Merger rate of black hole binaries from globular clusters: Theoretical error bars and comparison to gravitational wave data from GWTC-2

Abstract

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 $\ensuremath{\sim}2\text{ }\text{ }\mathrm{million}$ models to explore the parameter space that is relevant to real globular clusters and overall mass scales. We show that when uncertainties on the initial cluster mass function and their initial half-mass density are properly taken into account, they become the two dominant factors in setting the theoretical error bars on merger rates. Uncertainties in other model parameters (e.g., natal kicks, black hole masses, and metallicity) have virtually no effect on the local merger rate density, although they affect the masses of the merging black holes. Modeling the merger rate density as a function of redshift as $\mathcal{R}(z)={\mathcal{R}}_{0}{(1+z)}^{\ensuremath{\kappa}}$ at $z<2$, and marginalizing over uncertainties, we find: ${\mathcal{R}}_{0}=7.{2}_{\ensuremath{-}5.5}^{+21.5}\text{ }\text{ }{\mathrm{Gpc}}^{\ensuremath{-}3}\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$ and $\ensuremath{\kappa}=1.{6}_{\ensuremath{-}0.6}^{+0.4}$ (90% credibility). The rate parameters for binaries that merge inside the clusters are ${\mathcal{R}}_{0,\mathrm{in}}=1.{6}_{\ensuremath{-}1.0}^{+1.9}\text{ }\text{ }{\mathrm{Gpc}}^{\ensuremath{-}3}\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$ and ${\ensuremath{\kappa}}_{\mathrm{in}}=2.{3}_{\ensuremath{-}1.0}^{+1.3}$; $\ensuremath{\sim}20%$ of these form as the result of a gravitational-wave capture, implying that eccentric mergers from globular clusters contribute $\ensuremath{\lesssim}0.4\text{ }\text{ }{\mathrm{Gpc}}^{\ensuremath{-}3}\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$ to the local rate. A comparison to the merger rate reported by Laser Interferometer Gravitational Wave Observatory-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 $\ensuremath{\gtrsim}{10}^{4}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}\text{ }{\mathrm{pc}}^{\ensuremath{-}3}$. Interestingly, these models also reproduce the inferred black hole mass function in the range $13--30\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. However, all models underpredict the data outside this range, suggesting that other mechanisms might be responsible for the formation of these sources.

Topics & Concepts