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 flux level F(E > 1 TeV) in the 1999/2000 season was (1.43 +/- 0.04) x 10(-11) ph cm(-2) s(-1), whereas in the 2000/2001 season the average integral flux increased to (4.19 +/- 0.04) x 10(-11) ph cm(-2) s(-1). Both energy spectra are curved and well fit 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 respective energy spectra averaged over each of the two time periods indicate a spectral hardening for the 2000/2001 spectrum. The photon index changes from 2.39 +/- 0.09(stat) for 1999/2000 to 2.19 +/- 0.02(sta)t in 2000/2001. The energy spectra derived for different average flux levels ranging from 0.5 to 10 x 10(-11) ph cm(-2) s(-1) 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 min), 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 DeltaE = 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.