Considering lensing effect on gravitational wave signals from black holes in mass gap

The pair-instability supernova (PISN) mechanism predicts a mass gap in the black hole population, where no stellar-origin black holes are expected to form. However, several binary black hole (BBH) merger events exhibit component masses that appear to lie within the PISN mass gap. If a gravitational-wave (GW) source is lensed, neglecting lensing effects leads to an underestimation of the luminosity distance and hence the redshift, resulting in an overestimation of the source-frame masses and potentially placing them within the mass-gap region. In this work, we analyze two representative events, GW190521 and GW231123. We establish a direct mapping between the lensing magnification and the fraction of posterior samples with source-frame masses below the mass-gap boundary. Adopting a lower bound of $65\,M_{\odot}$, we find that the magnifications required for $90\%$ of the posterior samples to fall below this boundary are $\mu=444$ for GW231123 and $\mu=39$ for GW190521. At these magnifications, the corresponding source-frame masses of the primary black hole are $52^{+10}_{-10}\,M_{\odot}$ and $42^{+19}_{-14}\,M_{\odot}$, with lensed source redshifts of $2.3^{+0.8}_{-0.5}$ and $2.7^{+1.5}_{-1.2}$, respectively. These results provide a quantitative framework for assessing the lensing hypothesis as a possible explanation for BBH mergers observed within the PISN mass gap, and highlight that the extreme magnifications required for GW231123 may challenge the astrophysical plausibility of simple strong-lensing interpretations.