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 ∼1 TeV reported by the Whipple
Observatory in the case of a 1 day 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 which is allowed by
the homogeneous synchrotron self-Compton model for the case of no significant
photon-photon absorption in the source.Comment: 5 pages, 2 figures, LaTeX uses mn.sty, submitted to MNRA
