An explanation about the flat radio spectrum for Mrk 421

It is well known that the flat radio spectrum is a common property in the spectral energy distribution of blazars. Although the one-zone leptonic models are generally successful in explaining the multi-wave band emission, they are problematic in reproducing the radio spectrum. In the study of Mrk 421, one-zone models suggest that in order to avoid overproducing the radio flux, the minimum electron Lorentz factor should be larger than a few hundred at least, even considering the synchrotron self-absorption effect. This result suggests that the model predicted spectral index in the radio band of Mrk 421 should be -1/3. On the basis of this result, by assuming there is a neglected region that will also contribute the radio emission and its electron energy index is naturally originate from the simplest first-order Fermi acceleration mechanism, we can get a superimposed flat radio spectrum. In this paper, a two-zone model is proposed to reproduce the quiescent state spectral energy distribution of Mrk 421. In addition to taking into account the emission from a conventional radiation zone, we further consider the emission from the acceleration zone in which particles are accelerated at a shock front. With the present model, our fitting result suggests that the low frequency flat radio spectrum of Mrk 421 might be explained as a superposition of the synchrotron emission from acceleration zone and radiation zone.