Electromagnetic cascade masquerade: a way to mimic $\gamma$--axion-like   particle mixing effects in blazar spectra
  Context. Most of the studies on extragalactic {\gamma}-ray propagation performed up to now only accounted for primary gamma-ray absorption and adiabatic losses ("absorption-only model"). However, there is growing evidence that this model is oversimplified and must be modified in some way. In particular, it was found that the intensity extrapolated from the optically-thin energy range of some blazar spectra is insufficient to explain the optically-thick part of these spectra. This effect was interpreted as an indication for {\gamma}-axion-like particle (ALP) oscillation. On the other hand, there are many hints that a secondary component from electromagnetic cascades initiated by primary {\gamma}-rays or nuclei may be observed in the spectra of some blazars. Aims. We study the impact of electromagnetic cascades from primary {\gamma}-rays or protons on the physical interpretation of blazar spectra obtained with imaging Cherenkov telescopes. Methods. We use the publicly-available code ELMAG to compute observable spectra of electromagnetic cascades from primary {\gamma}-rays. For the case of primary proton, we develop a simple, fast and reasonably accurate hybrid method to calculate the observable spectrum. We perform the fitting of the observed spectral energy distributions (SEDs) with various physical models: the absorption-only model, the "electromagnetic cascade model" (for the case of primary {\gamma}-rays), and several versions of the hadronic cascade model (for the case of primary proton). We distinguish the following species of hadronic cascade models: 1) "basic hadronic model", where it is assumed that the proton beam travels undisturbed by extragalactic magnetic field and that all observable {\gamma}-rays are produced by primary protons through photohadronic processes with subsequent development of electromagnetic cascades /abridged 
T.A. Dzhatdoev, E.V. Khalikov, A.P. Kircheva, A.A. Lyukshin
astro-ph.HE