  There exists a growing evidence for the anomalous transparency of the
Universe for energetic gamma rays. Popular explanations include conversion of
photons into hypothetical axion-like particles (ALPs) and back in astrophysical
magnetic fields. Two distinctive scenarios of this conversion have been put
forward: either it happens in the (host galaxy of the) gamma-ray source and in
the Milky Way, or the photon-ALP oscillations take place in the intergalactic
magnetic fields all along the way between the source and the observer. Here we
point out that, given recent astrophysical constraints on ALPs and on
intergalactic magnetic fields, these two mechanisms imply very different ALP
masses and couplings. Therefore, confirmation of the anomalies and
identification of one of the scenarios would mean cornering of ALP parameters
to a particular narrow region. We discuss approaches to distinguish between the
two mechanisms and present some preliminary indications in favour of the
galactic scenario.
