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H. Krawczynski, F.A. Aharonian (Max-Planck-Institut f\"ur Kernphysik, Heidelberg, Germany), P. Coppi, T. Maccarone (Yale University, New Haven, US)
During 1997, the BL Lac object Mkn 501 was in an exceptionally bright state. Flares were observed with flux amplitudes at 1 TeV of about 10 Crab units. During 6 months, the source was monitored in the TeV energy range on a regular basis by several Cherenkov telescope installations in the Northern Hemisphere, especially by the HEGRA stereoscopic Cherenkov telescope system. The high activity of the source and the signal to noise ratio achieved with the HEGRA system, made it possible to determine diurnal differential spectra with reasonable statistics for more than 60 individual nights. For several nights simultaneous and nearly simultaneous data was taken in the keV energy range with the RXTE, Beppo Sax and OSSE instruments. Based on detailed modeling of the spectral and temporal characteristics of the X-ray and TeV data, we derive constraints on the most important jet parameters and attempt to determine the intrinsic TeV \gamma-ray spectra. The comparison of the intrinsic TeV spectra with the observed ones over many nights gives us an estimate of the intergalactic absorption caused by gamma-ray pair production on diffuse background radiation (in the wavelength region ~1-60\mu). In this contribution we focus on the various uncertainties that enter this estimate and suggest ways to improve it via future observations.
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