Swift observations of the very intense flaring activity of Mrk 421 during 2006. I. Phenomenological picture of electron acceleration and predictions for MeV/GeV emission

Aims. We present the results of a deep spectral analysis of all Swift observations of Mrk 421 between April 2006 and July 2006, when it reached its highest X-ray flux recorded until the end of 2006. The peak flux was about 85 milli-Crab in the 2.0-10.0 keV band, and the peak energy (E(p)) of the spectral energy distribution ( SED) was often at energies higher than 10 keV. We study trends between the spectral parameters, and the physical insights the parameters provide into the underlying acceleration and emission mechanisms. Methods. We performed a spectral analysis of Swift observations to investigate trends between the spectral parameters. We searched for acceleration and energetic features phenomenologically linked to the SSC model parameters, by predicting their effects in the gamma-ray band, and in particular, the spectral shape expected in the Fermi Gamma-ray Space Telescope-LAT band. Results. We confirm that the X-ray spectrum is described well by a log-parabolic distribution close to E(p), that the peak flux of the SED (S(p)) is correlated with E(p), and that E(p) is anti-correlated with the curvature parameter (b). The spectral evolution in the Hardness-ratio-flux plane shows both clockwise and counter-clockwise patterns. During the most energetic flares, the UV-to-soft-X-ray spectral shape requires an electron distribution spectral index of s similar or equal to 2.3. Conclusions. We demonstrate that the UV-to-X-ray emission from Mrk 421 is probably generated by a population of electrons that is actually curved, and has a low energy power-law tail. The observed spectral curvature is consistent with both stochastic acceleration or energy-dependent acceleration probability mechanisms, whereas the power-law slope of XRT-UVOT data is close to that inferred from the GRBs X-ray afterglow and in agreement with the universal first-order relativistic shock acceleration models. This scenario implies that magnetic turbulence may play a twofold role: spatial diffusion relevant to the first order process and momentum diffusion relevant to the second order process.