An expanding one-zone model for studying blazars emission

Context.Blazars, a sub-category of Active Galactic Nuclei, are characterized by their non-thermal variable emission. This emission extends over the whole electromagnetic spectrum and is a consequence of particle acceleration inside their relativistic jets. However, especially the relation of radio emission to that at higher frequencies remains an open question. Aims. Observations of blazar emission show that the location of radio might be very different from the one where the rest of the spectrum is produced and often requires separate modeling. We aim to produce both emissions within the context of one model. Methods. We construct a self-consistent one-zone expanding leptonic model for studying the connection between the radio emission and the emission at higher frequencies and we apply it to the flaring states of blazars. Assuming an accelerating episode as the source moves down the jet and expands, we numerically study the electron evolution as they lose energy due to adiabatic expansion and synchrotron/inverse Compton radiation. Results. We find that high-frequency radiation mimics the electron injection and is mainly produced close to the acceleration site where cooling is strong. In contrast, the radio emission is produced further down the jet when the emitting region has become optically thin to synchrotron self-absorption due to expansion. We present briefly the role of the initial parameters, such as the magnetic field strength, the electron luminosity and expansion velocity, on the localization of the radio emission site. We show that the expanding one-zone model is inherently different from the non-expanding one and, in addition, it requires more parameters. For example, we apply our approach to the observational data of a Mrk 421 $\gamma$-ray - radio flare observed in 2013.