Stimulated Axion Decay in Superradiant Clouds around Primordial Black Holes

The superradiant instability can lead to the generation of extremely dense axion clouds around rotating black holes. We show that, despite the long lifetime of the QCD axion with respect to spontaneous decay into photon pairs, stimulated decay becomes significant above a minimum axion density and leads to extremely bright lasers. The lasing threshold can be attained for axion masses $\mu \gtrsim {10}^{-8}\mathrm{eV}$, which implies superradiant instabilities around spinning primordial black holes with mass $\lesssim 0.01M_{\odot }$. Although the latter are expected to be nonrotating at formation, a population of spinning black holes may result from subsequent mergers. We further show that lasing can be quenched by Schwinger pair production, which produces a critical electron-positron plasma within the axion cloud. Lasing can nevertheless restart once annihilation lowers the plasma density sufficiently, resulting in multiple laser bursts that repeat until the black hole spins down sufficiently to quench the superradiant instability. In particular, axions with a mass $\sim {10}^{-5}\mathrm{eV}$ and primordial black holes with mass $\sim {10}^{24}\mathrm{kg}$, which may account for all the dark matter in the Universe, lead to millisecond bursts in the GHz radio-frequency range, with peak luminosities $\sim {10}^{42}\mathrm{erg}/\mathrm{s}$, suggesting a possible link to the observed fast radio bursts.

Figure 1

Model of the superradiant $2p$-axion cloud around a central Kerr black hole.

Figure 2

Numerical evolution of (a) the axion (blue) and photon (red) numbers within the $2p$-toroidal cloud for an axion with $\mu ={10}^{-5}\mathrm{eV}$ and $K=1$, and a BH with $M_{\mathrm{BH}}=8\times {10}^{23}\mathrm{kg}$ and $\tilde{a}=0.7$ (${\alpha }_{\mu }\simeq 0.03$). The corresponding dashed lines give the critical axion and photon numbers and the inset plot shows a detail of the evolution around the lasing threshold. In (b) we show the evolution of the average photon luminosity after the onset of lasing, with the inset plot enlarging the first laser pulse (solid red curve) and its approximate analytical description (dashed red curve).