Polytropic spheres modelling dark matter halos of dwarf galaxies
  Dwarf galaxies and their dark matter (DM) halos have the velocity curves of a
different character than those in large galaxies. They are modelled by a simple
pseudo iso-thermal model containing only two parameters that do not allow to
obtain insight into physics of the DM halo. We would like to obtain some
insight into the physical conditions in DM halos of dwarf galaxies by using a
simple physically based model of DM halos. In order to treat a diversity of the
dwarf galaxy velocity profiles in a unifying framework, we apply the polytropic
spheres characterised by the polytropic index $n$ and the relativistic
parameter $\sigma$ as a model of dwarf-galaxy DM halos and match the velocity
of circular geodesics of the polytropes to the velocity curves observed in the
dwarf galaxies from the LITTLE THINGS ensemble. We introduce three classes of
the LITTLE THINGS dwarf galaxies in accord with the polytrope models, due to
the different character of the velocity profile. The first class corresponds to
polytropes having $n < 1$ with linearly increasing velocity along with the
whole profile, the second class has $1 < n < 2$ and the velocity profile
becomes flat in the external region, the third class has $n > 2$ and the
velocity profile reaches a maximum and demonstrated a decline in the external
region. The $\sigma$ parameter has to be strongly non-relativistic ($\sigma <
10^{-8}$) for all dwarf galaxy models -- it varies for the models of each
class, but these variations have a negligible influence on the character of the
velocity profile. Our results indicate the possibility that at least two
different kinds of dark matter are behind the composition of DM halos. The
matches of the observational velocity curves are of the same quality as those
obtained by the pseudo-isothermal, core-like models of dwarf galaxy DM halos.
