# Time dependent spectral modeling of Markarian 421 during a violent outburst in 2010

## TL;DR

This study models the spectral energy distribution of blazar Mrk 421 during a 2010 outburst, revealing how physical parameters like particle energy, magnetic field, and bulk motion evolve during the flare.

## Contribution

It introduces a time-dependent multi-zone leptonic jet model with radiation feedback to explain spectral evolution during a blazar outburst.

## Key findings

- Spectral hardening correlates with increased flux in X-ray and VHE gamma-ray bands.
- The model successfully reproduces the observed spectral states and light curves.
- Higher bulk kinetic energy and harder particle populations are associated with high-flux states.

## Abstract

We present the results of extensive modeling of the spectral energy distributions (SEDs) of the closest blazar (z=0.031) Markarian 421 (Mrk 421) during a giant outburst in February 2010. The source underwent rapid flux variations in both X-rays and very high energy (VHE) gamma-rays as it evolved from a low-flux state on 2010 February 13-15 to a high-flux state on 2010 February 17. During this period, the source exhibited significant spectral hardening from X-rays to VHE gamma-rays while exhibiting a "harder when brighter" behavior in these energy bands. We reproduce the broadband SED using a time-dependent multi-zone leptonic jet model with radiation feedback. We find that an injection of the leptonic particle population with a single power-law energy distribution at shock fronts followed by energy losses in an inhomogeneous emission region is suitable for explaining the evolution of Mrk 421 from low- to high-flux state in February 2010. The spectral states are successfully reproduced by a combination of a few key physical parameters, such as the maximum $\&$ minimum cutoffs and power-law slope of the electron injection energies, magnetic field strength, and bulk Lorentz factor of the emission region. The simulated light curves and spectral evolution of Mrk 421 during this period imply an almost linear correlation between X-ray flux at 1-10 keV energies and VHE gamma-ray flux above 200 GeV, as has been previously exhibited by this source. Through this study, a general trend that has emerged for the role of physical parameters is that, as the flare evolves from a low- to a high-flux state, higher bulk kinetic energy is injected into the system with a harder particle population and a lower magnetic field strength.