Optically thick, nonlocal, inhomogeneous, stationary jet model for high-energy radiation from blazars: Application to Mrk 421

Department of Astrophysics, Faculty of Physics and Applied Informatics, University of Lodz, ul. Pomorska 149/153, 90-236 Lodz, Poland
e-mail: pgbanasinski@gmail.com; wlodzimierz.bednarek@uni.lodz.pl

Received: 16 May 2022
Accepted: 22 September 2022

Abstract

Context. There is an increasing number of observational evidence that very high energy γ-rays in radio-loud activ galactic nuclei are produced in the direct vicinity of a supermassive black hole (SMBH), close to the base of a relativistic jet. In the case of some blazars, the angle between the jet axis and the observer’s line of sight is smaller than the angular extent of the jet. γ-rays that are produced close to SMBH therefore have to propagate in the nonthermal radiation of the extended jet before reaching the observer. This γ-ray emission can be strongly absorbed in the extended jet radiation, producing a second generation of e^± pairs that loses energy mainly via the synchrotron process.

Aims. We developed a nonlocal, inhomogeneous, stationary jet model in order to describe the multiwavelength emission from blazars. With this advanced model, we investigated the impact of the extended jet radiation on the propagation of γ-rays that are ejected from the direct vicinity of SMBH toward an observer located within the solid angle of the jet. We determined the conditions under which γ-rays are absorbed in the jet radiation and explored the effect of this absorption process on the γ-ray spectra and on the hard X-ray emission observed from some blazars.

Methods. We first developed an inhomogeneous, stationary jet model in which the radiation that is produced nonlocally in the jet was taken into account when we calculated the nonthermal emission in the broad energy range. This emission serves as a target on which γ-rays, produced close to SMBH, can be absorbed. As a result, the cascade is initiated within the jet through inverse Compton and synchrotron processes.

Results. We show that this advanced inhomogeneous jet model can explain the multiwavelength spectrum of the BL Lac object Mrk 421 in a nonflaring state for reasonable parameters of the jet and the SMBH. Moreover, we argue that synchrotron emission from the secondary e^± pairs, which appear as a result of absorption of γ-rays that are produced close to the SMBH within the jet radiation, is consistent with the concave hard X-ray emission observed from Mrk 421.