Establishing a particle distribution for multi-wavelength emission from BL Lac objects

TL;DR

This paper proposes a new particle distribution model for electrons in BL Lac objects' jets, successfully reproducing their broadband spectra by considering shock acceleration and downstream flow dynamics.

Contribution

It introduces a novel particle distribution for downstream electrons in BL Lac jets, accounting for shock acceleration and boundary conditions to match observed spectra.

Findings

The model reproduces the broadband spectrum of Mrk 421.

Electrons with higher energies dominate the emission.

Four cases of downstream particle distributions are identified.

Abstract

Electrons are accelerated at the shock wave diffuse and advect outward, and subsequently drift away into the emitting region of the jet that is located in the downstream flow from the plane shock. The current work considers the acceleration of the electrons in the shock front. Assuming a proper boundary condition at the interface between the shock and the downstream zones, a novel particle distribution in the downstream flow is proposed in this work to reproduce the broadband spectral energy distribution of BL Lac objects. We find that (1) we can obtain the particle distribution downstream of the shock wave in four cases; (2) electrons with higher energy ($\gamma>\gamma_{0}$) dominate the emission spectrum; (3) the distinctly important physical parameters assumed in our model can reasonably reproduce the multi-wavelength spectrum of the high-synchrotron-peaked BL Lac object Markarian 421 (Mrk 421).