Primordial Black Hole Hot Spots and Nucleosynthesis

TL;DR

This work analyzes how local hot spots around evaporating primordial black holes (PBHs) modify the injection and propagation of photons during Big-Bang Nucleosynthesis (BBN). By modeling a radial hotspot temperature profile and two key processes—shielding of Hawking-emitted photons and reprocessing into local blackbody radiation—and by connecting these with the universal low-energy photon spectrum, the authors derive a transfer function that scales the PBH photon flux and impacts photodissociation constraints. They find substantial suppression of the low-energy photon flux for PBHs with masses around $10^{11}$–$10^{12}$ g, reducing the strength of BBN limits in that range, with the effect depending strongly on the hotspot profile and the coupling $\alpha$. The results emphasize the need for detailed hotspot dynamics in PBH phenomenology and motivate future work to refine the hotspot temperature profile and a full Boltzmann treatment of photon cascades.

Abstract

Upon their evaporation via Hawking radiation, primordial black holes (PBHs) may deposit energy in the ambient plasma on scales smaller than the typical distance between two black holes, leading to the formation of hot spots around them. We investigate how the corresponding rise of the local temperature during the evaporation may act as a shield against the release of low-energy photons, affecting PBH's capacity to dissociate light nuclei after Big-Bang Nucleosynthesis through photo-dissociation. We study the different ways PBH hot spots affect the flux of low-energy photons expected from PBH evaporation, and we find that such effects can be particularly relevant to the physics of photo-dissociation during Big-Bang Nucleosynthesis for PBHs with masses between $10^{11}$g and $3\times 10^{12}$g. We emphasize that the magnitude of this effect is highly dependent on the specific shape of the temperature profile around PBHs and its time evolution. This underscores the necessity for a comprehensive study of PBH hot spots and their dynamics in the future.

Figures (3)

• Figure 1: Different contributions to the photon energy distributions, for PBHs with masses $10^{11}\mathrm{g}$ (left), $10^{12}\mathrm{g}$ (center), and $10^{13}\mathrm{g}$ (right), when considering (ignoring) the presence of a hot spot are depicted using plain (dashed) lines.
• Figure 2: BBN limits on PBHs as derived in Acharya_2020 and Carr:2020gox when considering (plain lines) or ignoring (dashed lines) the effect of the hot spot.
• Figure 3: Variation of the BBN limit on PBHs from Ref. Acharya_2020 for varying values of $\alpha$.