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Bounds on self-interacting fermion dark matter from observations of old neutron stars

The existence of old neutron stars deeply constrains self-interacting fermion dark matter, which can form star-killing black holes. We quantify this constraint on dark matter-nucleon scattering, considering collapse scenarios that broaden bounds over intermediate masses. We then find the self- and co-annihilation rates necessary to lift these dark matter-nucleon scattering bounds. For Yukawa-coupled dark matter that fits dwarf galaxy halo profiles with a coupling $α= 10^{-1}-10^{-4}$, a scalar mediator mass $m_ϕ= 1-500$ MeV, and DM mass $m_X = 0.1-10^7$ GeV, we show that fermion dark matter is unconstrained if it self-annihilates at a rate greater than $10^{-40} ~ \rm{cm^3/s}$ or co-annihilates with baryons at a rate greater than $10^{-50} ~ \rm{cm^3/s}$.