Formation of hot spots around small primordial black holes

TL;DR

This paper studies how Hawking radiation from small primordial black holes creates hot spots in the early universe, revealing a non-trivial temperature profile influenced by interference effects, with potential phenomenological implications.

Contribution

It introduces a detailed analysis of hot spot formation around evaporating primordial black holes, incorporating the Landau-Pomeranchuk-Migdal effect and characterizing the hot spot's properties.

Findings

Hot spots have a large core radius exceeding the black hole horizon.

Maximum temperature of hot spots is independent of initial PBH mass.

Hot spot temperature depends on the fine-structure constant.

Abstract

In this paper, we investigate the thermalization of Hawking radiation from primordial black holes (PBHs) in the early Universe, taking into account the interference effect on thermalization of high energy particles, known as Landau-Pomeranchuk-Migdal (LPM) effect. Small PBHs with masses $ \lesssim 10^9 \, \mathrm{g} $ completely evaporate before the big bang nucleosynthesis (BBN). The Hawking radiation emitted from these PBHs heats up the ambient plasma with temperature lower than the Hawking temperature, which results in a non-trivial temperature profile around the PBHs, namely a hot spot surrounding a PBH with a broken power-law tail. We find that the hot spot has a core with a radius much larger than the black hole horizon and its highest temperature is independent of the initial mass of the PBH such as $2 \times 10^{9} \, {\rm GeV} \times (\alpha/0.1)^{19/3}$, where $\alpha$ generically represents the fine-structure constants. We also briefly discuss the implications of the existence of the hot spot for phenomenology.