MOCCA-SURVEY Database I: Assessing GW kick retention fractions for BH-BH mergers in globular clusters

TL;DR

This study estimates the retention fractions of black hole merger products in globular clusters considering different spin models, cluster properties, and merger stages, revealing key dependencies on cluster density and evolution.

Contribution

It introduces a comprehensive analysis of GW kick retention fractions using MOCCA simulation data, incorporating various spin models and cluster conditions, and explores implications for intermediate mass black hole formation.

Findings

Retention fractions are about 30% for realistic models.

Retention fractions depend strongly on cluster density.

Higher retention occurs in the late stages of cluster evolution.

Abstract

Anisotropy of gravitational wave (GW) emission results in a net momentum gained by the black hole (BH) merger product, leading to a recoil velocity up to $\sim10^3\text{ km s}^{-1}$, which may kick it out of a globular cluster (GC). We estimate GW kick retention fractions of merger products assuming different models for BH spin magnitude and orientation (MS0 - random, MS1 - spin as a function of mass and metalicity, MS2 - constant value of $0.5$). We check how they depend on BH-BH merger time and properties of the cluster. We analyze the implications of GW kick retention fractions on intermediate massive BH (IMBH) formation by repeated mergers in a GC. We also calculate final spin of the merger product, and investigate how it correlates with effective spin of the binary. We used data from MOCCA (MOnte Carlo Cluster simulAtor) GC simulations to get a realistic sample of BH-BH mergers, assigned each BH spin value according to a studied model, and calculated recoil velocity and final spin based on most recent theoretical formulas. We discovered that for physically motivated models, GW kick retention fractions are about $30\%$ and display small dependence on assumptions about spin, but are much more prone to cluster properties. In particular, we discovered a strong dependence of GW kick retention fractions on cluster density. We also show that GW kick retention fractions are high in final life stages of the cluster, but low at the beginning. Finally, we derive formulas connecting final spin with effective spin for primordial binaries, and with maximal effective spin for dynamical binaries.