# Precise LIGO Lensing Rate Predictions for Binary Black Holes

## TL;DR

This paper predicts how gravitational lensing by galaxies can amplify signals from distant binary black hole mergers detectable by LIGO, affecting inferred properties and increasing detection rates at high redshifts.

## Contribution

It provides detailed simulations of lensed binary black hole signals, incorporating realistic waveforms, lensing effects, and LIGO's detection sensitivities to estimate future detection rates.

## Key findings

- Estimated current detection rate of lensed events: rateEarly{}.
- Projected detection rate at design sensitivity: rateDesign{}.
- Lensing can significantly bias mass and redshift estimates if unrecognized.

## 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.