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Due to shielding, direct detection experiments are in some cases insensitiveto dark matter candidates with very large scattering cross sections withnucleons. In this paper, we revisit this class of models, and derive a simpleanalytic criterion for conservative but robust direct detection limits. Whilelarge spin-independent cross sections seem to be ruled out, we identifypotentially viable parameter space for dark matter with a spin-dependent crosssection with nucleons in the range of $10^{-27} {\rm cm}^2 < \sigma_{{\rmDM}-p} < 10^{-24} \, {\rm cm}^{2}$. With these parameters, cosmic-rayscattering with dark matter in the extended halo of the Milky Way couldgenerate a novel and distinctive gamma-ray signal at high galactic latitudes.Such a signal could be observable by Fermi or future space-based gamma-raytelescopes.

Robust Constraints and Novel Gamma-Ray Signatures of Dark Matter That Interacts Strongly With Nucleons