Beyond the detector horizon: Forecasting gravitational-wave strong lensing

TL;DR

This paper forecasts the rate of gravitational-wave strong lensing detections, analyzes the role of lensing statistics in searches, and proposes methods to reduce false alarms by incorporating expected time delays, with implications for current and future detectors.

Contribution

It provides new forecasts for strong lensing event rates at various detector sensitivities and introduces a novel approach to improve lensing searches by using expected time delays to reduce false alarms.

Findings

Reasonable detection rates for multiple images at current sensitivities.

Including time delays reduces false alarm probability growth from quadratic to linear.

Most lensed events originate from redshifts 1-4.

Abstract

When gravitational waves pass near massive astrophysical objects, they can be gravitationally lensed. The lensing can split them into multiple wave-fronts, magnify them, or imprint beating patterns on the waves. Here we focus on the multiple images produced by strong lensing. In particular, we investigate strong lensing forecasts, the rate of lensing, and the role of lensing statistics in strong lensing searches. Overall, we find a reasonable rate of lensed detections for double, triple, and quadruple images at the LIGO--Virgo--KAGRA design sensitivity. We also report the rates for A+ and LIGO Voyager and briefly comment on potential improvements due to the inclusion of sub-threshold triggers. We find that most galaxy-lensed events originate from redshifts $z \sim 1-4$ and report the expected distribution of lensing parameters for the observed events. Besides forecasts, we investigate the role of lensing forecasts in strong lensing searches, which explore repeated event pairs. One problem associated with the searches is the rising number of event pairs, which leads to a rapidly increasing false alarm probability. We show how knowledge of the expected galaxy lensing time delays in our searches allow us to tackle this problem. Once the time delays are included, the false alarm probability increases linearly (similar to non-lensed searches) instead of quadratically with time, significantly improving the search. For galaxy cluster lenses, the improvement is less significant. The main uncertainty associated with these forecasts are the merger-rate density estimates at high redshift, which may be better resolved in the future.