In-depth analysis of the clustering of dark matter particles around primordial black holes I: density profiles

TL;DR

This paper investigates the detailed density profiles of dark matter mini-spikes around primordial black holes, revealing new phase-space effects and deriving analytical formulas to explain their power-law behaviors.

Contribution

It introduces a refined analysis of dark matter mini-spike profiles around primordial black holes, including overlooked phase-space effects and analytical expressions for different regimes.

Findings

Identification of a previously overlooked phase-space contribution.

Derivation of analytical formulas for density profiles.

Explanation of power-law behaviors in mini-spike profiles.

Abstract

Primordial black holes may have been produced in the early stages of the thermal history of the Universe after cosmic inflation. If so, dark matter in the form of elementary particles can be subsequently accreted around these objects, in particular when it gets non-relativistic and further streams freely in the primordial plasma. A dark matter mini-spike builds up gradually around each black hole, with density orders of magnitude larger than the cosmological one. We improve upon previous work by carefully inspecting the computation of the mini-spike radial profile as a function of black hole mass, dark matter particle mass and temperature of kinetic decoupling. We identify a phase-space contribution that has been overlooked and that leads to changes in the final results. We also derive complementary analytical formulae using convenient asymptotic regimes, which allows us to bring out peculiar power-law behaviors for which we provide tentative physical explanations.