  We investigate a theory of dark matter called wave dark matter, also known as
scalar field dark matter (SFDM) and boson star dark matter or Bose-Einstein
condensate (BEC) dark matter (also see axion dark matter), and its relation to
the Tully-Fisher relation. We exhibit two boundary conditions that give rise to
Tully-Fisher-like relations for spherically symmetric static wave dark matter
halos: (BC1) Fixing a length scale at the outer edge of wave dark matter halos
gives rise to a Tully-Fisher-like relation of the form $M/v^4=\text{constant}$.
(BC2) Fixing the density of dark matter at the outer edge of wave dark matter
halos gives rise to a Tully-Fisher-like relation of the form
$M/v^{3.4}=\text{const}$.
