  We study the kinetic cooling (heating) of old neutron stars due to coherent
scattering with relic neutrinos (sterile neutrino dark matter) via Standard
Model neutral-current interactions. We take into account several important
physical effects, such as gravitational clustering, coherent enhancement,
neutron degeneracy and Pauli blocking. We find that the anomalous cooling of
nearby neutron stars due to relic neutrino scattering might actually be
observable by current and future telescopes operating in the optical to
near-infrared frequency band, such as the James Webb Space Telescope (JWST),
provided there is a large local relic overdensity that is still allowed.
Similarly, the anomalous heating of neutron stars due to coherent scattering
with keV-scale sterile neutrino dark matter, could also be observed by JWST or
future telescopes, which would probe hitherto unexplored parameter space in the
sterile neutrino mass-mixing plane.
