Testing the homogeneous synchrotron self-Compton model for gamma-ray production in Mrk 421

Based on the detected variability time-scales of X-ray and TeV gamma-ray emission, and the observed multiwavelength photon spectrum, of MrK 421 we place constraints on the allowed parameter space (magnetic field and Doppler factor of the emission region) for the homogeneous synchrotron self-Compton model. The spectra calculated for the allowed parameters are marginally consistent with the available spectral information above similar to 1 TeV reported by the Whipple Observatory in the case of a 1-d flare time-scale. However, for the recently reported very short duration flares varying on a time-scale of 15 min, the calculated spectra are significantly steeper, suggesting that the homogeneous synchrotron self-Compton model has problems in describing the relatively flat observed spectra extending above a few TeV. We determine the maximum ratio of TeV gamma-ray luminosity to X-ray luminosity during flaring that is allowed by the homogeneous synchrotron self-Compton model for the case of no significant photon-photon absorption in the source.