Dynamical evolution of axion condensates under stimulated decays into photons

Dark matter axion condensates may experience stimulated decays into photon pairs. This effect has been often interpreted as a parametric resonance of photons from the axion-photon coupling, leading to an exponential growth of the photon occupation number in a narrow instability band. Most of the previous literature does not consider the possible evolution of the axion field due to the photon growth. We revisit this effect presenting a mean field solution of the axion-photon kinetic equations, in terms of number of photons and pair correlations. We study the limit of no axion depletion, recovering the known instability. Moreover, we extend the results including a possible depletion of the axion field. In this case we find that the axion condensate exhibits the behaviour of an inverted pendulum. We discuss the relevance of these effects for two different cases: an homogeneous axion field at recombination and a localized axion clump and discuss constraints that could result from the induced photon background.