  We consider possibly observable effects of asymmetric dark matter (ADM) in
neutron stars. Since dark matter does not self-annihilate in the ADM scenario,
dark matter accumulates in neutron stars, eventually reaching the Chandrasekhar
limit and forming a black hole. We focus on the case of scalar ADM, where the
constraints from Bose-Einstein condensation and subsequent black hole formation
are most severe due to the absence of Fermi degeneracy pressure. We also note
that in some portions of this constrained parameter space, non-trivial effects
from Hawking radiation can modify our limits. We find that for scalar ADM with
mass between 100 keV and 10^5 GeV, the constraint from pulsars in globular
clusters on the scattering cross-section with neutrons ranges from \sigma_n <
10^{-45} cm^2 to 10^{-52} cm}^2. In particular, for scalar ADM with mass
between 1 GeV and 1 TeV (in the case where black hole evaporation due to
Hawking radiation is unimportant), the constraint on the scattering
cross-section is below what is reachable with ton scale direct detection
experiments.
