Constraining the Stellar Initial Mass Function with Gravitational Wave Data

Observations of globular clusters indicate that the stellar initial mass function (IMF) may vary over space and time, becoming more top-heavy with decreasing metallicity and increasing gas density. As the IMF regulates the number of massive stars that are formed within star clusters, it significantly affects their lifetime, with clusters born with a top-heavy IMF dissolving faster than those with a bottom-heavy IMF. Clusters born with a top-heavy IMF will also produce a large number of stars that eventually collapse to form black holes (BHs), which can merge in the cluster core producing gravitational wave (GW) events. We run a set of simulations using the Cluster Monte Carlo (CMC) code to model the population of merging BHs in dense star clusters with varying IMFs. We study how the binary BH merger rate and merger mass distribution depend on the slope of the IMF, with top-heavy IMFs leading to a larger number of mergers. We compare these distributions to the events observed by the LIGO/Virgo/KAGRA collaboration and place an upper limit on the density of star clusters born with different IMFs.