Populating the Black Hole Mass Gaps In Stellar Clusters: General Relations and Upper Limits

TL;DR

This paper investigates how stellar clusters contribute to forming black holes in the mass gaps through in-cluster gravitational wave mergers, providing new relations for binary evolution and assessing cluster efficiency.

Contribution

It introduces analytical relations for binary evolution in clusters and evaluates the efficiency of globular clusters in populating black hole mass gaps.

Findings

Globular clusters are inefficient at populating the lower mass gap.

Clusters can effectively populate the upper mass gap through mergers.

Derived relations help understand the dynamical evolution of compact binaries.

Abstract

Theory and observations suggest that single-star evolution is not able to produce black holes (BHs) with masses in the range $3-5M_{\odot}$ and above $\sim 45M_{\odot}$, referred to as the lower mass gap (LMG) and the upper mas gap (UMG), respectively. However, it is possible to form BHs in these gaps through merger of compact objects in dense clusters, e.g. the LMG and the UMG can be populated through binary neutron star- and BBH mergers, respectively. This implies that if binary mergers are observed in gravitational waves (GWs) with at least one mass gap object, then either clusters are effective in assembling binary mergers, or our single-star models have to be revised. Understanding how effective clusters are at populating both mass gaps have therefore major implications for both stellar- and GW astrophysics. In this paper we present a systematic study on how efficient stellar clusters are at populating both mass gaps through in-cluster GW mergers. For this, we derive a set of closed form relations for describing the evolution of compact object binaries undergoing dynamical interactions and GW merger inside their cluster. By considering both static and time evolving populations, we find in particular that globular clusters are clearly inefficient at populating the LMG in contrast to the UMG. We further describe how these results relate to the characteristic mass, time, and length scales associated with the problem.