A Novel Approach in Constraining Electron Spectra in Blazar Jets: The Case of Markarian 421

We report results from the observations of the well-studied TeV blazar Mrk 421 with the Swift and the Suzaku satellites in 2008 December. During the observation, Mrk 421 was found in a relatively low activity state, with the corresponding 2-10 keV flux of 3 x 10(-10) erg s(-1) cm(-2). For the purpose of robustly constraining the UV-to-X-ray emission continuum we selected only the data corresponding to truly simultaneous time intervals between Swift and Suzaku, allowing us to obtain a good-quality, broadband spectrum despite a modest length (0.6 ks) exposure. We analyzed the spectrum with the parametric forward-fitting SYNCHROTRON model implemented in XSPEC assuming two different representations of the underlying electron energy distribution, both well motivated by the current particle acceleration models: a power-law distribution above the minimum energy gamma(min) with an exponential cutoff at the maximum energy gamma(max), and a modified ultra-relativistic Maxwellian with an equilibrium energy gamma(eq). We found that the latter implies unlikely physical conditions within the blazar zone of Mrk 421. On the other hand, the exponentially moderated power-law electron distribution gives two possible sets of the model parameters: (1) flat spectrum dN'(e)/d gamma proportional to gamma(-1.91) with low minimum electron energy gamma(min) < 10(3), and (2) steep spectrum proportional to gamma(-2.77) with high minimum electron energy gamma(min) similar or equal to 2 x 10(4). We discuss different interpretations of both possibilities in the context of a diffusive acceleration of electrons at relativistic, sub- or superluminal shocks. We also comment on exactly how the gamma-ray data can be used to discriminate between the different proposed scenarios.