Time-dependent modelling of the Markarian 501 X-ray and TeV gamma-ray data taken during 1997 March and April

If the high-energy emission from TeV blazars is produced by the Synchrotron Self-Compton (SSC) mechanism, then simultaneous X- ray and gamma-ray observations of these objects are a powerful probe of the electron (and positron) populations responsible for this emission. Understanding the emitting particle distributions and their temporal evolution in turn allows us to probe physical conditions in the inner blazar jet and test, for example, various acceleration scenarios. Furthermore, by constraining the SSC model parameters, such observations enable us to predict the intrinsic (unabsorbed) gamma-ray energy spectra of these sources, a major uncertainty in current attempts to use gamma-ray observations to constrain the intensity of the Diffuse Extragalactic Background Radiation (DEBRA) at optical/infrared wavelengths. As a next step in testing the SSC model and as a demonstration of the potential power of coordinated X-ray and gamma-ray observations, we model in detail the X-ray and gamma-ray light curves of the TeV blazar Mrk 501 during its 1997 April-May outburst with a time- dependent SSC model. Extensive, quasi-simultaneous X-ray and gamma-ray coverage exists for this period. We discuss and explore quantitatively several of the flare scenarios presented in the literature. We show that simple two-component models (with a soft, steady X-ray component plus a variable SSC component) involving substantial pre-acceleration of electrons to Lorentz factors on the order of gamma(min) = 10(5) describe the data train surprisingly well. All considered models imply an emission region that is strongly out of equipartition and low radiative efficiencies (ratio between kinetic jet luminosity and comoving radiative luminosity) of 1 per-mill and less. Degeneracy in both, model variant and jet parameters, prevents us from using the time-resolved SSC calculations to tighten substantially the constraints on the amount of extragalactic gamma-ray extinction by the DEBRA in the relevant 0.5-50 mum wavelength range, compared with earlier work