Coherent and Stochastic Axion Dark Matter from Thermal Relaxation

Abstract

An axion driven toward a thermal minimum need not remain a coherent condensate. We derive the coupled attenuation of the field mean and production of stochastic momentum modes in an expanding plasma. A single momentum dependent optical depth partitions every mode between coherent power and Bose occupation, placing standard misalignment, partial relaxation, and stochastic production in one dynamical relation. Finite spatial and temporal response suppresses high momentum production, so the stochastic relic has lower mean momentum and a shorter free streaming length than an equilibrium population at fixed mass and bath temperature. A weakly coupled realization produces the dark matter abundance, reduces inherited coherent isocurvature, and confines production correlations to scales removed by collisionless propagation. Thermal relaxation therefore determines the composition, momentum distribution, and transported structure of axion dark matter.