Dark radiation from Kerr primordial black holes: the role of superradiance

TL;DR

This paper investigates how superradiance around Kerr primordial black holes affects dark radiation production, showing it generally suppresses dark radiation and alters previous bounds on black hole properties.

Contribution

It introduces a comprehensive evolution model of black hole spin, mass, and superradiant cloud occupation, revealing superradiance's impact on dark radiation constraints.

Findings

Superradiance suppresses dark radiation by extracting black hole angular momentum.

Gravitational waves from superradiant clouds can partially offset dark radiation loss.

Existing bounds on primordial black holes need revision if BSM bosons enable superradiance.

Abstract

Light primordial black holes (PBHs) that fully evaporate before Big Bang Nucleosynthesis (BBN) produce dark radiation (DR) via Hawking radiation of gravitons, contributing to the effective number of relativistic species $\Delta N_{\rm eff}$. If the particle spectrum contains a beyond-the-Standard-Model (BSM) boson with Compton wavelength comparable to the black hole (BH) gravitational radius, superradiant instability extracts angular momentum from the BH into a bosonic cloud, whose gravitational wave (GW) emission contributes an additional source of DR. By simultaneously evolving the BH mass and spin, superradiant mode occupation numbers, comoving entropy and cosmological energy densities in an expanding early-universe background, we find that superradiance generically suppresses $\Delta N_{\rm eff}$: by extracting angular momentum before Hawking radiation can convert it into gravitons, superradiance starves the dominant dark-radiation channel. The GWs emitted by the superradiant cloud can partially compensate this loss, but only when the superradiant and BH evaporation timescales are comparable; otherwise the cloud GWs are emitted too early and diluted by cosmological expansion. The results imply that existing $\Delta N_{\rm eff}$ bounds on PBH mass and spin derived without superradiance must be revisited if BSM bosons are present in the particle spectrum.