Dynamic Assembly of Black Hole Binary Mergers in Globular Clusters

Abstract

In this work we focus on the formation of Black Hole Binary (BHB) mergers in globular cluster (GC) systems via dynamical assembly from weak and strong binary-single interactions. BHBs in clusters exchange energy and angular momentum from interactions with a perturber on an outbound parabolic or hyperbolic orbit. Previous works have analytically computed, to first (i.e., quadrupole) order, the effects on the change of BHB eccentricity $\delta e$ assuming orbital averaging and expansions of the equations of motion (EOM). Recent work has found that in the high eccentricity limit, in which weak perturbations can drive a BHB to merge, the first order perturbation scheme breaks down, and a second order scheme has been derived as a result. We implement stochastic algorithms using seconder order perturbation theory to model binary-single weak interactions, and use modeling assumptions to simulate strong binary-single interactions. We then use these models to show the importance of including weak perturbations on BHB evolution with demonstrating the difference in the peak frequency distribution of gravitational wave GW emission, $f_{\rm GW}^{\rm peak}$, for ejected and 2-body BHB mergers. This work is motivated by recent studies that show that surveys such as LISA are sensitive to detect the population of BHBs in GCs that undergo 2-body mergers in between hardening interactions. Constraining the BHB merger rate can be used to predict LISA sources and BHB mergers in GCs, which will aid in our understanding of high stellar mass BHB evolution.