  We analyze the processes relevant for star formation in a model with dark
matter in the form of sterile neutrinos. Sterile neutrino decays produce an
X-ray background radiation that has a two-fold effect on the collapsing clouds
of hydrogen. First, the X-rays ionize the gas and cause an increase in the
fraction of molecular hydrogen, which makes it easier for the gas to cool and
to form stars. Second, the same X-rays deposit a certain amount of heat, which
could, in principle, thwart the cooling of gas. We find that, in all the cases
we have examined, the overall effect of sterile dark matter is to facilitate
the cooling of gas. Hence, we conclude that dark matter in the form of sterile
neutrinos can help the early collapse of gas clouds and the subsequent star
formation.
