  We put constraints on asymmetric dark matter candidates with spin-dependent
interactions based on the simple existence of white dwarfs and neutron stars in
globular clusters. For a wide range of the parameters (WIMP mass and
WIMP-nucleon cross section), WIMPs can be trapped in progenitors in large
numbers and once the original star collapses to a white dwarf or a neutron
star, these WIMPs might self-gravitate and eventually collapse forming a
mini-black hole that eventually destroys the star. We impose constraints
competitive to direct dark matter search experiments, for WIMPs with masses
down to the TeV scale.
