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

astrophysical journal/the astrophysical journal

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