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.