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

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 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 ~ 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 $\chi \chi \to \nu \bar{\nu },{\tau }^{-}{\tau }^{+}$ as examples. The PINGU sensitivities to DM self-interaction cross section ${\sigma }_{\chi \chi }$ are estimated for track and cascade events.