estimate the neutrino emission energy.

We report the results of a first study that uses numerical simulations to estimate the accuracy with which one can use gravitational wave observations of double neutron-star inspiral to measure parameters of the neutron-star equation of state. The simulations use the evolution and initial-data codes of Shibata and Uryū to compute the last several orbits and the merger of neutron stars, with matter described by a parametrized equation of state. Previous work suggested the use of an effective cutoff frequency to place constraints on the equation of state. We find, however, that greater accuracy is obtained by measuring departures from the point-particle limit of the gravitational waveform produced during the late inspiral. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly for smaller values of the neutron-star compactness (the ratio of the mass of the neutron-star to its radius). We estimate that realistic equations of state will lead to gravitational waveforms that are distinguishable from point-particle inspirals at an effective distance (the distance to an optimally oriented and located system that would produce an equivalent waveform amplitude) of 100 Mpc or less. As Lattimer and Prakash observed, neutron-star radius is closely tied to the pressure at density not far above nuclear. Our results suggest that broadband gravitational wave observations at frequencies between 500 and 1000 Hz will constrain this pressure, and we estimate the accuracy with which it can be measured. Related first estimates of radius measurability show that the radius can be determined to an accuracy of R $ 1 km at 100 Mpc.

We have performed 3D numerical simulations for merger of equal mass binary neutron stars in full general relativity. We adopt a Γ-law equation of state in the form P = (Γ − 1)ρε where P , ρ, ε and Γ are the pressure, rest mass density, specific internal energy, and the adiabatic constant with Γ = 2. As initial conditions, we adopt models of corotational and irrotational binary neutron stars in a quasi-equilibrium state which are obtained using the conformal flatness approximation for the three geometry as well as an assumption that a helicoidal Killing vector exists. In this paper, we pay particular attention to the final product of the coalescence. We find that the final product depends sensitively on the initial compactness parameter of the neutron stars : In a merger between sufficiently compact neutron stars, a black hole is formed in a dynamical timescale. As the compactness is decreased, the formation timescale becomes longer and longer. It is also found that a differentially rotating massive neutron star is formed instead of a black hole for less compact binary cases, in which the rest mass of each star is less than 70 − 80% of the maximum allowed mass of a spherical star. In the case of black hole formation, we roughly evaluate the mass of the disk around the black hole. For the merger of corotational binaries, a disk of mass ∼ 0.05 − 0.1M * may be formed, where M * is the total rest mass of the system. On the other hand, for the merger of irrotational binaries, the disk mass appears to be very small : < 0.01M * .04.25. Dm, 04.40.D

We present results of three dimensional numerical simulations of the merger of unequal-mass binary neutron stars in full general relativity. A ⌫-law equation of state Pϭ(⌫Ϫ1) is adopted, where P, , , and ⌫ are the pressure, rest mass density, specific internal energy, and the adiabatic constant, respectively. We take ⌫ϭ2 and the baryon rest-mass ratio Q M to be in the range 0.85-1. The typical grid size is (633,633,317) for (x,y,z). We improve several implementations since the latest work. In the present code, the radiation reaction of gravitational waves is taken into account with a good accuracy. This fact enables us to follow the coalescence all the way from the late inspiral phase through the merger phase for which the transition is triggered by the radiation reaction. It is found that if the total rest mass of the system is more than ϳ1.7 times of the maximum allowed rest mass of spherical neutron stars, a black hole is formed after the merger, irrespective of the mass ratios. The gravitational waveforms and outcomes in the merger of unequal-mass binaries are compared with those in equal-mass binaries. It is found that the disk mass around the so formed black holes increases with decreasing rest-mass ratios and decreases with increasing compactness of neutron stars. The merger process and the gravitational waveforms also depend strongly on the rest-mass ratios even for the range Q M ϭ0.85-1.

We propose a new numerical method to compute quasi-equilibrium sequences of general relativistic irrotational binary neutron star systems. It is a good approximation to assume that (1) the binary star system is irrotational, i.e. the vorticity of the flow field inside component stars vanishes everywhere (irrotational flow), and (2) the binary star system is in quasi-equilibrium, for an inspiraling binary neutron star system just before the coalescence as a result of gravitational wave emission. We can introduce the velocity potential for such an irrotational flow field, which satisfies an elliptic partial differential equation (PDE) with a Neumann type boundary condition at the stellar surface. For a treatment of general relativistic gravity, we use the Wilson-Mathews formulation, which assumes conformal flatness for spatial components of metric. In this formulation, the basic equations are expressed by a system of elliptic PDEs. We have developed a method to solve these PDEs with appropriate boundary conditions. The method is based on the established prescription for computing equilibrium states of rapidly rotating axisymmetric neutron stars or Newtonian binary systems. We have checked the reliability of our new code by comparing our results with those of other computations available. We have also performed several convergence tests. By using this code, we have obtained quasi-equilibrium sequences of irrotational binary star systems with strong gravity as models for final states of real evolution of binary neutron star systems just before coalescence. Analysis of our quasi-equilibrium sequences of binary star systems shows that the systems may not suffer from dynamical instability of the orbital motion and that the maximum density does not increase as the binary separation decreases.

We performed 3D numerical simulations of the merger of equal-mass binary neutron stars in full general relativity using a new large-scale supercomputer. We take the typical grid size as (505, 505, 253) for (x, y, z) and the maximum grid size as (633, 633, 317). These grid numbers enable us to put the outer boundaries of the computational domain near the local wave zone and hence to calculate gravitational waveforms of good accuracy (within ∼ 10% error) for the first time. To model neutron stars, we adopt a Γ -law equation of state in the form P = (Γ − 1)ρε, where P , ρ, ε and Γ are the pressure, rest mass density, specific internal energy and adiabatic constant. It is found that gravitational waves in the merger stage have characteristic features that reflect the formed objects. In the case that a massive, transient neutron star is formed, its quasi-periodic oscillations are excited for a long duration, and this property is reflected clearly by the quasi-periodic nature of waveforms and the energy luminosity. In the case of black hole formation, the waveform and energy luminosity are likely damped after a short merger stage. However, a quasi-periodic oscillation can still be seen for a certain duration, because an oscillating transient massive object is formed during the merger. This duration depends strongly on the initial compactness of neutron stars and is reflected in the Fourier spectrum of gravitational waves. To confirm our results and to calibrate the accuracy of gravitational waveforms, we carried out a wide variety of test simulations, changing the resolution and size of the computational domain. * ) Hereafter, we refer to the stage after which the hydrodynamic interaction between two neutron stars sets in as the 'merger stage'. The stage before the merger stage is referred to as the 'early stage'.

We consider compact binary systems, modeled in general relativity as vacuum or perfect-fluid spacetimes with a helical Killing vector k α , heuristically, the generator of time-translations in a corotating frame. Systems that are stationary in this sense are not asymptotically flat, but have asymptotic behavior corresponding to equal amounts of ingoing and outgoing radiation. For blackhole binaries, a rigidity theorem implies that the Killing vector lies along the horizon's generators, and from this one can deduce the zeroth law (constant surface gravity of the horizon). Remarkably, although the mass and angular momentum of such a system are not defined, there is an exact first law, relating the change in the asymptotic Noether charge to the changes in the vorticity, baryon mass, and entropy of the fluid, and in the area of black holes.Binary systems with M Ω small have an approximate asymptopia in which one can write the first law in terms of the asymptotic mass and angular momentum. Asymptotic flatness is precise in two classes of solutions used to model binary systems: spacetimes satisfying the post-Newtonian equations, and solutions to a modified set of field equations that have a spatially conformally flat metric. (The spatial conformal flatness formalism with helical symmetry, however, is consistent with maximal slicing only if replaces the extrinsic curvature in the field equations by an artificially tracefree expression in terms of the shift vector.) For these spacetimes, nearby equilibria whose stars have the same vorticity obey the relation δM = ΩδJ, from which one can obtain a turning point criterion that governs the stability of orbits.

We present our latest results for simulation for merger of black hole (BH)neutron star (NS) binaries in full general relativity which is performed preparing a quasicircular state as initial condition. The BH is modeled by a moving puncture with no spin and the NS by the Γ-law equation of state with Γ = 2 and corotating velocity field as a first step. The mass of the BH is chosen to be ≈ 3.2M ⊙ or 4.0M ⊙ , and the rest-mass of the NS ≈ 1.4M ⊙ with relatively large radius of the NS ≈ 13-14 km. The NS is tidally disrupted near the innermost stable orbit but ∼ 80-90% of the material is swallowed into the BH and resulting disk mass is not very large as ∼ 0.3M ⊙ even for small BH mass ∼ 3.2M ⊙ . The result indicates that the system of a BH and a massive disk of ∼ M ⊙ is not formed from nonspinning BH-NS binaries irrespective of BH mass, although a disk of mass ∼ 0.1M ⊙ is a possible outcome for this relatively small BH mass range as ∼ 3-4M ⊙ . Our results indicate that the merger of low-mass BH and NS may form a central engine of short-gamma-ray bursts.