Globular cluster formation histories, masses, and radii inferred from gravitational waves

ABSTRACT Globular clusters (GCs) are found in all types of galaxies and harbour some of the most extreme stellar systems, including black holes that may dynamically assemble into merging binary black holes (BBHs). Uncertain GC properties, including when they formed, their initial masses and sizes, affect their production rate of BBH mergers. Using the gravitational-wave transient catalogue (GWTC-3), we measure that dynamically assembled BBHs – those that are consistent with isotropic spin directions – make up 61^{+29-₄₄\%} of the total merger rate, with a local merger rate of 10. 9^{+16. 8-₉. ₃} Gpc−3 yr−1 rising to 58. 9^{+149. 4-₄₆. ₀} Gpc−3 yr−1 at z = 1. We assume that this inferred rate describes the contribution from GCs and compare it against the Cluster Monte Carlo (cmc) simulation catalogue to directly fit for the GC initial mass function, virial radius distribution, and formation history. We find that GC initial masses are consistent with a Schechter function with slope ₘ = -1. 9^{+0. 8-₀. ₈}. Assuming a mass function slope of βm = −2 and a mass range between 104–10⁸\, M_, we infer a GC formation rate at z = 2 of 5. 0^{+9. 4-₄. ₀} Gpc−3 yr−1, or 2. 1^{+3. 9-₁. ₇} 10⁶\, M_ Gpc−3 yr−1 in terms of mass density. We find that the GC formation rate probably rises more steeply than the global star formation rate between z = 0 and z = 3 (82 per cent credibility) and implies a local number density that is fₑv = 22. 6^{+29. 9-₁₆. ₂} times higher than the observed density of survived GCs. This is consistent with expectations for cluster evaporation, but may suggest that other environments contribute to the rate of BBH mergers with significantly tilted spins.