Low mass axions could have additional structure at the galactic scale. If they continuously fall into galaxies from the intergalactic medium, they would be denser in " caustic " rings, just as the stream of water in a continuously flowing fountain is thicker at its peak. The gravitational effects of these rings on galactic structure and rotation might then be observable. Other cold dark matter theoretical candidates, such as WIMPs and MACHOs, could also form such rings, but because such candidates are fermionic and thus experience friction or scattering among themselves, the rings would be less sharply defined.