  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).
