  Considering the existence of old neutron stars puts strong limits on the dark
matter/nucleon cross section for bosonic asymmetric dark matter. Key to these
bounds is formation of a Bose-Einstein condensate (BEC) of the asymmetric dark
matter particles. We consider the effects of the host neutron star's
gravitational field on the BEC transition. We find this substantially shifts
the transition temperature and so strengthens the bounds on cross section. In
particular, for the well-motivated mass range of ~5-15 GeV, we improve previous
bounds by an order of magnitude.
