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). Wave dark matter describes dark matter as a scalar field which satisfies the Einstein-Klein-Gordon equations. These equations rely on a fundamental constant gamma (also known as the "mass term" of the Klein-Gordon equation), which can be interpreted physically as a characteristic frequency of the scalar field. In this work, we compare the wave dark matter model to observations to obtain an estimate of gamma. Specifically, we compare the mass pro files of spherically symmetric static states of wave dark matter to certain Burkert mass pro files recently shown to predict well the velocity dispersion pro files of the eight classical dwarf spheroidal galaxies. We outline a procedure for estimating gamma in these circumstances and show that under precise assumptions the value of gamma can be bounded above by 1000 yr(-1). We also show that a reasonable working value for this constant is gamma = 50 yr(-1).