Analysis of Dark Matter Axion Clumps with Spherical Symmetry
  Recently there has been much interest in the spatial distribution of light
scalar dark matter, especially axions, throughout the universe. When the local
gravitational interactions between the scalar modes are sufficiently rapid, it
can cause the field to re-organize into a BEC of gravitationally bound clumps.
While these clumps are stable when only gravitation is included, the picture is
complicated by the presence of the axion's attractive self-interactions, which
can potentially cause the clumps to collapse. Here we perform a detailed
stability analysis to determine under what conditions the clumps are stable. In
this paper we focus on spherical configurations, leaving aspherical
configurations for future work. We identify branches of clump solutions of the
axion-gravity-self-interacting system and study their stability properties. We
find that clumps that are (spatially) large are stable, while clumps that are
(spatially) small are unstable and may collapse. Furthermore, there is a
maximum number of particles that can be in a clump. We map out the full space
of solutions, which includes quasi-stable axitons, and clarify how a recent
claim in the literature of a new ultra-dense branch of stable solutions rests
on an invalid use of the non-relativistic approximation. We also consider
repulsive self-interactions that may arise from a generic scalar dark matter
candidate, finding a single stable branch that extends to arbitrary particle
number.
