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

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.