Neutron stars as dark matter probes

We examine whether the accretion of dark matter onto neutron stars could ever have any visible external effects. Captured dark matter which subsequently annihilates will heat the neutron stars, although it seems the effect will be too small to heat close neutron stars at an observable rate while those at the galactic center are obscured by dust. Nonannihilating dark matter would accumulate at the center of the neutron star. In a very dense region of dark matter such as that which may be found at the center of the galaxy, a neutron star might accrete enough to cause it to collapse within a period of time less than the age of the Universe. We calculate what value of the stable dark matter-nucleon cross section would cause this to occur for a large range of masses.