  If light sterile neutrinos exist and mix with the active neutrino flavors,
this mixing will affect the propagation of high-energy neutrinos from dark
matter annihilation in the Sun. In particular, new Mikheyev-Smirnov-Wolfenstein
resonances can occur, leading to almost complete conversion of some active
neutrino flavors into sterile states. We demonstrate how this can weaken
IceCube limits on neutrino capture and annihilation in the Sun and how
potential future conflicts between IceCube constraints and direct detection or
collider data might be resolved by invoking sterile neutrinos. We also point
out that, if the dark matter--nucleon scattering cross section and the allowed
annihilation channels are precisely measured in direct detection and collider
experiments in the future, IceCube can be used to constrain sterile neutrino
models using neutrinos from the dark matter annihilation.
