Constraining the host galaxy halos of massive black holes from LISA event rates

The coalescence of massive black hole binaries (with masses $10^4 - 10^7 M_{\odot}$) leads to gravitational wave emission that is detectable out to high redshifts ($z \sim 20$) with the forthcoming LISA observatory. We combine the theoretically derived merger rates for dark matter haloes at various redshifts, with an empirically motivated prescription that connects the mass of a dark matter halo and that of its central black hole. Using the expected constraints on the (chirp or reduced) masses of binary black holes, their mass ratios and redshift uncertainties, we forecast the measurement precision on the occupation fraction, normalization and slope of the black hole mass - halo mass relation at various redshifts, assuming a five-year LISA survey for three different confidence scenarios. We use the expected sizes of the LISA localization ellipses on the sky to estimate the number of electromagnetic counterparts to the gravitational wave sources which are detectable by future wide-field optical surveys, such as LSST.
17 pages, 3 figures; version accepted for publication in JCAP