  Black hole neutron star (BHNS) mergers have recently been detected through
their gravitational-wave (GW) emission. BHNS mergers could also produce
electromagnetic (EM) emission as a short gamma-ray burst (sGRB), and/or an sGRB
afterglow upon interaction with the circummerger medium. Here, 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 multimessenger analysis in inferring the
properties of the merging binary. We simulate a population of BHNS mergers and
estimate 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 (BH) spin, and the neutron star equation of state. We then perform a
multimessenger Bayesian inference study on a fiducial BHNS merger. We simulate
its sGRB afterglow and GW emission and take systematic errors into account. 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 like the Einstein Telescope, the chances of an sGRB localisation and
radio detection increase substantially. The unknown distribution of the BH spin
has a big influence on the detection rates, however, and it is a large source
of uncertainty. Furthermore, for our fiducial BHNS merger we are able to infer
both the binary source parameters as well as the parameters of the sGRB
afterglow simultaneously when combining the GW and radio data. The radio data
provides useful extra information on the binary parameters such as the mass
ratio but this is limited by the systematic errors involved. 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.
