Quantum Depletion and the Validity of the Quantum-Fluid Description of Axion Dark Matter

Axions are widely studied dark matter candidates that, in the high-occupation-number regime, admit an effective wave description on astrophysical scales. In this work, we derive a nonrelativistic quantum-fluid representation of axion dark matter by connecting the relativistic scalar-field theory to its hydrodynamic form through the Klein and Madelung transformations. The resulting equations contain a quantum-pressure term that modifies gravitational collapse and defines a quantum Jeans scale below which linear perturbations are suppressed. We extend the standard treatment by including cosmological expansion and leading nonlinear density corrections, obtaining a modified Jeans scale that depends on both the scale factor and the local overdensity. For axion masses near 10 −22 eV, this scale is of order kilo-parsecs today, consistent with cored halo structure on dwarf-galaxy scales. As a consistency check, we estimate the Bogoliubov depletion fraction in the weakly interacting regime and find it to be parametrically small within the assumptions of the analysis. These results support the use of an effective macroscopic wave framework for studying axion-induced departures from conventional cold dark matter structure formation.