For the high-frequency peaked BL Lac object Mrk 421 we study the variation of the spectral energy distribution (SED) as a function of source activity, from quiescent to active. We use a fully automatized chi-squared minimization procedure, instead of the "eyeball" procedure more commonly used in the literature, to model nine SED datasets with a one-zone Synchrotron-Self-Compton (SSC) model and examine how the model parameters vary with source activity. The latter issue can finally be addressed now, because simultaneous broad-band SEDs (spanning from optical to VHE photon energies) have finally become available. Our results suggest that in Mrk 421 the magnetic field decreases with source activity, whereas the electron spectrum's break energy and the Doppler factor increase -- the other SSC parameters turn out to be uncorrelated with source activity. In the SSC framework these results are interpreted in a picture where the synchrotron power and peak frequency remain constant with varying source activity, through a combination of decreasing magnetic field and increasing number density of electrons below the break energy: since this leads to an increased electron-photon scattering efficiency, the resulting Compton power increases, and so does the total (= synchrotron plus Compton) emission.Comment: Accepted for publication in Astrophysical Journal; 23 pages, 3 figures, 2 table
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