Context. Most of the studies on extragalactic γ-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 γ-axion-like particle (ALP) oscillation. On the other hand, there are many hints that a secondary component from electromagnetic cascades initiated by primary γ-rays or nuclei may be observed in the spectra of some blazars. Aims. We study the impact of electromagnetic cascades from primary γ-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 γ-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 absorptiononly model, the "electromagnetic cascade model" (for the case of primary γ-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 γ-rays are produced by primary protons through photohadronic processes with subsequent development of electromagnetic cascades 2) "intermediate hadronic model", the same as the basic hadronic model, but the primary beam is terminated at some redshift z c 3) "modified hadronic model" that includes the contribution from primary (redshifted and partially absorbed) γ-rays. Results. Electromagnetic cascades show at least two very distinct regimes labeled by the energy of the primary γ-ray (E 0 ): the onegeneration regime for the case of E 0 <10 T eV and the universal regime for E 0 >100 T eV and redshift to the source z s >0.02. Spectral signatures of the observable spectrum for the case of the basic hadronic model, z s = 0.186 and low energy (E<200 GeV) are nearly the same as for purely electromagnetic cascade, but for E>200 GeV the spectrum is much harder for the case of the basic hadronic model. In the framework of the intermediate hadronic model, the observable spectrum depends only slightly on the primary proton energy, but it strongly depends on z c at E>500 GeV. As a rule, both electromagnetic and hadronic cascade models provide acceptable fits to the observed SEDs. We show that the best-fit model intensity in the multi-T eV region of the spectrum in the framework of the electromagnetic cascade model is typically greater than the one for the case of th...
We review the physics of intergalactic electromagnetic cascades in the presence of the extragalactic magnetic field (EGMF). Various regimes of intergalactic electromagnetic cascades are considered depending on the number of cascade generations, the value of the cascade electron deflection angle, and the relations between the EGMF coherence length, typical cascade γ-ray mean free path, and electron energy loss length. We also review contemporary constraints on the EGMF parameters and explore the sensitivity of various γ-ray instruments to the EGMF parameters. *
Most of the recent research on extragalactic γ -ray propagation focused on the study of the γ γ → e + e − absorption process ("absorption-only model"). Starting from a possible anomaly at very high energies (VHE, E > 100 GeV), we briefly review several existing deviations from this model. The exotic interpretation of the VHE anomaly is not supported by the recent works. On the other hand, the process of intergalactic electromagnetic cascade development naturally explains these effects. We discuss phenomenology of intergalactic cascades and the main spectral signatures of the electromagnetic cascade model. We also briefly consider the hadronic cascade model; it also may explain the data, but requires low strength of magnetic field around the source of primary protons or nuclei.
Observations of extragalactic sources in the high energy (HE, E>100 MeV) and very high energy (VHE, E>100 GeV) domains allow to search for axion-like particles (ALP) and constrain the extragalactic magnetic field (EGMF) parameters. Such studies have recently received much attention thanks to the advent of new instruments and the progress of the extragalactic background light (EBL) models. Observations of blazars indicate that an additional component from electromagnetic (EM) cascades contributes to the observed flux, allowing for a possibility that the EGMF strength in voids of the large scale structure is smaller than 1 fG on the characteristic spatial scale of 1 Mpc. We consider various extragalactic γ-ray propagation models with an emphasis on the "electromagnetic cascade model", which assumes that primary particles are γ-rays, and has the following spectral signatures: 1) a high-energy cutoff caused by the γγ → e + e − absorption process 2) an "ankle" formed by the intersection of the primary and cascade components 3) a possible low-energy "magnetic cutoff", 4) a possible low-energy "second ankle" at the second intersection of the primary and cascade components. The ankle may mimic the signature of the γ-ALP oscillation process. Finally, we consider various species of the "hadronic cascade model", in which primary particles are protons and nuclei. This model has a number of difficulties, but, nevertheless, is not excluded.
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