Formation of the Electronic Spectrum in Relativistic Jets of Gamma-Ray Blazars

TL;DR

This paper develops a comprehensive theoretical framework for particle acceleration and transport in relativistic jets of gamma-ray blazars, emphasizing the importance of time-integrated electron distributions for spectral modeling.

Contribution

It introduces analytical solutions for particle-transport equations under various physical processes, enhancing the modeling of blazar emission spectra.

Findings

Analytical solutions for particle-transport equations in 11 cases.

Time-integrated electron distributions are crucial for modeling blazar spectra.

Theoretical framework for Fermi acceleration and turbulent processes in jets.

Abstract

We describe the theory of Fermi-type acceleration, including first-order Fermi acceleration at a parallel shock front and second-order Fermi acceleration in a test particle limit. Including the theory of the turbulent acceleration and the derivation of the general Fokker-Planck equation, we take into account the basic particle-transport equation and the Fokker-Planck equation with spatially homogeneous isotropic distribution. In the cases of some special physical processes, we construct the particle-transport equations, and compile the analytical or semi-analytical solutions in 11 different cases. Even though, traditionally, one of the electron energy distributions for these different cases can be used to reproduce the multi-wavelength emission of a blazar, due to very long integration times of high-energy observations, a time-integrated electron energy distribution should be introduced in approaches to modeling the multi-wavelength spectral energy distribution of blazars, especially in modeling the flaring state.