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

## TL;DR

This paper models the small-scale structure and velocities of primordial black hole dark matter, showing how these factors influence accretion bounds and cosmic signals, with implications for understanding PBH contributions to dark matter.

## Contribution

The authors develop an analytic model for PBH velocities that matches simulations and analyze its impact on accretion bounds across different cosmic epochs.

## Key findings

- PBH velocity effects are negligible at recombination, preserving CMB bounds.
- At redshift 20, PBH motions significantly suppress accretion, affecting 21 cm bounds.
- PBH velocity floors reduce accretion bounds in dwarf galaxies and smaller structures.

## Abstract

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.