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 ∼ 0.15 -0.25c and ∼ 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 , 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 , the outflow could generate an electromagnetic signal observable by the planned telescopes through the production of heavy-element unstable nuclei via the r-process [1][2][3] or through the formation of blast waves during the interaction with the interstellar matter [4], if the EOS and mass of the binary are favorable ones.

Three-dimensional simulations for the merger of binary neutron stars are performed in the framework of full general relativity. We pay particular attention to the black hole formation case and to the resulting mass of the surrounding disk for exploring possibility for formation of the central engine of short-duration gamma-ray bursts (SGRBs). Hybrid equations of state are adopted mimicking realistic, stiff nuclear equations of state (EOSs), for which the maximum allowed gravitational mass of cold and spherical neutron stars, M sph , is larger than 2M⊙. Such stiff EOSs are adopted motivated by the recent possible discovery of a heavy neutron star of mass ∼ 2.1 ± 0.2M⊙. For the simulations, we focus on binary neutron stars of the ADM mass M > ∼ 2.6M⊙. For an ADM mass larger than the threshold mass M thr , the merger results in prompt formation of a black hole irrespective of the mass ratio QM with 0.65 < ∼ QM ≤ 1. The value of M thr depends on the EOSs and is approximately written as 1.3-1.35M sph for the chosen EOSs. For the black hole formation case, we evolve the spacetime using a black hole excision technique and determine the mass of a quasistationary disk surrounding the black hole. The disk mass steeply increases with decreasing the value of QM for given ADM mass and EOS. This suggests that a merger with small value of QM is a candidate for producing central engine of SGRBs. For M < M thr , the outcome is a hypermassive neutron star of a large ellipticity. Because of the nonaxisymmetry, angular momentum is transported outward. If the hypermassive neutron star collapses to a black hole after the longterm angular momentum transport, the disk mass may be > ∼ 0.01M⊙ irrespective of QM . 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 frequency between 3 and 3.5 kHz are emitted irrespective of EOSs. The effective amplitude of gravitational waves can be > ∼ 5 × 10 −21 at a distance of 50 Mpc, and hence, it may be detected by advanced laser-interferometers. For the black hole formation case, the black hole excision technique enables a longterm computation and extraction of ring-down gravitational waves associated with a black hole quasinormal mode. It is found that the frequency and amplitude are ≈ 6.5-7 kHz and ∼ 10 −22 at a distance of 50 Mpc for the binary of mass M ≈ 2.7-2.9M⊙.

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.

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