Merger of binary neutron stars to a black hole: Disk mass, short gamma-ray bursts, and quasinormal mode ringing

Abstract

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 the 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, ${M}_{\mathrm{sph}}$, is larger than $2{M}_{\ensuremath{\bigodot}}$. Such stiff EOSs are adopted motivated by the recent possible discovery of a heavy neutron star of mass $\ensuremath{\sim}2.1\ifmmode\pm\else\textpm\fi{}0.2{M}_{\ensuremath{\bigodot}}$. For the simulations, we focus on binary neutron stars of the ADM mass $M\ensuremath{\gtrsim}2.6{M}_{\ensuremath{\bigodot}}$. For an ADM mass larger than the threshold mass ${M}_{\mathrm{thr}}$, the merger results in prompt formation of a black hole irrespective of the mass ratio ${Q}_{M}$ with $0.65\ensuremath{\lesssim}{Q}_{M}\ensuremath{\le}1$. The value of ${M}_{\mathrm{thr}}$ depends on the EOSs and is approximately written as $1.3--1.35{M}_{\mathrm{sph}}$ for the chosen EOSs. For the black hole formation case, we evolve the space-time 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 ${Q}_{M}$ for given ADM mass and EOS. This suggests that a merger with small value of ${Q}_{M}$ is a candidate for producing central engine of SGRBs. For $M<{M}_{\mathrm{thr}}$, 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 long-term angular momentum transport, the disk mass may be $\ensuremath{\gtrsim}0.01{M}_{\ensuremath{\bigodot}}$ irrespective of ${Q}_{M}$. 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 $\ensuremath{\gtrsim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ 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 long-term computation and extraction of ring-down gravitational waves associated with a black hole quasinormal mode. It is found that the frequency and amplitude are $\ensuremath{\approx}6.5--7\text{ }\text{ }\mathrm{kHz}$ and $\ensuremath{\sim}{10}^{\ensuremath{-}22}$ at a distance of 50 Mpc for the binary of mass $M\ensuremath{\approx}2.7--2.9{M}_{\ensuremath{\bigodot}}$.