On detecting oscillations of gamma rays into axion-like particles in turbulent and coherent magnetic fields

Background radiation fields pervade the Universe, and above a certain energy any $\gamma$-ray flux emitted by an extragalactic source should be attenuated due to $e^{+}{e}^{-}$ pair production. The opacity could be alleviated if photons oscillated into hypothetical axion-like particles (ALPs) in ambient magnetic fields, leading to a $\gamma$-ray excess especially at high optical depths that could be detected with imaging air Cherenkov telescopes (IACTs). Here, we introduce a method to search for such a signal in $\gamma$-ray data and to estimate sensitivities for future observations. Different magnetic fields close to the $\gamma$-ray source are taken into account in which photons can convert into ALPs that then propagate unimpeded over cosmological distances until they re-convert in the magnetic field of the Milky Way. Specifically, we consider the coherent field at parsec scales in a blazar jet as well as the turbulent field inside a galaxy cluster. For the latter, we explicitly derive the transversal components of a magnetic field with gaussian turbulence which are responsible for the photon-ALP mixing. To illustrate the method, we apply it to a mock IACT array with characteristics similar to the Cherenkov Telescope Array and investigate the dependence of the sensitivity to detect a $\gamma$-ray excess on the magnetic-field parameters.