  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.
