Asymmetric dark matter: residual annihilations and self-interactions

Dark matter (DM) coupled to light mediators has been invoked to resolve theputative discrepancies between collisionless cold DM and galactic structureobservations. However, $\gamma$-ray searches and the CMB strongly constrainsuch scenarios. To ease the tension, we consider asymmetric DM. We show that,contrary to the common lore, detectable annihilations occur even for largeasymmetries, and derive bounds from the CMB, $\gamma$-ray, neutrino andantiproton searches. We then identify the viable space for self-interacting DM.Direct detection does not exclude this scenario, but provides a way to test it.