Black-hole–neutron-star mergers: Disk mass predictions

Abstract

Determining the final result of black-hole--neutron-star mergers, and, in particular, the amount of matter remaining outside the black hole at late times and its properties, has been one of the main motivations behind the numerical simulation of these systems. Black-hole--neutron-star binaries are among the most likely progenitors of short gamma-ray bursts---as long as massive (probably a few percents of a solar mass), hot accretion disks are formed around the black hole. Whether this actually happens strongly depends on the physical characteristics of the system, and, in particular, on the mass ratio, the spin of the black hole, and the radius of the neutron star. We present here a simple two-parameter model, fitted to existing numerical results, for the determination of the mass remaining outside the black hole a few milliseconds after a black-hole--neutron-star merger (i.e., the combined mass of the accretion disk, the tidal tail, and the potential ejecta). This model predicts the remnant mass within a few percents of the mass of the neutron star, at least for remnant masses up to 20% of the neutron star mass. Results across the range of parameters deemed to be the most likely astrophysically are presented here. We find that, for $10{M}_{\ensuremath{\bigodot}}$ black holes, massive disks are only possible for large neutron stars (${R}_{\mathrm{NS}}\ensuremath{\gtrsim}12\text{ }\text{ }\mathrm{km}$), or quasiextremal black hole spins (${a}_{\mathrm{BH}}/{M}_{\mathrm{BH}}\ensuremath{\gtrsim}0.9$). We also use our model to discuss how the equation of state of the neutron star affects the final remnant, and the strong influence that this can have on the rate of short gamma-ray bursts produced by black-hole--neutron-star mergers.