Merger of black hole and neutron star in general relativity: Tidal disruption, torus mass, and gravitational waves

Abstract

We study the properties of the merger of black hole--neutron star (BH-NS) binaries in fully general relativistic simulation, 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 $\ensuremath{\Gamma}$-law equation of state with $\ensuremath{\Gamma}=2$ and the irrotational velocity field. We change the BH mass in the range ${M}_{\mathrm{BH}}\ensuremath{\approx}3.3{M}_{\ensuremath{\bigodot}}--4.6{M}_{\ensuremath{\bigodot}}$, while the rest mass of the NS is fixed to be ${M}_{*}=1.4{M}_{\ensuremath{\bigodot}}$ (i.e., the NS mass ${M}_{\mathrm{NS}}\ensuremath{\approx}1.3{M}_{\ensuremath{\bigodot}}$). The radius of the corresponding spherical NS is set in the range ${R}_{\mathrm{NS}}\ensuremath{\approx}12--15\text{ }\text{ }\mathrm{km}$ (i.e., the compactness $G{M}_{\mathrm{NS}}/{R}_{\mathrm{NS}}{c}^{2}\ensuremath{\approx}0.13--0.16$). We find for all the chosen initial conditions that the NS is tidally disrupted near the innermost stable circular orbit. The numerical results indicate that, for the model of ${R}_{\mathrm{NS}}=12\text{ }\text{ }\mathrm{km}$, more than $\ensuremath{\sim}95%$ of the rest mass is quickly swallowed by the BH and the resultant torus mass surrounding the BH is less than $\ensuremath{\sim}0.05{M}_{\ensuremath{\bigodot}}$. For the model of ${R}_{\mathrm{NS}}\ensuremath{\approx}14.7\text{ }\text{ }\mathrm{km}$, by contrast, the torus mass is $\ensuremath{\sim}0.15{M}_{\ensuremath{\bigodot}}$ for the BH mass $\ensuremath{\approx}4{M}_{\ensuremath{\bigodot}}$. The thermal energy of the material in the torus increases due to the shock heating that occurs in the collision between the spiral arms, resulting in the temperature ${10}^{10}--{10}^{11}\text{ }\text{ }\mathrm{K}$. Our results indicate that the merger between a low-mass BH and its companion NS may form a central engine of short gamma-ray bursts of the total energy of order ${10}^{49}\text{ }\text{ }\mathrm{ergs}$ if the compactness of the NS is fairly small, $\ensuremath{\lesssim}0.145$. However, for the canonical values ${M}_{\mathrm{NS}}=1.35{M}_{\ensuremath{\bigodot}}$ and ${R}_{\mathrm{NS}}=12\text{ }\text{ }\mathrm{km}$, the merger results in small torus mass, and hence it can be a candidate only for the low-energy, short gamma-ray bursts of total energy of order ${10}^{48}\text{ }\text{ }\mathrm{ergs}$. We also present gravitational waveforms during the inspiral, tidal disruption of the NS, and subsequent evolution of the disrupted material. We find that the amplitude of gravitational waves quickly decreases after the onset of tidal disruption. Although the quasinormal mode is excited, its gravitational wave amplitude is much smaller than that of the late inspiral phase. This is reflected in the fact that the spectrum amplitude sharply falls above a cutoff frequency which is determined by the tidal disruption process. We also find that the cutoff frequency is 1.25--1.4 times larger than the frequency predicted by the study for the sequence of the quasicircular orbits, and this factor of the deviation depends on the compactness of the NS.