The jets of blazars are renowned for their multi-wavelength flares and rapid extreme variability; however, there are still some important unanswered questions about the physical processes responsible for these spectral and temporal changes in emissio
n properties. In this paper, we develop a time-dependent particle evolution model for the time-varying emission spectrum of blazars. In the model, we introduce time-dependent electric and magnetic fields, which consistently include the variability of relevant physical quantities in the transport equation. The evolution on the electron distribution is numerically solved from a generalized transport equation that contains the terms describing the electrostatic, first-order and second-order emph{Fermi} acceleration, escape of particles due to both advection and spatial diffusion, as well as energy losses due to the synchrotron emission and inverse-Compton scattering of both synchrotron and external ambient photon fields. We find that the light curve profiles of blazars are consistent with the particle spectral evolution resulting from time-dependent electric and magnetic fields, rather than the effects of the acceleration or the cooling processes. The proposed model is able to simultaneously account for the variability of both the energy spectrum and the light curve profile of the BL Lac object Mrk 421 with reasonable assumptions about the physical parameters. The results strongly indicate that the magnetic field evolution in the dissipated region of a blazar jet can account for the variabilities.
It is surprising to find a fact for migration in the peak positions of synchrotron spectra energy distribution component during in the activity epochs of Mrk 421, accompanying with an orphan flaring at the X-ray and GeV-TeV $gamma$-ray bands. A geome
tric interpretation and standard shock or stochastic acceleration models of blazar emission have difficulty reproducing these observed behaviours. The present paper introduces a linear acceleration by integrating the reconnection electric field into the particle transport model for the observed behaviours of Mrk 421. We note that the strong evidence for evolution of multi-wavelength spectral energy distribution characteristic by shifting the peak frequency, accompanying with an orphan flaring at the X-ray and GeV-TeV $gamma$-ray bands provides an important electrostatic acceleration diagnostic in blazar jet. Assuming suitable model parameters, we apply the results of the simulation to the 13-day flaring event in 2010 March of Mrk 421, concentrating on the evolution of multi-wavelength spectral energy distribution characteristic by shifting the peak frequency. It is clear that the ratio of the electric field and magnetic field strength plays an important role in temporal evolution of the peak frequency of synchrotron spectral energy distribution component. We suggest the electrostatic acceleration responsible for the evolution of multi-wavelength spectral energy distribution characteristic by shifting the peak frequency is reasonable. Based on the model results, we issue that the peak frequency of the synchrotron spectral energy distribution component may denote a temporary characteristic of blazars, rather than a permanent one.
There are still some important unanswered questions about the detailed particle acceleration and escape occurring during the quiescent epoches. As a result, the particle distribution that is adopted in the blazar quiescent spectral model have numerou
s unconstrained shapes. To help remedy this problem, we introduce a analytical particle transport model to reproduce quiescent broadband spectral energy distribution of blazar. In this model, the exact electron distribution is solved from a generalized transport equation that contains the terms describing first-order and secondary-order emph{Fermi} acceleration, escape of particle due to both the advection and spatial diffusion, energy losses due to synchrotron emission and inverse-Compton scattering of an assumed soft photon field. We suggest that the advection is a significant escape mechanism in blazar jet. We find that in our model the advection process tends to harden the particle distribution, which enhances the high energy components of resulting synchrotron and synchrotron self-Comptom spectrum from jet. Our model is able to roughly reproduce the observed spectra of extreme BL Lac object 1ES 0414+009 with reasonable assumptions about the physical parameters.
A model-dependent method is proposed to determine the location of the $gamma$-ray emitting region for a given flat spectrum radio quasar (FSRQ). In the model, the extra-relativistic electrons are injected at the base of the jet and non-thermal photon
s are produced by both synchrotron radiation and inverse-Comtpon (IC) scattering in the energy dissipation region. The target photons dominating inverse-Comtpon scattering originate from both synchrotron photons and external ambient photon fields, and the energy density of external radiation field is a function of the distance between the position of dissipation region and a central super-massive black hole, and their spectra are seen in the comoving frame. Moreover, the energy dissipation region could be determined by the model parameter through reproducing the $gamma$-ray spectra. Such a model is applied to reproduce the quasi-simultaneous multi-wavelength observed data for 36 FSRQs. In order to define the width of the broad-line region shell and dusty molecular torus shell, a simple numerical constraint is used to determine the outer boundary of the broad-line region and dusty molecular torus. Our results show that 1) the $gamma$-ray emitting regions are located at the range from 0.1 pc to 10 pc; 2) the $gamma$-ray emitting regions are located outside the broad-line regions and within the dusty molecular tori; and 3) the $gamma$-ray emitting region are located closer to the dusty molecular torus ranges than the broad-line regions. Therefore, it may concluded that a direct evidence for the emph{far site} scenario could be obtained on the basis of the model results.
