Gamma-ray boxes from axion-mediated dark matter

We compute the gamma-ray output of axion-mediated dark matter and derive the corresponding constraints set by recent data. In such scenarios the dark matter candidate is a Dirac fermion that pair-annihilates into axions and/or scalars. Provided that the axion decays (at least partly) into photons, these models naturally give rise to a box-shaped gamma-ray spectrum that may present two distinct phenomenological behaviours: a narrow box, resembling a line at half the dark matter mass, or a wide box, spanning an extensive energy range up to the dark matter mass. Remarkably, we find that in both cases a sizable gamma-ray flux is predicted for a thermal relic without fine-tuning the model parameters nor invoking boost factors. This large output is in line with recent Fermi-LAT observations towards the galactic centre region and is on the verge of being excluded. We then make use of the Fermi-LAT and H.E.S.S. data to derive robust, model-independent upper limits on the dark matter annihilation cross section for the narrow and wide box scenarios. H.E.S.S. constraints, in particular, turn out to match the ones from Fermi-LAT at hundreds of GeV and extend to multi-TeV masses. Future ?erenkov telescopes will likely probe gamma-ray boxes from thermal dark matter relics in the whole multi-TeV range, a region hardly accessible to direct detection, collider searches and other indirect detection strategies.