Scalar Field Wave (Fuzzy) Dark Matter and the Formation of Galaxies
  We investigate Scalar Field Wave Dark Matter in the context of galactic Dark
Matter halos. In particular, we offer an analysis of the Baryonic Tully-Fisher
Relation (BTFR). We detail a particular family of excited state solutions to
the Einstein-Klein-Gordon equations, and use it to provide a novel theoretical
model for producing the BTFR. We then solve this model computationally to
simulate the BTFR. Interpreting the Dark Matter scalar field as an ultralight
boson, this returns a conservative mass constraint of $m\geq 10^{-23}eV$.
Assuming slightly stronger conditions suggests $m\geq 10^{-22}eV$ to be more
compatible with the BTFR. We provide a discussion of Scalar Field Dark Matter
rotation curves and the structure of Scalar Field Dark Matter halos.
Compatibility with the BTFR requires the excited state solutions to obey
particular boundary conditions; this may have implications for the behavior of
Dark Matter halos and the formation of galaxies.
