On the detection and precise localization of merging black holes events through strong gravitational lensing

To unlock the full spectrum of astrophysical and cosmological applications of gravitational-wave detections, it is essential to localize the associated black hole mergers to high precision inside their host galaxies. One possible method to achieve this is to compare the properties of multiple detections of gravitationally lensed binary black hole merger events with the properties of strong gravitational lens systems located in the joint sky localization of the gravitational-wave detections. In this work, we simulate the population of binary black hole mergers lensed by galaxy-scale lenses and detectable by LIGO-Virgo-Kagra in the coming decade and the population of galaxy-scale strong lenses that will be detected by Euclid. We use these simulations to investigate the prospects for localizing strongly lensed binary black hole mergers inside the lensed galaxies of 'Euclid-like' galaxy-scale strong lenses. We find that for 20- of strongly lensed gravitational-wave events the lens system is detectable with Euclid, if the event falls in its survey footprint. Of these, we expect to correctly identify the strongly lensed host galaxy as likely (with posterior probability) host galaxy - based on Bayesian evidence ranking of candidate hosts - for 34.6- of quadruply lensed gravitational-wave events when given an a priori 1-5 gravitational-wave-only sky localization. For triply and doubly lensed gravitational-wave events, this becomes 29.8- and 16.4- respectively. If successfully identified, however, the localization can be better than a fraction of the host-galaxy size, i.e. of order milli-arcseconds. A first detection in the coming decade, however, probably requires dedicated deep and high-resolution follow-ups and continued upgrades in the current and planned gravitational-wave detectors.