Effects of Hawking evaporation on PBH distributions

TL;DR

This paper studies how Hawking evaporation alters the distribution of primordial black holes over time, impacting gamma-ray constraints and the likelihood of observing black hole explosions.

Contribution

It introduces a semi-analytic model for evolving PBH distributions considering Hawking evaporation and reassesses observational constraints accordingly.

Findings

The shape of PBH distributions significantly changes from formation to present.

Corrected gamma-ray constraints on PBH dark matter are derived using evolved distributions.

The rate of black hole explosions in the Milky Way is very low, making observation unlikely.

Abstract

Primordial black holes (PBHs) may lose mass by Hawking evaporation. For sufficiently small PBHs, they may lose a large portion of their formation mass by today, or evaporate completely if they form with mass $M<M_\mathrm{crit}\sim5\times10^{14}~\mathrm{g}$. We investigate the effect of this mass loss on extended PBH distributions, showing that the shape of the distribution is significantly changed between formation and today. We reconsider the $\gamma$-ray constraints on PBH dark matter in the Milky Way center with a correctly `evolved' lognormal distribution, and derive a semi-analytic time-dependent distribution which can be used to accurately project monochromatic constraints to extended distribution constraints. We also derive the rate of black hole explosions in the Milky Way per year, finding that although there can be a significant number, it is extremely unlikely to find one close enough to Earth to observe. Along with a more careful argument for why monochromatic PBH distributions are unlikely to source an exploding PBH population today, we (unfortunately) conclude that we are unlikely to witness any PBH explosions.