Small-scale structure of primordial black hole dark matter and its implications for accretion

Primordial black hole (PBH) dark matter (DM) nonlinear small-scale structure formation begins before the epoch of recombination due to large Poisson density fluctuations. Those small-scale effects still survive today, distinguishing physics of PBH DM structure formation from the one involving WIMP DM. We construct an analytic model for the small-scale PBH velocities that reproduces the velocity floor seen in numerical simulations, and investigate how these motions impact PBH accretion bounds at different redshifts. We find that the effect is small at the time of recombination, leaving the cosmic microwave background bounds on PBH abundance unchanged. However, already at $z=20$ the PBH internal motion significantly reduces their accretion due to the additional $1/v^6$ suppression, affecting the 21 cm bounds. Today the accretion bounds arising from dwarf galaxies or smaller PBH substructures are all reduced by the PBH velocity floor. We also investigate the feasibility for the PBH clusters to coherently accrete gas leading to a possible enhancement proportional to the cluster's occupation number but find this effect to be insignificant for PBH around $10 M_{\odot}$ or lighter. Those results should be reconsidered if the initial PBH distribution is not Poisson, for example, in the case of large initial PBH clustering.