Preprint number: CP3-Origins-2011-41 and DIAS-2011-36
We impose new severe constraints on the self-interactions of fermionic asymmetric dark matter based on observations of nearby old neutron stars. WIMP self-interactions mediated by Yukawa- type interactions can lower significantly the number of WIMPs necessary for gravitational collapse of the WIMP population accumulated in a neutron star. Even nearby neutron stars located at regions of low dark matter density can accrete sufficient number of WIMPs that can potentially collapse, form a mini black hole, and destroy the host star. Based on this, we derive constraints on the WIMP self-interactions which in some cases are by several orders of magnitude stricter than the ones from the bullet cluster (which are currently considered the most stringent).