We entertain the exotic possibility that dark matter (DM) decays or annihilations taking place in our galaxy may produce a flux of relativistic very weakly-coupled bosons, axions or dark photons. We show that there exist several upper bounds for this flux on Earth assuming generic minimal requirements for DM, such as a lifetime longer than the age of the Universe or an annihilation rate that leaves unaffected the background evolution during matter domination. These bounds do not depend on the identity or the couplings of the bosons. We then show that this new flux cannot be large enough to explain the recent XENON1T excess, while assuming that the bosons couplings to the Standard Model are consistent with all current experimental and observational constraints. We also discuss a possible caveat to these bounds and a route to explain the excess.
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