Blasts of Light from Axions

The nature of dark matter is one of the longest-standing puzzles in science. Axions or axionlike particles are a key possibility and arise in mechanisms to solve the strong $CP$ problem, but also in low-energy limits of string theory. Extensive experimental and observational efforts are actively looking for “axionic” imprints. Independent of their nature, abundance, and contribution to the dark matter problem, axions form dense clouds around spinning black holes, grown by superradiant mechanisms. It was recently suggested that once couplings to photons are considered, an exponential (quantum) stimulated emission of photons ensues at large enough axion number. Here we solve numerically the classical problem in different setups. We show that laserlike emission from clouds exists at the classical level, and we provide the first quantitative description of the problem.

Figure 1

Time evolution of the monopole part of the EM scalar $F_{\mu \nu }{F}^{\mu \nu }$ for a coupling $M\mu =0.2$ at $r=20M$ when $k_{\text{axion}}{A}_0=0.01$ (upper panel) and $k_{\text{axion}}{A}_0=0.4$ (lower panel), in a Minskowski background. The scalar field is kept fixed and described by (15). The initial profile is described by $(E_0/A_0,w/M,r_0/M)=(0.001,5.0,40.0)$, but the qualitative features of the evolution are independent of these. For small couplings $k_{\text{axion}}{A}_0$ there is no instability and the initial EM fluctuation decays exponentially. For large couplings, on the other hand, an exponential growth ensues.

Figure 2

The relation between the growth rate $M\lambda$ and coupling $k_{\text{axion}}{A}_0$ in a Minkowski background with a scalar frozen to be given by (15). The rate is extracted from the $x$ or $y$ component of the electric field at $r=60M$. The instability is only present for large enough couplings, strongly suggesting the existence of a critical coupling $k_{\text{axion}}{A}_0$. Such conclusions are consubstantiated by an analytical description of this system [27].

Figure 3

Time evolution of ${\mathrm{\Phi }}_1$ (upper panel), $F{F}_0$ (middle panel) at $r=20M$, and the energy flux (lower panel) for an axion with mass $M\mu =0.2$ around a BH with $a=0.5M$. The coupling constant is supercritical with $k_{\text{axion}}{A}_0=0.3$. The initial EM profile is described by $(E_0/A_0,w/M)=({10}^{-3},5),({10}^{-3},20),({10}^{-4},5)$ for run 7,8,9, respectively, and $r_0=40$. The overall behavior and growth rate of the instability at large timescales are insensitive to the initial conditions.

Figure 4

Evolution of an initially subcritical axion, driven supercritical by a superradiantlike term. After the axion becomes supercritical, an instability sets in which gives rise to a burst of EM radiation, leading to a depletion of the scalar, until a new superradiant growth sets in. Our results are consistent with the triggering of periodic bursts. These results describe an axion with mass $M\mu =0.2$ around a BH with $a=0.5M$. The coupling constant is subcritical $k_{\text{axion}}{A}_0=0.15$. The initial EM profile is described by $(E_0/A_0,w/M)=(10^{-3},5)$ and $r_0=40$.