Probing Velocity Dependent Self-Interacting Dark Matter with Neutrino
  Telescopes
  Self-interacting dark matter models constitute an attractive solution to
problems in structure formation on small scales. A simple realization of these
models considers the dark force mediated by a light particle which can couple
to the Standard Model through mixings with the photon or the $Z$ boson. Within
this scenario we investigate the sensitivity of the IceCube-DeepCore and PINGU
neutrino telescopes to the associated muon neutrino flux produced by dark
matter annihilations in the Sun. Despite the model's simplicity, several
effects naturally appear: momentum suppressed capture by nuclei, velocity
dependent dark matter self-capture, Sommerfeld enhanced annihilation, as well
as the enhancement on the neutrino flux due to mediator late decays. Taking all
these effects into account, we find that most of the model relevant parameter
space can be tested by the three years of data already collected by the
IceCube-DeepCore. We show that indirect detection through neutrinos can compete
with the strong existing limits from direct detection experiments, specially in
the case of isospin violation.
