Simulation of the gravitational wave frequency distribution of neutron star-black hole mergers

LIGO-Virgo have observed the gravitational waves (GWs) from the coalescence of binary black hole (BBH) and binary neutron star (BNS) during O1 and O2, and that from NS-BH is expected to be hunted in the operating O3 run. The population properties and mass distribution of NS-BH mergers are poorly understood now, thus researchers simulated their chirp mass ($\mathcal{M}$) distribution by a synthetic model, in which the BHs and NSs were inferred by LIGO-Virgo (O1/O2), and obtained the values in the range of $2.1M_{\odot}<\mathcal{M}<7.3M_{\odot}$. In this paper, we further simulated the GW frequency ($f_{\mathrm{GW}}$) distribution of NS-BH mergers by above synthetic model, with a basic binary system model through the Monte Carlo method. Our results predicted that the median with 90% credible intervals for which is $165_{-64}^{+475}$ Hz in the case of Schwarzschild BH when the system just before merger, and this GW frequency is expected to increase several times in the merger stage, which is lying in the frequency band of LIGO-Virgo, i.e., about 15 Hz to a few kHz. Our results provide an important reference for hunting the NS-BH mergers by the on-going O3 run of LIGO-Virgo.