  Dark matter substructure has the potential to discriminate between broad
classes of dark matter models. With this in mind, we construct novel solutions
to the equations of motion governing condensate dark matter candidates, namely
axion Bose-Einstein condensates and superfluids. These solutions are highly
compressed along one axis and thus have a disk-like geometry. We discuss linear
stability of these solutions, consider the astrophysical implications as a
large-scale dark disk or as small scale substructure, and find a characteristic
signal in strong gravitational lensing. This adds to the growing body of work
that indicates that the morphology of dark matter substructure is a powerful
probe of the nature of dark matter.
