  This work continues the construction of a recently proposed model of dark
matter stars. In this model, dark matter quanta are sterile massless particles
that are emitted from the central regions of the galaxy in the radial
direction. As a result, at large distances $r$ from the center of the galaxy,
the mass density of dark matter has the form $\rho \sim r^{-2}$, in contrast to
the homogeneous model $\rho=Const$. In the cosmological context, the
homogeneous model with massless particles corresponds to the radiation epoch of
the expansion of the universe, while the proposed inhomogeneous model turns out
to be equivalent to $\Lambda$CDM. In this paper, scenarios will be considered
in which the radial emission of dark matter is brought into hydrostatic
equilibrium with a uniform background. It is shown that solutions exist if the
uniform background has an equation of state typical for dark energy. Thus, this
model describes a phase transition from dark matter inside the galaxy to dark
energy outside of it. The specific mechanism for such a transition could be
Bose-Einstein condensation. In addition, the question of what happens if dark
matter particles are not sterile, for example, are photons of the Standard
Model, is considered.
