  Motivated by the recent "Cosmos Project" observation of dark-matter
concentrations with no ordinary matter in the same place, we study the question
of the existence of compact objects made of pure dark matter. We assume that
the dark matter is neutralino, and compare its elastic and annihilation cross
sections. We find that the two cross sections are of the same order of
magnitude. This result has a straightforward and important consequence that
neutralinos comprising a compact object can not achieve thermal equilibrium. To
substantiate our arguments, by solving Oppenheimer-Volkoff equation we
constructed a model of the star made of pure neutralinos. We explicitly showed
that the condition for the thermal equilibrium supported by the Fermi pressure
is never fulfilled inside the star. This neutralino state can not be described
by the Fermi-Dirac distribution. Thus, a stable neutralino star, which is
supported by the Fermi pressure, can not exist. We also estimated that a stable
star can not contain more than a few percents of neutralinos, most of the mass
must be in the form of the standard model particles.
