Event Rate of Strongly Lensed Gravitational Waves of Stellar Binary Black Hole Mergers Produced by Dynamical Interactions

TL;DR

This paper estimates the rate of strongly lensed gravitational waves from stellar binary black hole mergers produced by dynamical interactions, highlighting their potential dominance and implications for understanding black hole formation channels.

Contribution

It provides the first detailed rate estimates for lensed sBBHs from the dynamical channel using Monte Carlo simulations, comparing them to the EMBS channel.

Findings

Lensed sBBH event rate from dynamical channel: ~16-21 per year for future detectors.

Median rate is about twice that of the EMBS channel.

Potential to constrain black hole formation channels through observed lensed event statistics.

Abstract

Gravitational waves emitted from stellar binary black hole (sBBH) mergers can be gravitationally lensed by intervening galaxies and detected by future ground-based detectors. A large amount of effort has been put into the estimation of the detection rate of lensed sBBH originating from the evolution of massive binary stars (EMBS channel). However, sBBHs produced by the dynamical interaction in dense clusters (dynamical channel) may also be dominant in our universe and their intrinsic distribution of physical properties can be significantly different from those produced by massive stars, especially mass and redshift distribution. In this paper, we investigate the event rate of lensed sBBHs produced via dynamical channel by Monte Carlo simulations and the number is $16_{-12}^{+4.7} $ $\rm yr^{-1}$ for the Einstein telescope and $24_{-17}^{+6.8}$ $ \rm yr^{-1}$ for Cosmic Explorer, of which the median is about $\sim 2$ times the rate of sBBHs originated from EMBS channel (calibrated by the local merger rate density estimated for the dynamical and the EMBS channel, i.e., $\sim 14_{-10}^{+4.0}$ and $19_{-3.0}^{+42} \rm Gpc^{-3}yr^{-1}$ respectively). Therefore, one may constrain the fraction of both EMBS and dynamical channels through the comparison of the predicted and observed number of lensed sBBH events statistically.