Gravitational lensing aided luminosity distance estimation for compact binary coalescences

The luminosity distance is a key observable of gravitational-wave (GW) observations. We demonstrate how one can correctly retrieve the luminosity distance of compact binary coalescences (CBCs) if the GW signal is strongly lensed. We perform a proof-of-concept parameter estimation for the luminosity distance supposing (i) strong lensing produces two lensed GW signals emitted from a CBC, (ii) the Advanced LIGO-Virgo network detects both lensed signals as independent events, and (iii) the two events are identified as strongly lensed signals originated from the same source. Taking into account the maximum magnification allowed in two lensing scenarios and simulated GW signals emitted from four different binary black holes, we find that the strong lensing can improve the precision of the distance estimation of a CBC by up to a factor of a few compared to that can be expected without lensing.