Precise LIGO lensing rate predictions for binary black holes

Abstract

We show how LIGO is expected to detect coalescing binary black holes at z>1 that are lensed by the intervening galaxy population. Gravitational magnification, μ, strengthens gravitational-wave signals by √μ without altering their frequencies, which if unrecognized leads to an underestimate of the event redshift and hence an overestimate of the binary mass. High magnifications can be reached for coalescing binaries, because the region of intense gravitational-wave emission during coalescence is so small (∼100 km), permitting very close projections between lensing caustics and gravitational-wave events. Our simulations use the current LIGO event-based mass function and incorporate accurate waveforms convolved with the LIGO power spectral density. Importantly, we include the detection dependence on sky position and orbital orientation, which for the LIGO configuration translates into a wide spread in observed redshifts and chirp masses. Currently, we estimate a detectable rate of lensed events 0.06[superscript +0.02][subscript -0.02] yr[superscript -1] that rises to 5[superscript +5][subscript -3] yr[superscript -1] at LIGO design sensitivity limit, depending on the high redshift rate of black hole coalescence.