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 \mathrm { TeV } ) in the 1999/2000 season was ( 1.43 \pm 0.04 ) \cdot 10 ^ { -11 } ph cm ^ { -2 } s ^ { -1 } , whereas in the 2000/2001 season the average integral flux increased to ( 4.19 \pm 0.04 ) \cdot 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 \pm 0.09 _ { stat } for 1999/2000 to 2.19 \pm 0.02 _ { stat } in 2000/2001 .
The energy spectra derived for different average flux levels ranging from 0.5 to 10 \cdot 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 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 \Delta E = 2.6 \pm 0.6 _ { \mathrm { stat } } \pm 0.6 _ { \mathrm { 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 .