How do stars affect $\psi$DM halos?
  Wave dark matter ($\psi$DM) predicts a compact soliton core and a granular
halo in every galaxy. This work presents the first simulation study of an
elliptical galaxy by including both stars and $\psi$DM, focusing on the
systematic changes of the central soliton and halo granules. With the addition
of stars in the inner halo, we find the soliton core consistently becomes more
prominent by absorbing mass from the host halo than that without stars, and the
halo granules become "non-isothermal", "hotter" in the inner halo and "cooler"
in the outer halo, as opposed to the isothermal halo in pure $\psi$DM
cosmological simulations. Moreover, the composite (star+$\psi$DM) mass density
is found to follow a $r^{-2}$ isothermal profile near the half-light radius in
most cases. Most striking is the velocity dispersion of halo stars that
increases rapidly toward the galactic center by a factor of at least 2 inside
the half-light radius caused by the deepened soliton gravitational potential, a
result that compares favorably with observations of elliptical galaxies and
bulges in spiral galaxies. However in some rare situations we find a phase
segregation turning a compact distribution of stars into two distinct
populations with high and very low velocity dispersions; while the
high-velocity component mostly resides in the halo, the very low-velocity
component is bound to the interior of the soliton core, resembling stars in
faint dwarf spheroidal galaxies.
