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

Dark matter can capture in neutron stars from scattering off ultra-relativistic electrons. We present a method to calculate the capture rate on degenerate targets with ultra-relativistic momenta in a compact astronomical object. Our treatment accounts for the target momentum and the Fermi degeneracy of the system. We derive scaling relations for scattering with relativistic targets and confirm consistency with the non-relativistic limit and Lorentz invariance. The potential observation of kinetic heating of neutron stars has a larger discovery reach for dark matter-lepton interactions than conventional terrestrial direct detection experiments. We map this reach onto a set of bosonic and fermionic effective contact interactions between dark matter and leptons as well as nucleons. We show the results for the contact operators up to dimension 6 for spin-0 and spin-1/2 dark matter interactions with relativistic as well as non-relativistic Standard Model fermions. Highlights of this program in the case of vector mediated interactions are presented in a companion letter [1]. Our method is generalizable to dark matter scattering in any degenerate medium where the Pauli exclusion principle leads to relativistic targets with a constrained phase space for scattering.