Corrections to Hawking radiation from asteroid-mass primordial black holes: Numerical evaluation of dissipative effects

Abstract

Primordial black holes (PBHs) are theorized objects that may make up some - or all - of the dark matter in the universe. At the lowest allowed masses, Hawking radiation (in the form of photons or electrons and positrons) is the primary tool to search for PBHs. This paper is part of an ongoing series in which we aim to calculate the $O(α)$ corrections to Hawking radiation from asteroid-mass primordial black holes, based on a perturbative quantum electrodymanics (QED) calculation on Schwarzschild background. Silva et. al. (2023) divided the corrections into dissipative and conservative parts; this work focuses on the numerical computation of the dissipative $O(α)$ corrections to the photon spectrum. We generate spectra for primordial black holes of mass $M=1$-$8 \times 10^{21} m_{\rm planck}$. This calculation confirms the expectation that at low energies, the inner bremsstrahlung radiation is the dominant contribution to the Hawking radiation spectrum. At high energies, the main $O(α)$ effect is a suppression of the photon spectrum due to pair production (emitted $γ\rightarrow e^+e^-$), but this is small compared to the overall spectrum. We compare the low-energy tail in our curved spacetime QED calculation to several approximation schemes in the literature, and find deviations that could have important implications for constraints from Hawking radiation on primordial black holes as dark matter.