The intrinsic spectra of some distant blazars known as “extreme TeV blazars” have shown a hint at an anomalous hardening in the TeV energy region. Several extragalactic propagation models have been proposed to explain this possible excess transparency of the Universe to gamma-rays starting from a model which assumes the existence of so-called axion-like particles (ALPs) and the new process of gamma-ALP oscillations. Alternative models suppose that some of the observable gamma-rays are produced in the intergalactic cascades. This work focuses on investigating the spectral and angular features of one of the cascade models, the Intergalactic Hadronic Cascade Model (IHCM) in the contemporary astrophysical models of Extragalactic Magnetic Field (EGMF). For IHCM, EGMF largely determines the deflection of primary cosmic rays and electrons of intergalactic cascades and, thus, is of vital importance. Contemporary Hackstein models are considered in this paper and compared to the model of Dolag. The models assumed are based on simulations of the local part of large-scale structure of the Universe and differ in the assumptions for the seed field. This work provides spectral energy distributions (SEDs) and angular extensions of two extreme TeV blazars, 1ES 0229+200 and 1ES 0414+009. It is demonstrated that observable SEDs inside a typical point spread function of imaging atmospheric Cherenkov telescopes (IACTs) for IHCM would exhibit a characteristic high-energy attenuation compared to the ones obtained in hadronic models that do not consider EGMF, which makes it possible to distinguish among these models. At the same time, the spectra for IHCM models would have longer high energy tails than some available spectra for the ALP models and the universal spectra for the Electromagnetic Cascade Model (ECM). The analysis of the IHCM observable angular extensions shows that the sources would likely be identified by most IACTs not as point sources but rather as extended ones. These spectra could later be compared with future observation data of such instruments as Cherenkov Telescope Array (CTA) and LHAASO.
Gamma-Ray Scattering from Point Sources by Infinite Plane Surfaces
