The time averaged TeV energy spectrum of MKN 501 of the extraordinary 1997 outburst as measured with the stereoscopic Cherenkov telescope system of HEGRA

During the several months of the outburst of Mkn 501 in 1997 the source has been monitored in TeV gamma -ray s with the HEGRA stereoscopic system of imaging atmospheric Cherenkov telescopes. Quite remarkably it turned out that the shapes of the daily gamma -ray energy spectra remained essentially stable throughout the entire state of high activity despite dramatic flux variations during this period. The derivation of a long term time-averaged energy spectrum, based on more than 38,000 detected TeV photons, is therefore physically meaningful. The unprecedented gamma -ray statistics combined with the 20% energy resolution of the instrument resulted in the first detection of gamma -rays from an extragalactic source well beyond 10 TeV, and the first high accuracy measurement of an exponential cutoff in the energy region above 5 TeV deeply into the exponential regime. From 500 GeV to 24 TeV the differential photon spectrum is well approximated by a power-law with an exponential cutoff: d N/d E=N_0 (E/1 TeV)(-alpha ) exp {(-E/E_0)}, with N_0=(10.8 +/-0.2_stat +/-2.1_sys) * 10(-11) cm(-2) s(-1) TeV(-1) , alpha =1.92 +/-0.03_stat +/-0.20_sys, and E_0=(6.2 +/-0.4_stat (-1.5 +2.9)_sys) TeV. We summarize the methods for the evaluation of the energy spectrum in a broad dynamical range which covers almost two energy decades, and study in detail the principal sources of systematic errors. We also discuss several important astrophysical implications of the observed result concerning the production and absorption mechanisms of gamma -ray s in the emitting jet and the modifications of the initial spectrum of TeV radiation due to its interaction with the diffuse extragalactic background radiation.