Rotating Drops of Axion Dark Matter

We consider how QCD axions produced by the misalignment mechanism could form galactic dark matter halos. We recall that stationary, gravitationally stable axion field configurations have the size of an asteroid with masses of order $10^{-13} $ solar masses (because gradient pressure is insufficient to support a larger object). We call such field configurations "drops". We explore whether rotating drops could be larger, and find that their mass could increase by a factor ~ 10. Remarkably this mass is comparable to the mass of miniclusters generated from misalignment axions in the scenario where the axion is born after inflation. We speculate that misalignment axions today are in the form of drops, contributing to dark matter like a distribution of asteroids (and not as a coherent oscillating background field). We consider some observational signatures of the drops, which seem consistent with a galactic halo made of axion dark matter.