2022ApJ...940...17C

A significant number of stellar binary black hole (sBBH) mergers may be lensed and detected by the third generation of gravitational wave (GW) detectors. Their lensed host galaxies may be detectable, which would thus help to accurately localize these sources and provide a new approach to study the origin of sBBHs. In this paper, we investigate the detectability of lensed host galaxies for lensed sBBH mergers. We find that the detection fraction of galaxies hosting lensed GW events can be significantly different for a survey with a given limiting magnitude if sBBHs are produced by different mechanisms, such as the evolution of massive binary stars, dynamical interactions in dense star clusters, and production assisted by active galactic nuclei or massive black holes. Furthermore, we illustrate that the statistical spatial distributions of those lensed sBBHs in their hosts resulting from different sBBH formation channels can differ. Therefore, with the third generation of GW detectors and future large-scale galaxy surveys, it is possible to independently constrain the origin of sBBHs via the detection fraction of those lensed events with identifiable lensing host signatures and/or even to constrain the fractional contributions from different sBBH formation mechanisms.