Characteristic Size and Mass of Galaxies in the Bose-Einstein Condensate
  Dark Matter Model
  We study the characteristic length scale of galactic halos in the
Bose-Einstein condensate (or scalar field) dark matter model. Considering the
evolution of the density perturbation we show that the average background
matter density determines the quantum Jeans mass and hence the spatial size of
galaxies at a given epoch. In this model the minimum size of galaxies increases
while the minimum mass of the galaxies decreases as the universe expands. The
observed values of the mass and the size of the dwarf galaxies are successfully
reproduced with the dark matter particle mass $m\simeq 5\times 10^{-22}eV$. The
minimum size is about $6\times 10^{-3}\sqrt{m/H}\lambda_c$ and the typical
rotation velocity of the dwarf galaxies is $O(\sqrt{H/m}$) c, where $H$ is the
Hubble parameter and $\lambda_c$ is the Compton wave length of the particle. We
also suggest that ultra compact dwarf galaxies are the remnants of the dwarf
galaxies formed in the early universe.
