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Dark matter can capture in neutron stars from scattering offultra-relativistic electrons. We present a method to calculate the capture rateon degenerate targets with ultra-relativistic momenta in a compact astronomicalobject. Our treatment accounts for the target momentum and the Fermi degeneracyof the system. We derive scaling relations for scattering with relativistictargets and confirm consistency with the non-relativistic limit and Lorentzinvariance. The potential observation of kinetic heating of neutron stars has alarger discovery reach for dark matter-lepton interactions than conventionalterrestrial direct detection experiments. We map this reach onto a set ofbosonic and fermionic effective contact interactions between dark matter andleptons as well as nucleons. We show the results for the contact operators upto dimension 6 for spin-0 and spin-1/2 dark matter interactions withrelativistic as well as non-relativistic Standard Model fermions. Highlights ofthis program in the case of vector mediated interactions are presented in acompanion letter [1]. Our method is generalizable to dark matter scattering inany degenerate medium where the Pauli exclusion principle leads to relativistictargets with a constrained phase space for scattering.

Dark Kinetic Heating of Neutron Stars from Contact Interactions with Relativistic Targets