Far from equilibrium dynamics of Bose-Einstein condensation for axion dark matter

Axions and similar very weakly interacting particles are increasingly compelling candidates for the cold dark matter of the Universe. Having very low mass and being produced nonthermally in the early universe, axions feature extremely high occupation numbers. It has been suggested that this leads to the formation of a Bose-Einstein condensate with potentially significant impact on observation and direct detection experiments. In this paper we aim to clarify that if Bose-Einstein condensation occurs for light and very weakly interacting dark matter particles, it does not happen in thermal equilibrium but is described by a far from equilibrium state. In particular we point out that the dynamics is characterized by two very different time scales, such that condensation occurs on a much shorter time scale than full thermalization.

Figure 1

Time evolution of the distribution function (a) and the condensate fraction (b).

Figure 2

Dependence of the condensate formation time on the volume of the patch. The red curve is for a condensate fraction of 60% and the blue curve is for 30%. Fitting this suggests a behavior $\sim V^{0.3–0.55}\sim L^{0.9–1.7}$.