Probing Dark Matter Self-Interaction in the Sun with IceCube-PINGU

We study the capture, annihilation and evaporation of dark matter (DM) inside the Sun. It has been shown that the DM self-interaction can increase the DM number inside the Sun. We demonstrate that this enhancement becomes more significant in the regime of small DM mass, given a fixed DM self-interaction cross section. This leads to the enhancement of neutrino flux from DM annihilation. On the other hand, for DM mass as low as a few GeVs, not only the DM-nuclei scatterings can cause the DM evaporation, DM self-interaction also provides non-negligible contributions to this effect. Consequently, the critical mass for DM evaporation (typically 3 $\sim$ 4 GeV without the DM self-interaction) can be slightly increased. We discuss the prospect of detecting DM self-interaction in IceCube-PINGU using the annihilation channels $\chi\chi \rightarrow \tau^{+}\tau^{-}, \nu\bar{\nu}$ as examples. The PINGU sensitivities to DM self-interaction cross section $\sigma_{\chi\chi}$ are estimated for track and cascade events.