Scalar Field Wave (Fuzzy) Dark Matter, the Baryonic Tully-Fisher Relation, and the Formation of Galaxies

Within the context of galactic Dark Matter halos, we investigate Scalar Field Wave Dark Matter and analyze the Baryonic Tully-Fisher Relation (BTFR). To understand the properties of Dark Matter, we provide a new model for deriving BTFR theoretically and computationally by solving the Einstein-Klein-Gordon equations based on a special family of excited state solutions. In the mass range m≥10^-22eV, we show that the BTFR is compatible. And this requires the excited state solutions to obey certain boundary conditions, which is interesting for implying the formation and morphology of galaxies. Our simulation also presents a possibility of Scalar Field Dark Matter rotation curves and the structure of Scalar Field Dark Matter halos.