Neutron star-black hole coalescence rate inferred from macronova/kilonova observations

Neutron star$-$black hole (NS$-$BH) coalescences are widely believed to be promising gravitational wave sources in the era of advanced detectors of LIGO/Virgo but such binaries have never been directly detected yet. Evidence for NS$-$BH coalescences have been suggested in short and hybrid GRB observations, which are examined critically. Based on the suggested connection between the observed macronovae/kilonovae events and NS$-$BH coalescences, we get a fiducial lower limit of NS$-$BH coalescence rate density ${\cal R}_{\rm nsbh} \approx 18.8^{+12.5}_{-8.6} ~{\rm Gpc^{-3}~ yr^{-1}~ (\theta_j/0.1~{\rm rad})^{-2}}$, where $\theta_{\rm j}$ is the typical half-opening angle of the GRB ejecta. The real value of ${\cal R}_{\rm nsbh}$ is likely at least $\sim {\rm a~few}$ times larger, depending upon the equation of state of NS material and the properties of the NS$-$BH system, such as the mass and spin distribution of the black hole. If the link between macronovae/kilonovae and NS$-$BH coalescence is valid, one can expect that at design sensitivity the aLIGO/AdVirgo network will detect NS$-$BH coalescence signals at a rate of at least a dozen per year, and to consequently place constraints on certain physical properties of NS$-$BH systems.