Black Hole Mergers from Star Clusters with Top-heavy Initial Mass Functions

Recent observations of globular clusters (GCs) provide evidence that the stellar initial mass function (IMF) may not be universal, suggesting specifically that the IMF grows increasingly top-heavy with decreasing metallicity and increasing gas density. Noncanonical IMFs can greatly affect the evolution of GCs, mainly because the high end determines how many black holes (BHs) form. Here we compute a new set of GC models, varying the IMF within observational uncertainties. We find that GCs with top-heavy IMFs lose most of their mass within a few gigayears through stellar winds and tidal stripping. Heating of the cluster through BH mass segregation greatly enhances this process. We show that, as they approach complete dissolution, GCs with top-heavy IMFs can evolve into dark clusters consisting of mostly BHs by mass. In addition to producing more BHs, GCs with top-heavy IMFs also produce many more binary BH (BBH) mergers. Even though these clusters are short-lived, mergers of ejected BBHs continue at a rate comparable to, or greater than, what is found for long-lived GCs with canonical IMFs. Therefore, these clusters, though they are no longer visible today, could still contribute significantly to the local BBH merger rate detectable by LIGO/Virgo, especially for sources with higher component masses well into the BH mass gap. We also report that one of our GC models with a top-heavy IMF produces dozens of intermediate-mass black holes (IMBHs) with masses M > 100 M-circle dot M > 500 M-circle dot. Ultimately, additional gravitational wave observations will provide strong constraints on the stellar IMF in old GCs and the formation of IMBHs at high redshift.

Automated summary

Recent observations of globular clusters suggest that the stellar initial mass function varies with metallicity and gas density, impacting black hole formation and cluster evolution. Calculating new GC models, it is found that clusters with top-heavy IMFs lose mass rapidly and evolve into dark clusters dominated by BHs. Additionally, these clusters produce more BBH mergers and even intermediate-mass black holes, contributing significantly to the local BBH merger rate detectable by LIGO/Virgo. Ultimately, further gravitational wave observations will shed light on the stellar IMF in old GCs and the formation of IMBHs at high redshifts.