Effect of gravitational lensing on the distribution of gravitational waves from distant binary black hole mergers

The detailed observation of the distribution of redshifts and chirp masses of binary black hole mergers is expected to provide a clue to their origin. In this paper, we develop a hybrid model of the probability distribution function of gravitational lensing magnification taking account of both strong and weak gravitational lensing, and use it to study the effect of gravitational lensing magnification on the distribution of gravitational waves from distant binary black hole mergers detected in ongoing and future gravitational wave observations. We find that the effect of gravitational lensing magnification is significant at high ends of observed chirp mass and redshift distributions. While a high mass tail in the observed chirp mass distribution is produced by highly magnified gravitational lensing events, we find that highly demagnified images of strong lensing events produce a high redshift ($z_{\rm obs}> 15$) tail in the observed redshift distribution, which can easily be observed in the third-generation gravitational wave observatories. Such a demagnified, apparently high redshift event is expected to be accompanied by a magnified image that is observed typically $10-100$ days before the demagnified image. For highly magnified events that produce apparently very high chirp masses, we expect pairs of events with similar magnifications with time delays typically less than a day. This work suggests the critical importance of gravitational lensing (de-)magnification on the interpretation of apparently very high mass or redshift gravitational wave events.