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 -rays with the HEGRA stereoscopic system of imaging atmospheric Cherenkov telescopes. Quite remarkably it turned out that the shapes of the daily -ray energy spectra remained essentially stable throughout the entire state of high activity despite dra- matic 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 meaning- ful. The unprecedented -ray statistics combined with the 20% energy resolution of the instrument resulted in the first detec- tion of -rays from an extragalactic source well beyond 10 TeV, and the first high accuracy measurement of an exponential cut- off in the energy region above 5 TeV deeply into the expo- nential regime. From 500 GeV to 24 TeV the differential pho- ton spectrum is well approximated by a power-law with an ex- ponential cutoff: dN=dE = N0 (E=1TeV) exp( E=E0), with N0 = (10:8 0:2stat 2:1sys) 10 11 cm 2 s 1 TeV 1 , =1 :92 0:03stat 0:20sys, and E0 =( 6:2 0:4stat( 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-rays in the emitting jet and the modifications of the initial spectrum of TeV radiation due to its interaction with the diffuse extragalactic background radiation.