X-ray and gamma-ray variability of Mrk 421

TL;DR

This paper models the energy spectra and variability of flares in Mrk 421 using a time-dependent one-zone synchrotron self-Compton model, comparing different electron diffusion regimes to match observed data.

Contribution

It introduces a detailed time-dependent model for Mrk 421's flares, analyzing electron acceleration and photon production with different diffusion assumptions.

Findings

Hard photon spectra result from Bohm diffusion.

Hard sphere approximation better reproduces observed flare properties.

Model successfully fits pre-flare and flare spectra.

Abstract

We present an ordinary case in the momentum diffusion equation for the electron spectrum evolution and investigate the energy spectra and time dependent properties of flare in Mrk 421 in the frame of a time-dependent one-zone synchrotron self-Compton model. In this model, electrons are accelerated to extra-relativistic energy through the strong magnetic turbulence and evolve with time, and non-thermal photons are produced by both synchrotron and inverse Comtpon scattering off synchrotron photons. Moreover, non-thermal photons during a pre-flare are produced by the relativistic electrons in the steady state and those during a flare are produced by the electrons whose injection rate is changed during some time interval. We apply the model to the energy spectra and time-dependent properties of flares in Mrk 421 by reproducing the pre-burst spectrum of the source and varying the injection rate in the Bohm diffusion (q=1) and the hard sphere approximation (q=2) case, respectively. Our results show that Bohm diffusion case leads to hard photon spectra, and hard sphere case approximation seems to reproduce the energy spectra and the time dependent properties of flare still better.