Avoiding a Cluster Catastrophe: Retention Efficiency and the Binary Black Hole Mass Spectrum

TL;DR

This paper investigates how hierarchical mergers in dense stellar environments can produce high-mass black holes, highlighting the importance of retention efficiency and environmental escape velocities in shaping the observed black hole mass spectrum.

Contribution

It introduces simple models to explore the impact of environment-driven retention on hierarchical black hole mergers and their compatibility with observed gravitational wave data.

Findings

Hierarchical mergers are efficient in environments with escape velocities >300 km/s.

Overproduction of high-mass mergers can occur if models are not properly tuned.

Tuning models is necessary to match the observed black hole mass spectrum.

Abstract

The population of binary black hole mergers identified through gravitational waves has uncovered unexpected features in the intrinsic properties of black holes in the universe. One particularly surprising and exciting result is the possible existence of black holes in the pair-instability mass gap, $\sim50-120~M_\odot$. Dense stellar environments can populate this region of mass space through hierarchical mergers, with the retention efficiency of black hole merger products strongly dependent on the escape velocity of the host environment. We use simple toy models to represent hierarchical merger scenarios in various dynamical environments. We find that hierarchical mergers in environments with high escape velocities $(\gtrsim300~\mathrm{km\,s}^{-1})$ are efficiently retained. If such environments dominate the binary black hole merger rate, this would lead to an abundance of high-mass mergers that is potentially incompatible with the empirical mass spectrum from the current catalog of binary black hole mergers. Models that efficiently generate hierarchical mergers, and contribute significantly to the observed population, must therefore be tuned to avoid a "cluster catastrophe" of overproducing binary black hole mergers within and above the pair-instability mass gap.