Black-Hole Remnants from Black-Hole–Neutron-Star Mergers

Observations of gravitational waves and their electromagnetic counterparts may soon uncover the existence of coalescing compact binary systems formed by a stellar-mass black hole and a neutron star. These mergers result in a remnant black hole, possibly surrounded by an accretion disk. The mass and spin of the remnant black hole depend on the properties of the coalescing binary. We construct a map from the binary components to the remnant black hole using a sample of numerical-relativity simulations of different mass ratios $q$, (anti)aligned dimensionless spins of the black hole $a_{\mathrm{BH}}$, and several neutron star equations of state. Given the binary total mass, the mass and spin of the remnant black hole can therefore be determined from the three parameters $(q,a_{\mathrm{BH}},\mathrm{\Lambda })$, where $\mathrm{\Lambda }$ is the tidal deformability of the neutron star. Our models also incorporate the binary black hole and test-mass limit cases and we discuss a simple extension for generic black-hole spins. We combine the remnant characterization with recent population synthesis simulations for various metallicities of the progenitor stars that generated the binary system. We predict that black-hole–neutron-star mergers produce a population of remnant black holes with masses distributed around $7M_{\odot }$ and $9M_{\odot }$. For isotropic spin distributions, nonmassive accretion disks are favored: no bright electromagnetic counterparts are expected in such mergers.

Figure 1

Contour plots of the remnant BH mass divided by the binary mass $X_{•}=M_{•}/M$ (top) and of the dimensionless spin parameter $a_{•}$ (bottom) as a function of the symmetric mass ratio $\nu$ and of the NS tidal polarizability parameter $\mathrm{\Lambda }$, at fixed values of the initial BH spin parameter $a_{\mathrm{BH}}$. The values of $a_{\mathrm{BH}}$ correspond to those of the NR simulations. No assumptions on the EOS are made for the NS, which is characterized solely by $\mathrm{\Lambda }$. White markers indicate the NR data used to construct the model.

Figure 2

The remnant BH mass distribution inferred from the remnant to a different value of the metallicity $Z$ of the progenitor stars. In this plot we employ the SLy EOS and the fiducial isotropic spin distribution peaked around $⟨a_{\mathrm{BH}}⟩=0.2$.

Figure 3

Remnant disk baryonic mass distribution for different EOSs and for low (left) and high (right) aligned BH spin distributions. The mass threshold represents the minimum mass of the disk that allows the production of SGRBs with 1 s duration. The percentage of binaries with disk mass bigger than the threshold is provided in the legend for each equation of state.