Dark kinetic heating of neutron stars from contact interactions with relativistic targets

Dark matter can capture in neutron stars from scattering off ultrarelativistic electrons. We present a method to calculate the capture rate on degenerate targets with ultrarelativistic 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 nonrelativistic 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-six for spin-0 and spin-1/2 dark matter interactions with relativistic as well as nonrelativistic Standard Model fermions. Highlights of this program in the case of vector mediated interactions are presented in a companion article [Joglekar et al., Phys. Lett. B 809, 135767 (2020)]. 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.