Modeling Wave Dark Matter in Dwarf Spheroidal Galaxies

This paper studies a model of dark matter called wave dark matter (also known as scalar field dark matter and boson stars) which has recently also been motivated by a new geometric perspective by Bray [arXiv:1212.5745]. Wave dark matter describes dark matter as a scalar field which satisfies the Einstein-Klein-Gordon equations. These equations rely on a fundamental constant Upsilon (also known as the "mass term" of the Klein-Gordon equation). In this work, we compare the wave dark matter model to observations to obtain a working value of Upsilon. Specifically, we compare the mass profiles of spherically symmetric static states of wave dark matter to the Burkert mass profiles that have been shown by Salucci et al. [arXiv:1111.1165] to predict well the velocity dispersion profiles of the eight classical dwarf spheroidal galaxies. We show that a reasonable working value for the fundamental constant in the wave dark matter model is Upsilon = 50 yr^{-1}. We also show that under precise assumptions the value of Upsilon can be bounded above by 1000 yr^{-1}.