Black Hole Mass Function of Coalescing Neutron Star-Black Hole Binary Systems: The Prospect of Reconstruction with the Gravitational Wave Observations

The discovery of gravitational waves from compact objects coalescence opens a brand-new window to observe the universe. With more events being detected in the future, statistical examinations would be essential to better understand the underlying astrophysical processes. In this work we investigate the prospect of measuring the mass function of black holes that are merging with the neutron stars. Applying Bayesian parameter estimation for hundreds of simulated neutron star$-$black hole (NSBH) mergers, we find that the parameters for most of the injected events can be well recovered. We also take a Bayesian hierarchical model to reconstruct the population properties of the masses of black holes, in the presence of a low mass gap, both the mass gap and power-law index ($\alpha$) of black hole mass function can be well measured, thus we can reveal where the $\alpha$ is different for binary black hole (BBH) and NSBH systems. In the absence of a low mass gap, the gravitational wave data as well as the electromagnetic data can be used to pin down the nature of the merger event and then measure the mass of these very light black holes. However, as a result of the misclassification of BBH into NSBH, the measurement of $\alpha$ is more challenging and further dedicated efforts are needed.