Numerically Solving the Particle Kinetic Equation to Study the Effect of Non-Thermal Cooling on1 Particle Spectra in Relativistic Jets

Abstract

Blazars exhibit broadband non-thermal emission characterized by a double-hump Spectral Energy Distribution¹⁷(SED) attributed to Synchrotron and Synchrotron Self-Compton (SSC) processes (P. Padovani et al. 2017; G.18Risaliti & M. Elvis 2004). The high-energy component extends to Very High Energy (VHE) gamma-rays, where 19Scattering often occurs in the Klein-Nishina (KN) regime, steepening the observed spectrum. A critical challenge 20in interpreting these sources is their rapid variability; observations suggest cooling and injection timescales are often 21shorter than the light crossing time (R/c) of the emission region (M. Chiaberge & G. Ghisellini 1999). In this regime, 22the observed flux is a convolution of different evolutionary stages, rendering the instantaneous particle distribution 23N (γ, t) is insufficient to reproduce light curves without accounting for geometric delays. In this Note, In this work, I24numerically solve the kinetic equation for relativistic electrons subject to radiative losses and escape following modified 25Chang-Cooper scheme. I explore the spectral evolution under different injection scenarios and rigorously calculate the 26.resulting photon spectra. Finally, I simulate the effects of finite light travel time to explain the time lags observed.²⁷between different frequency bands