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We study the capture, annihilation and evaporation of dark matter (DM) insidethe Sun. It has been shown that the DM self-interaction can increase the DMnumber inside the Sun. We demonstrate that this enhancement becomes moresignificant in the regime of small DM mass, given a fixed DM self-interactioncross section. This leads to the enhancement of neutrino flux from DMannihilation. On the other hand, for DM mass as low as as a few GeVs, not onlythe DM-nuclei scatterings can cause the DM evaporation, DM self-interactionalso provides non-negligible contributions to this effect. Consequently, thecritical mass for DM evaporation (typically 3 ~ 4 GeV without the DMself-interaction) can be slightly increased. We discuss the prospect ofdetecting DM self-interaction in IceCube- PINGU using the annihilation channels$\chi\chi\rightarrow\nu\bar{\nu},\:\tau^{-}\tau^{+}$ as examples. The PINGUsensitivities to DM self-interaction cross section $\sigma_{\chi\chi}$ areestimated for track and cascade events.

The dark matter self-interaction and its impact on the critical mass for dark matter evaporations inside the sun