ar X iv : a st ro - p h / 99 10 46 0 v 1 2 6 O ct 1 99 9 Modeling the April 1997 flare of Mkn

The April 1997 giant flare of Mkn 501 is modelled by a stationary Synchrotron-Proton-Blazar model. Our derived model parameters are consistent with X-ray-to-TeV-data in the flare state and diffusive shock acceleration of e − and p in a Kolmogorov/Kraichnan turbulence sprectrum. While the emerging pair-synchrotron cascade spectra initiated by photons from π 0-decay and electrons from π ± → µ ± → e ±-decay turn out to be relatively featureless, µ ± and p synchrotron radiation and their cascade radiation produce a double-humped spectral energy distribution. For the present model we find p synchrotron radiation to dominate the TeV emission, while the contribution from the synchrotron radiation of the pairs, produced by the high energy hump, is only minor. With its giant outburst in 1997, emitting photons up to 24 TeV and 0.5 MeV in the γ-ray and X-ray bands, Mkn 501 has proved to be the most extreme TeV-blazar observed so far (e.g. Catanese et al 1997, Pian et al 1997, Aharonian et al 1999). In this paper, we consider the April 1997 flare of Mkn 501 in the light of a modified version of the Synchrotron Proton Blazar model (SPB) (Mannheim 1993), and present a preliminary model fit. In the model, shock accelerated protons (p) interact in the synchrotron photon field generated by the electrons (e −) co-accelerated at the same shock. This scenario may put constraints on the maximum achievable particle energies. The usual process considered for accelerating charged particles in the plasma jet is diffusive shock acceleration (see e.g. Drury 1983, Biermann & Strittmatter 1987). If the particle spectra are cut off due to synchrotron losses, the ratio of the maximum particle energies γ p,max /γ e,max can be derived by equating t acc,p /t acc,e = t syn,p /t syn,e , with t syn,p and t syn,e being the synchrotron loss time scales for p and e − , respectively. We find that for shocks of compression ratio 4 (see Mücke & Protheroe 1999 for a detailed derivation)