Simulating Binary Primordial Black Hole Mergers in Dark Matter Halos

Abstract: Primordial black holes (PBHs), possibly constituting a non-negligible fraction of dark matter (DM), might be responsible for a number of gravitational wave events detected by LIGO/Virgo/KAGRA. In this paper, we simulate the evolution of PBH binaries in DM halos and calculate their merger rate up to redshift of 10. We assume that DM halos are made entirely by a combination of single PBHs and PBH binaries. We present the resulting merger rates from the two main channels that lead to merging PBH binaries: two-body captures and binary-single interactions. We account for alternative assumptions on the dark matter halo mass-concentration relationship versus redshift. We also study what impact the PBH mass distribution, centered in the stellar-mass range, has on the PBH merger rate that the ground-based gravitational-wave observatories can probe. We find that under reasonable assumptions on the abundance of PBH binaries relative to single PBHs, the binary-single interaction rates can be dominant over the two-body capture channel. Our work studies in detail the dynamics of PBHs inside DM halos, advancing our understanding on how the current gravitational-wave events constrain the properties of PBHs. Moreover, we make predictions in a redshift range to be probed by future observatories.