  Neutron stars serve as excellent next-generation thermal detectors of dark
matter, heated by the scattering and annihilation of dark matter accelerated to
relativistic speeds in their deep gravitational wells. However, the dynamics of
neutron star cores are uncertain, making it difficult at present to
unequivocally compute dark matter scattering in this region. On the other hand,
the physics of an outer layer of the neutron star, the crust, is more robustly
understood. We show that dark matter scattering solely with the low-density
crust still kinetically heats neutron stars to infrared temperatures detectable
by forthcoming telescopes. We find that for both spin-independent and
spin-dependent scattering on nucleons, the crust-only cross section sensitivity
is $10^{-43} - 10^{-41}$~cm$^2$ for dark matter masses of 100 MeV $-$ 1 PeV,
with the best sensitivity arising from dark matter scattering with a crust
constituent called nuclear pasta (including gnocchi, spaghetti, and lasagna
phases). For dark matter masses from 10 eV to 1 MeV, the sensitivity is
$10^{-39} - 10^{-34}$~cm$^2$, arising from exciting collective phonon modes in
a neutron superfluid in the inner crust. Furthermore, for any $s$-wave or
$p$-wave annihilating dark matter, we show that dark matter will efficiently
annihilate by thermalizing just with the neutron star crust, regardless of
whether the dark matter ever scatters with the neutron star core. This implies
efficient annihilation in neutron stars for any electroweakly interacting dark
matter with inelastic mass splittings of up to 200 MeV, including Higgsinos. We
conclude that neutron star crusts play a key role in dark matter scattering and
annihilation in neutron stars.
