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

TL;DR

This paper forecasts how LISA gravitational wave observations can constrain the relationship between massive black holes and their host galaxy halos across cosmic time, using merger rate models and electromagnetic counterpart detection prospects.

Contribution

It combines theoretical merger rates with empirical black hole-halo relations to predict LISA's ability to measure black hole-host galaxy correlations at high redshifts.

Findings

LISA can measure the black hole-halo mass relation parameters with high precision.

Electromagnetic counterparts are detectable for a significant fraction of LISA sources.

Constraints improve with increased observation time and better localization.

Abstract

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.