Abstract
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.
Highlights
Astronomical data unambiguously establishes the existence of dark matter
We present the general behavior of dark matter capture on relativistic targets
A new result in this paper is a classification of the kinematic regimes for dark matter capture in compact objects according to the target and dark matter masses relative to the target Fermi momentum
Summary
Astronomical data unambiguously establishes the existence of dark matter. Interactions between dark matter and visible matter are predicted by many models to set the cosmological abundance of dark matter. The discovery reach of such an observation is favorable compared to terrestrial direct detection experiments [1,2] Recent efforts in this program focus on dark matter that interacts primarily with leptons [9]. Work on this subject assumes scattering with nonrelativistic targets that are at rest in the neutron star frame [10,11]. This study opens a new frontier for the capture of dark matter on neutron stars, a subject that began 30 years ago in studies of black hole formation [12,13]. Some of these are known results that may not be obvious, and others are technical calculations that confirm the qualitative discussions in the paper
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