Evidence for hierarchical black hole mergers in the second LIGO--Virgo gravitational-wave catalog

TL;DR

This paper provides evidence for hierarchical black hole mergers in the LIGO-Virgo gravitational-wave catalog, highlighting the importance of cluster properties and offering insights into black hole population characteristics.

Contribution

The study introduces a population model that infers black hole mass and spin distributions while accounting for hierarchical mergers, demonstrating strong evidence for such mergers in certain cluster environments.

Findings

Hierarchical mergers are favored in clusters with escape velocities > 100 km/s.

The catalog likely contains at least one second-generation merger with 99% credibility.

GW190521 is highly likely to contain two second-generation black holes.

Abstract

We study the population properties of merging binary black holes in the second LIGO--Virgo Gravitational-Wave Transient Catalog assuming they were all formed dynamically in gravitationally bound clusters. Using a phenomenological population model, we infer the mass and spin distribution of first-generation black holes, while self-consistently accounting for hierarchical mergers. Considering a range of cluster masses, we see compelling evidence for hierarchical mergers in clusters with escape velocities $\gtrsim 100~\mathrm{km\,s^{-1}}$. For our most probable cluster mass, we find that the catalog contains at least one second-generation merger with $99\%$ credibility. We find that the hierarchical model is preferred over an alternative model with no hierarchical mergers (Bayes factor $\mathcal{B} > 1400$) and that GW190521 is favored to contain two second-generation black holes with odds $\mathcal{O}>700$, and GW190519, GW190602, GW190620, and GW190706 are mixed-generation binaries with $\mathcal{O} > 10$. However, our results depend strongly on the cluster escape velocity, with more modest evidence for hierarchical mergers when the escape velocity is $\lesssim 100~\mathrm{km\,s^{-1}}$. Assuming that all binary black holes are formed dynamically in globular clusters with escape velocities on the order of tens of $\mathrm{km\,s^{-1}}$, GW190519 and GW190521 are favored to include a second-generation black hole with odds $\mathcal{O}>1$. In this case, we find that $99\%$ of black holes from the inferred total population have masses that are less than $49\,M_{\odot}$, and that this constraint is robust to our choice of prior on the maximum black hole mass.