Effect of the Memory Burden on Primordial Black Hole Hot Spots

TL;DR

This work assesses how memory-burden (MB) modifications to PBH evaporation alter the formation and morphology of surrounding hot spots. It introduces transfer functions $\eta_M$ and $\eta_T$ to encode MB in the evaporation rate and Hawking temperature, and derives general expressions for the hot-spot core temperature $T_c$ and core radius $r_c$ via $T_c = (\eta_M^2/\eta_T)^{1/3} T_{c,\mathrm{SC}}$ and $r_c = (\eta_T/\eta_M) r_{c,\mathrm{SC}}$, while MB also reshapes the radial temperature profile and diffusion scale. Two illustrative MB realizations are analyzed: a rigid MB where the rate and $T_H$ freeze after MB onset, generally suppressing hot spots and restricting their formation to limited mass ranges and low MB exponents; and a self-similar MB where the suppression scales with $M$, which can still yield sizeable hot spots with a hotspot temperature largely independent of the PBH mass. The framework thus provides a versatile tool to study nonstandard PBH evaporation scenarios and their cosmological imprints, highlighting MB’s potential impact on detecting evaporating PBHs through their thermal footprints.

Abstract

When primordial black holes (PBHs) evaporate, they deposit energy in the surrounding plasma, leading to temperature gradients, or hot spots, that evolve during the evaporation process. Motivated by recent studies suggesting that a memory burden may slow down PBH evaporation, we explore how a suppression of the evaporation rate affects the morphology of such hot spots. We include such a suppression in the form of transfer functions and derive general formulas for the hot-spot core temperature and radius. Applying our results to illustrative scenarios, we find that in the vanilla memory burden scenario in which the evaporation rate and Hawking temperature are exactly constant, the hot-spot temperature is substantially lowered. Nonetheless, we show that alternative scenarios may lead to sizeable hot spots with morphologies that differ significantly from the semi-classical case.

Figures (2)

• Figure 1: Hot-spot core temperature (plain coloured lines) compared to the Universe's temperature at the time of evaporation (dotted lines) for different values of $k$, and as a function of $M=qM_{\rm ini}$. Regions where hot spot core is colder than the ambient Universe, and where the PBH is stable on cosmological time scales are shaded in grey and brown, respectively.
• Figure 2: Same as in FIG. \ref{['fig:rigid']}, but in the case of self-similar MB rate and Hawking temperature.