Superradiant dark matter production from primordial black holes: Impact of multiple modes and gravitational wave emission

TL;DR

This paper tackles the problem of producing heavy bosonic dark matter in the early universe via gravitational channels from rotating primordial black holes (PBHs) that evaporate before BBN. The authors develop a two-mode (and effectively two-level) treatment of black hole superradiance, including gravitational wave emission from the cloud, and solve the coupled evolution of PBH mass, spin, and DM occupation numbers alongside Hawking radiation and UV freeze-in. They find that the growth of a second superradiant mode typically leads to decay of the first mode, so the DM yield from SR is not enhanced beyond the first-saturation level and can be further diminished by GW emission; scalar DM sees moderated enhancement relative to Hawking radiation, while vector DM can be suppressed below Hawking-only production in some regions. UV UV freeze-in remains an irreducible contribution and can dominate in small PBH mass scenarios, especially when the reheating temperature is high enough to suppress SR effects. Overall, the work refines the parameter space for PBH-induced DM genesis and highlights the nontrivial interplay of multi-mode SR and GW emission in gravity-only DM production.

Abstract

Rotating primordial black holes (PBHs) in the early universe can emit particles through superradiance, a process particularly efficient when the particle's Compton wavelength is comparable to the PBH's gravitational radius. Superradiance leads to an exponential growth of particle occupation numbers in gravitationally bound states. We present an analysis of heavy bosonic dark matter (DM) production through three gravitational mechanisms: Hawking radiation, superradiant instabilities, and ultraviolet (UV) freeze-in. We consider PBHs that evaporate before Big Bang Nucleosynthesis (BBN). For both scalar and vector DM, our analysis incorporates the evolution of a second superradiant mode. We demonstrate that the growth of a second superradiant mode causes the decay of the first mode, and thus the second mode cannot further enhance the DM abundance beyond that already achieved by the first mode. Our study also reveals that while superradiance generally enhances DM production, gravitational wave (GW) emission from the superradiant cloud may significantly modify this picture. For scalar DM, GW emission reduces the parameter space where superradiance effectively augments relic abundance. For vector DM, rapid GW emission from the superradiant cloud may yield relic abundances below those achieved through Hawking radiation alone. These findings demonstrate that multiple-mode effect and GW emission play critical roles in modeling DM production from PBHs in the early universe.

Figures (3)

• Figure 1: Evolution of key quantities in scalar superradiance, as functions of the scale factor $a$ ($a=1$ corresponds to time of PBH formation): (a) PBH mass $M$; (b) dimensionless PBH spin $a_*$; (c) number of DM particles in a comoving volume $\mathcal{N}_\mathrm{DM} \equiv n_\mathrm{DM} a^3$; (d) total occupation number $N^\mathrm{sr}$ of the superradiant cloud; and (e) number of DM particles from Hawking radiation $N^\mathrm{hr}$ . The initial parameters are PBH mass $M_\mathrm{ini} = 3 \times 10^4~\mathrm{g}$, spin $a_{*\mathrm{ini}} = 0.999$, abundance $\beta = 4.8 \times 10^{-21}$, and scalar DM particle mass $\mu = 10^9~\mathrm{GeV}$. Hawking radiation and superradiance are abbreviated as "HR" and "SR" respectively. The solid curves depict the scenario considering the interplay of Hawking radiation, superradiance, and GW emission, which reproduces the observed DM relic abundance ($\Omega_\mathrm{DM}h^2 \approx 0.12$). The dotted curves represent the Hawking radiation-only case, leading to the underproduction of DM ($\Omega_\mathrm{DM}h^2 \approx 0.076$). The dashed curves show the results when GW emission is ignored, leading to the overproduction of DM ($\Omega_\mathrm{DM}h^2 \approx 0.72$).
• Figure 2: Evolution of key quantities in vector superradiance, as functions of the scale factor $a$ ($a=1$ corresponds to time of PBH formation): (a) PBH mass $M$; (b) dimensionless PBH spin $a_*$; (c) number of DM particles in a comoving volume $\mathcal{N}_\mathrm{DM} \equiv n_\mathrm{DM} a^3$; (d) total occupation number $N^\mathrm{sr}$ of the superradiant cloud; and (e) number of DM particles from Hawking radiation $N^\mathrm{hr}$. The initial parameters are PBH mass $M_\mathrm{ini} = 3 \times 10^4~\mathrm{g}$, spin $a_{*\mathrm{ini}} = 0.999$, abundance $\beta = 4.8 \times 10^{-21}$, and vector DM particle mass $\mu = 10^9~\mathrm{GeV}$. Hawking radiation and superradiance are abbreviated as "HR" and "SR" respectively. The solid curves depict the scenario considering the interplay of Hawking radiation, superradiance, and GW emission, resulting in the DM relic abundance $\Omega_\mathrm{DM}h^2 \approx 0.017$. The dotted curves represent the Hawking radiation-only case, resulting in $\Omega_\mathrm{DM}h^2 \approx 0.031$. The dashed curves show the results when GW emission is ignored, leading to $\Omega_\mathrm{DM}h^2 \approx 0.58$.
• Figure 3: Viable parameter space for DM production in the $M_\mathrm{ini}$-$\beta$ plane. Contours show parameter combinations yielding the observed DM relic density ($\Omega_\mathrm{DM}h^2=0.12$) for a nearly extremal initial PBH spin ($a_{*\mathrm{ini}}=0.999$). Shaded regions indicate excluded parameter space from BBN (eq.\ref{['eq:BBN']}), CMB (eq.\ref{['eq:CMB']}), and GW bounds (eq.\ref{['eq:GW']}). The grey dashed line marks the threshold for a PBH-dominated era to present (eq.\ref{['eq:PBHD']}). For DM masses from $10^3$ to $10^{15}$ GeV, we compare three scenarios: PBH evolution with superradiance including GW emission and also the effect of gravitational UV freeze-in (solid curves), superradiance without GW emission (dashed curves), and pure Hawking radiation (dotted curves).