Condensate dark matter stars
  We investigate the structure and stability properties of compact
astrophysical objects that may be formed from the Bose-Einstein condensation of
dark matter. Once the critical temperature of a boson gas is less than the
critical temperature, a Bose-Einstein Condensation process can always take
place during the cosmic history of the universe. Therefore we model the dark
matter inside the star as a Bose-Einstein condensate. In the condensate dark
matter star model, the dark matter equation of state can be described by a
polytropic equation of state, with polytropic index equal to one. We derive the
basic general relativistic equations describing the equilibrium structure of
the condensate dark matter star with spherically symmetric static geometry. The
structure equations of the condensate dark matter stars are studied
numerically. The critical mass and radius of the dark matter star are given by
$M_{crit}\approx 2(l_a/1fm)^{1/2}(m_{\chi}/1\;{\rm GeV})^{-3/2}M_{\odot}$ and
$R_{crit}\approx 1.1 \times 10^6(l_a/1\;{\rm fm})^{1/2}(m_{\chi}/1\;{\rm
GeV})^{-3/2}$ cm respectively, where $l_a$ and $m_{\chi}$ are the scattering
length and the mass of dark matter particle, respectively.
