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-annihilation and coannihilation rates necessary to lift these dark matter-nucleon scattering bounds. For Yukawa-coupled dark matter that fits dwarf galaxy halo profiles with a coupling $\alpha =10^{-1}–10^{-4}$, a scalar mediator mass $m_{\varphi }=1–500\mathrm{MeV}$, and dark matter mass $m_X=0.1–10^7\mathrm{GeV}$, we show that fermion dark matter is unconstrained if it self-annihilates at a rate greater than $10^{-40}{\mathrm{cm}}^3/\mathrm{s}$ or coannihilates with baryons at a rate greater than $10^{-50}{\mathrm{cm}}^3/\mathrm{s}$.

• Received 21 October 2013

DOI:https://doi.org/10.1103/PhysRevD.89.015010