Mengye Wang, Qingwen Wu, Yiqiu Ma

Stellar-mass binary black hole\,(BBH) mergers resulting from binary-single interactions\,(BSIs) in active galactic nucleus\,(AGN) disks are a potential source of gravitational wave\,(GW) events with measurable eccentricities. Previous hydrodynamical simulations have shown that ambient gas can significantly influence the dynamics of BSIs. However, due to limitations such as the use of purely Newtonian dynamics and small sample sizes, a direct estimation of the BBH merger probability during BSI has remained elusive. In this work, we directly quantify the merger probability, based on a suite of 1800 two-dimensional hydrodynamical simulations coupled with post-Newtonian \emph{N}-body calculations. Our results demonstrate that dense gas can enhance the merger probability by both shrinking the spatial scale of the triple system and increasing the number of binary-single encounters. These two effects together boost the merger probability by a factor of $\sim$5, from 4\% to as high as 20\%. Among the two effects, our analysis suggests that the increase in encounter frequency plays a slightly more significant role in driving the enhancement. Moreover, this enhancement becomes more significant at larger radial distances from the central SMBH, since the total gas mass enclosed within the Hill sphere of the triple system increases with radius. Finally, the BSI process in AGN disks can naturally produce double GW merger events within a timescale of $\sim$year, which may serve as potential observational signatures of BSI occurring in AGN disk environments.