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Self-interacting dark matter (SIDM) naturally gives rise to a coredisothermal density profile, which is favored in observations of many dwarfgalaxies. The dark matter distribution in the presence of a central black holein an isothermal halo develops a density spike with a power law of $r^{-7/4}$,which is shallower than $r^{-7/3}$ as expected for collisionless dark matter(CDM). Thus, indirect detection constraints on dark matter annihilations fromthe density spike could be relaxed in SIDM. Taking the most dense satellitegalaxy of the Milky Way Draco as an example, we derive upper limits on theannihilation cross section and the black hole mass for both SIDM and CDM halos.For the former case, Draco could host an intermediate mass black hole even ifdark matter is composed of thermal relics. We further explore the constraintsfrom the Milky Way and M87, which host supermassive black holes, and show theupper limits on the annihilation cross section are significantly weakened inSIDM. Our results also indicate that the Event Horizon Telescope could providea unique test of SIDM spikes.

Density spikes near black holes in self-interacting dark matter halos and indirect detection constraints