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Stochastic conversions of TeV photons into axion-like particles in extragalactic magnetic fields

Very-high energy photons emitted by distant cosmic sources are absorbed on the extragalactic background light (EBL) during their propagation. This effect can be characterized in terms of a photon transfer function at Earth. The presence of extragalactic magnetic fields could also induce conversions between very high-energy photons and hypothetical axion-like particles (ALPs). The turbulent structure of the extragalactic magnetic fields would produce a stochastic behaviour in these conversions, leading to a statistical distribution of the photon transfer functions for the different realizations of the random magnetic fields. To characterize this effect, we derive new equations to calculate the mean and the variance of this distribution. We find that, in presence of ALP conversions, the photon transfer functions on different lines of sight could have relevant deviations with respect to the mean value, producing both an enhancement or a suppression in the observable photon flux with respect to the expectations with only absorption. As a consequence, the most striking signature of the mixing with ALPs would be a reconstructed EBL density from TeV photon observations which appears to vary over different directions of the sky: consistent with standard expectations in some regions, but inconsistent in others.