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Motivated by the hypothesis that dark matter self-interactions provide asolution to the small-scale structure formation problems, we investigate thepossibilities that the relic density of a self-interacting dark mattercandidate can proceed from the thermal freeze-out of annihilations intoStandard Model particles. We find that scalar and Majorana dark matter in themass range of $10-500$ MeV, coupled to a slightly heavier massive gauge boson,are the only possible candidates in agreement with multiple currentexperimental constraints. Here dark matter annihilations take place at a muchslower rate than the self-interactions simply because the interactionconnecting the Standard Model and the dark matter sectors is small. We alsodiscuss prospects of establishing or excluding these two scenarios in futureexperiments.

Can the relic density of self-interacting dark matter be due to annihilations into Standard Model particles?