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, $\mu$, strengthens gravitational wave signals by $\sqrt{\mu}$, without altering their frequencies, which if unrecognised 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 ($\sim$100km), permitting very close projections between lensing caustics and gravitational-wave events. Our simulations 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 \rateEarly{}, that rises to \rateDesign{}, at LIGO's design sensitivity limit, depending on the high redshift rate of black hole coalescence.