Merger rate of initially clustered primordial black holes for the two-body channel

Abstract

Primordial black holes (PBHs) may form an initially clustered population depending on their production mechanism. Motivated by binary black-hole merger events observed by gravitational-wave interferometers, we revisit the evaluation of the merger rate of PBH binaries and extend the formalism to include the effects of clustering. We show that, in the presence of relatively weak PBH clustering, the LIGO-Virgo-KAGRA events can be explained with a smaller value of $f_{\mathrm{PBH}}$ than in scenarios with Poisson-distributed PBHs, at least in the early two-body channel. However, for stronger clustering, the merger rate in the two-body channel is significantly suppressed due to the formation of three-body systems.