  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}.
