  The behavior of light scalar dark matter has been a subject of much interest
recently as it can lead to interesting small scale behavior. In particular,
this can lead to the formation of gravitationally bound clumps for these light
scalars, including axions. In Ref. [1] we analyzed the behavior of these
clumps, assuming spherical symmetry, allowing for both attractive and repulsive
self-interactions. There is a maximum allowed mass for the clumps in the case
of attractive interactions, and a minimum radius for the clumps in the case of
repulsive interactions, which is saturated at large mass. Here we extend this
work to include non-spherically symmetric clumps. Since the system tries to
re-organize into a BEC ground state, we consider configurations with a
conserved non-zero angular momentum, and construct minimum energy
configurations at fixed particle number and fixed angular momentum. We find
generalizations of the previous spherically symmetric results. In particular,
while there is still a maximum mass for the attractive case, its value
increases with angular momentum. Also, the minimum radius in the repulsive case
is raised to higher radii. We clarify how a recent claim in the literature of
an upper bound on angular momentum is due to inaccurate numerics. In a
forthcoming paper we shall investigate the possibility of resonance of axion
clumps into both visible and hidden sector photons, and analyze how the altered
mass and radius from non-zero angular momentum affects the resonance.
