Dynamical evolution of stellar mass black holes in dense stellar clusters: estimate for merger rate of binary black holes originating from globular clusters

Abstract

We have performed N -body simulations of globular clusters (GCs) in order to estimate a detection rate of mergers of Binary stellar-mass Black Holes (BBHs) by means of gravitational wave (GW) observatories. For our estimate, we have only considered mergers of BBHs which escape from GCs (BBH escapers). BBH escapers merge more quickly than BBHs inside GCs because of their small semi-major axes. N -body simulation can not deal with a GC with the number of stars N ∼ 10 6 due to its high calculation cost. We have simulated dynamical evolution of small-N clusters (10 4 N 10 5 ), and have extrapolated our simulation results to large-N clusters. From our simulation results, we have found the following dependence of BBH properties on N . BBHs escape from a cluster at each two-body relaxation time at a rate proportional to N . Semi-major axes of BBH escapers are inversely proportional to N , if initial mass densities of clusters are fixed. Eccentricities, primary masses, and mass ratios of BBH escapers are independent of N . Using this dependence of BBH properties, we have artificially generated a population of BBH escapers from a GC with N ∼ 10 6 , and have estimated a detection rate of mergers of BBH escapers by next-generation GW observatories. We have assumed that all the GCs are formed 10 or 12 Gyrs ago with their initial numbers of stars N i = 5 × 10 5 -2 × 10 6 and their initial stellar mass densities inside their half-mass radii ρ h,i = 6 × 10 3 -10 6 M ⊙ pc −3 . Then, the detection rate of BBH escapers is 0.5 -20 yr −1 for a BH retention fraction R BH = 0.5. A few BBH escapers are components of hierarchical triple systems, although we do not consider secular perturbation on such BBH escapers for our estimate. Our simulations have shown that BHs are still inside some of GCs at the present day. These BHs may marginally contribute to BBH detection.

In Search of the Thermal Eccentricity Distribution

“…In contrast, the eccentricity distribution for binaries containing BHs in the CMC model we investigated (Section 5), is consistent with thermal. A similar result was also found by Tanikawa (2013) in their N -body models. The high-mass regime investigated in Figure 4, is somewhat analogous to BHs in globular clusters.…”

Binary Black Hole Mergers from Globular Clusters: Implications for Advanced LIGO

“…Previous studies have explored the contribution of BBHs from GCs to the Advaned LIGO detection rate [12][13][14][15][16][17]; however, the majority of these studies have relied on either approximate analytic arguments or simpli-fied N -body models with N 10 5 particles and have assumed a single black hole mass of 10M . The one exception is [15], which used a Monte Carlo approach to model GCs of a realistic size (N = 5 × 10 5 ).…”

Gravitational-wave emission from binary black holes formed in open clusters

“…The core of globular clusters (10 5 -10 6 M ⊙ ) has long been investigated as a formation site of BBHs in many previous works (e.g. Portegies Zwart & McMillan 2000;O'Leary et al 2006;Sadowski et al 2008;Downing et al 2010Downing et al , 2011Banerjee et al 2010;Tanikawa 2013;Bae et al 2014;Rodriguez et al 2015Rodriguez et al , 2016Fujii et al 2017;Park et al 2017;Askar et al 2017;Hong et al 2018;Zevin et al 2019).…”