Variations of the TeV energy spectrum at different flux levels of Mkn 421 observed with the HEGRA system of Cherenkov telescopes

The nearby BL Lacertae (BL Lac) object Markarian~421 (Mkn~421) at a red shift z=0.031 was observed to undergo strong TeV Gamma-ray outbursts in the observational periods from December 1999 until May 2001. The time averaged energy spectrum is well described by a power law with an exponential cut-off energy at 3.6(+0.4-0.3)_{stat}(+0.9-0.8)_{sys} TeV. The energy spectra derived for different average flux levels ranging from 0.5 to 10 * 10^{-11}ph/cm**2/s follow a clear correlation of photon index and flux level. Generally, the energy spectra are harder for high flux levels. From January to April 2001 Mkn~421 showed rapid variability (doubling time as short as 20 minutes), accompanied with a spectral hardening with increasing flux level within individual nights. For two successive nights (MJD 51989-51991, March 21-23,2001), this correlation of spectral hardness and change in flux has been observed within a few hours. The cut-off energy for the Mkn~421 TeV spectrum remains within the errors constant for the different flux levels and differs by 2.6+/-0.6_stat+/-0.6_sys TeV from the value determined for Mkn~501. This indicates that the observed exponential cut-off in the energy spectrum of Mkn~421 is not solely caused by absorption of multi-TeV photons by pair-production processes with photons of the extragalactic near/mid infrared background radiation.