Investigating the detection rates and inference of gravitational-wave and radio emission from black hole neutron star mergers

Context. Black hole neutron star (BHNS) mergers have recently been detected through their gravitational-wave (GW) emission. While no electromagnetic emission has yet been confidently associated with these systems, observing any such emission could provide information on, for example, the neutron star equation of state. Black hole neutron star mergers could produce electromagnetic emission as a short gamma-ray burst (sGRB) and/or an sGRB afterglow upon interaction with the circum-merger medium. Aims. We make predictions for the expected detection rates with the Square Kilometre Array Phase 1 (SKA1) of sGRB radio afterglows associated with BHNS mergers. We also investigate the benefits of a multi-messenger analysis in inferring the properties of the merging binary. Methods. We simulated a population of BHNS mergers, making use of recent stellar population synthesis results, and estimated their sGRB afterglow flux to obtain the detection rates with SKA1. We investigate how this rate depends on the GW detector sensitivity, the primary black hole spin, and the neutron star equation of state. We then performed a multi-messenger Bayesian inference study on a fiducial BHNS merger. We simulated its sGRB afterglow and GW emission as input to this study, using recent models for both, and take systematic errors into account. Results. The expected rates of a combined GW and radio detection with the current-generation GW detectors are likely low. Due to the much increased sensitivity of future GW detectors such as the Einstein Telescope, the chances of an sGRB localisation and radio detection increase substantially. The unknown distribution of the black hole spin has a big influence on the detection rates, however, and it is a large source of uncertainty. Furthermore, when placing our fiducial BHNS merger at 50 and 100 Mpc, we are able to infer both the binary source parameters and the parameters of the sGRB afterglow simultaneously if we combine the GW and radio data. The radio data provide useful extra information on the binary parameters, such as the mass ratio, but this is limited by the systematic errors involved. For our fiducial binary at 200 Mpc, it is considerably more difficult to adequately infer the parameters of the system. Conclusions. The probability of finding an sGRB afterglow of a BHNS merger is low in the near future but will rise significantly when the next-generation GW detectors come online. Combining information from GW data with radio data is crucial for characterising the jet properties. A better understanding of the systematics will further increase the amount of information on the binary parameters that can be extracted from this radio data