Merger rate of black hole binaries from globular clusters: theoretical error bars and comparison to gravitational wave data

Fabio Antonini, Mark Gieles

Published 2020-09-03Version 1

Black hole binaries formed dynamically in globular clusters are believed to be one of the main sources of gravitational waves in the Universe. Here, we use our new population synthesis code, cBHBd, to determine the redshift evolution of the merger rate density and masses of black hole binaries formed in globular clusters. We simulate $\sim 20$ million models to explore the parameter space that is relevant to real clusters and over all mass scales. We show that when uncertainties on the initial cluster mass function and half-mass radius relation are properly taken into account, they become the two dominant factors in setting the theoretical error bars on merger rates. Other model parameters (e.g., natal kicks, black hole masses, metallicity) have virtually no effect on the local merger rate density, although they affect the masses of the merging black holes. Modelling the merger rate density as a function of redshift as $R(z)=R_0(1+z)^\lambda$ at $z<2$, and marginalizing over uncertainties, we find: $R_0=7.2^{+21.5}_{-5.5}{\rm Gpc^{-3}yr^{-1}}$ and $\lambda=1.6^{+0.4}_{-0.6}$ ($90\%$ credibility). The rate parameters for binaries that merge inside the clusters are ${R}_{\rm 0,in}=1.6^{+1.9}_{-1.0}{\rm Gpc^{-3}yr^{-1}}$ and $\lambda_{\rm in}=2.3^{+1.3}_{-1.0}$; $\sim 20\%$ of these form as the result of a gravitational-wave capture, implying that eccentric mergers from globular clusters contribute $\lesssim 0.4 \rm Gpc^{-3}yr^{-1}$ to the local rate. A comparison to the merger rate reported by LIGO-Virgo shows that a scenario in which most of the detected black hole mergers are formed in globular clusters is consistent with current constraints, and requires initial cluster half-mass densities $\gtrsim 10^4 M_\odot \rm pc^{-3}$. Interestingly, such higher density models also result in a better match to the inferred black hole mass distribution.