Energy-dependent X-ray variability of MKN 421

MKN421, repeatedly monitored with BeppoSAX in 1997-2000, showed recurrent similar to 1 day duration dares with quasi-symmetric profiles. We show here the most important results of our comprehensive temporal analysis aiming at quantifying time lags between low and high energy photons. Interestingly, time lags were detected in each isolated flare, and constrained to a small range from flare to flare (similar to 1 hour between the 0.1-1.5 keV and the 3.5-10 keV bands) with various attributes: soft lags, hard lags or zero lags, but no correlation between time lags and flare intensities was found. To account for variable time lags, relative changes of values in the dominant time scales involved in the emitting region must occur in order to produce a variety of complex energy-dependent variability behaviors. The energy-dependence of time lags was well determined for the flares in which a large enough time lags is detected, from which magnetic fields have been constrained to be 0.15-3.0 Gauss (assuming Doppler factor delta = 20), if soft and hard lags are simply related to the energy-dependent synchrotron cooling and acceleration time scales, respectively. Both symmetric structure and time lags detected in some hares indicate that the emitting region sizes are energy-dependent.