Effect of lensing magnification on the apparent distribution of black hole mergers

The recent detection of gravitational waves indicates that stellar-mass black hole binaries are likely to be a key population of sources for forthcoming observations. With future upgrades, ground-based detectors could detect merging black hole binaries out to cosmological distances. Gravitational wave bursts from high redshifts ($z \gtrsim 1$) can be strongly magnified by gravitational lensing due to intervening galaxies along the line of sight. In the absence of electromagnetic counterparts, the mergers' intrinsic mass scale and redshift are degenerate with the unknown magnification factor $\mu$. Hence, strongly magnified low-mass mergers from high redshifts appear as higher-mass mergers from lower redshifts. We assess the impact of this degeneracy on the mass-redshift distribution of observable events for generic models of binary black hole formation from normal stellar evolution, Pop III star remnants, or a primordial black hole population. We find that strong magnification ($\mu \gtrsim 3$) generally creates a heavy tail of apparently massive mergers in the event distribution from a given detector. For LIGO and its future upgrades, this tail may dominate the population of intrinsically massive, but unlensed mergers in binary black hole formation models involving normal stellar evolution or primordial black holes. Modeling the statistics of lensing magnification can help account for this magnification bias when testing astrophysical scenarios of black hole binary formation and evolution.