Impact of astrophysical binary coalescence timescales on the rate of lensed gravitational wave events

TL;DR

This paper investigates how the delay time between formation and merger of binary systems affects the rate of detectable lensed gravitational wave events, revealing that longer delays decrease the expected event rate.

Contribution

It demonstrates for the first time that lensing event rates can probe different binary formation channels by analyzing both detected and sub-threshold events.

Findings

Longer delay times shift merger rates to lower redshifts.

Lensed event rate drops below one per year for delay times around 10 Gyr.

Lensed sub-threshold events are more frequent with shorter delay times.

Abstract

The expected event rate of lensed gravitational wave sources scales with the merger rate at redshift $z\geq 1$, where the optical depth for lensing is high. It is commonly assumed that the merger rate of the astrophysical compact objects is closely connected with the star formation rate, which peaks around redshift $z\sim 2$. However, a major source of uncertainty is the delay time between the formation and merger of compact objects. We explore the impact of delay time on the lensing event rate. We show that as the delay time increases, the peak of the merger rate of gravitational wave sources gets deferred to a lower redshift. This leads to a reduction in the event rate of the lensed events which are detectable by the gravitational wave detectors. We show that for a delay time of around $10$ Gyr or larger, the lensed event rate can be less than one per year for the design sensitivity of LIGO/Virgo. We also estimate the merger rate for lensed sub-threshold for different delay time scenarios, finding that for larger delay times the number of lensed sub-threshold events is reduced, whereas for small-delay time models they are significantly more frequent. This analysis shows for the first time that lensing is a complementary probe to explore different formation channels of binary systems by exploiting the lensing event rate from the well-detected events and sub-threshold events which are measurable using the network of gravitational wave detectors.