Earthly probes of the smallest dark matter halos
  Dark matter kinetic decoupling involves elastic scattering of dark matter off
of leptons and quarks in the early universe, the same process relevant for
direct detection and for the capture rate of dark matter in celestial bodies;
the resulting size of the smallest dark matter collapsed structures should thus
correlate with quantities connected with direct detection rates and with the
flux of high-energy neutrinos from dark matter annihilation in the Sun or in
the Earth. In this paper we address this general question in the context of two
widely studied and paradigmatic weakly-interacting particle dark matter models:
the lightest neutralino of the minimal supersymmetric extension of the Standard
Model, and the lightest Kaluza-Klein particle of Universal Extra Dimensions
(UED). We argue and show that while the scalar neutralino-nucleon cross section
correlates poorly with the kinetic decoupling temperature, the spin-dependent
cross section exhibits a strong correlation in a wide range of models. In UED
models the correlation is present for both cross sections, and is
extraordinarily tight for the spin-dependent case. A strong correlation is also
found, for both models, for the flux of neutrinos from the Sun, especially for
fluxes large enough to be at potentially detectable levels. We provide analytic
guidance and formulae that illustrate our findings.
