Reconciling hints on axion-like-particles from high-energy gamma rays with stellar bounds

It has been recently claimed by two different groups that the spectral modulation observed in gamma rays from Galactic pulsars and supernova remnants can be due to conversion of photons into ultra-light axion-like-particles (ALPs) in large-scale Galactic magnetic fields. While we show the required best-fit photon-ALP coupling, $g_{a\gamma} \sim 2 \times 10^{-10}$ GeV${}^{-1}$, to be consistent with constraints from observations of photon-ALPs mixing in vacuum, this is in conflict with other bounds, specifically from the CAST solar axion limit, from the helium-burning lifetime in globular clusters, and from the non-observations of gamma rays in coincidence with SN 1987A. In order to reconcile these different results, we propose that environmental effects in matter would suppress the ALP production in dense astrophysical plasma, allowing to relax previous bounds and make them compatible with photon-ALP conversions in the low-density Galactic medium. If this explanation is correct, the claimed ALP signal would be on the reach of next-generations laboratory experiments such as ALPS II.
Comment: v2: major corrections to match the published version. 28 pages, 14 figures