We present the results of a detailed temporal analysis of the bright BL Lac object Mrk 421 using the three available long timing mode observations by the EPIC PN camera .
This detector mode is characterized by its long life time and is largely free of photon pile-up problems .
The source was found in different intensity and variability states differing by up to more than a factor of three in count rate .
A time resolved cross correlation analysis between the soft and hard energy bands revealed that the characteristics of the correlated emission , with lags of both signs , change on time scales of a few 10 ^ { 3 } seconds .
Individual spectra , resolved on time scales of \sim 100 s , can be quite well fitted by a broken power law and we find significant spectral variations on time scales as short as \sim 500 - 1000 sec .
Both the hard and the soft band spectral indices show a non-linear correlation with the source flux .
A simple power law model of the form \Gamma \propto { \mathrm { flux } } ^ { - a } with a _ { \mathrm { hard } } \sim 0.13 and a _ { \mathrm { soft } } \sim 0.22 describes rather well the observed trend of decreasing \Gamma values with increasing flux , which appear to “ saturate ” at the same limiting value of \Gamma \sim 1.8 at the highest flux levels .
A comparison of the observed light curves with numerical results from relativistic hydrodynamic computer simulations of the currently favored shock-in-jet models indicates that any determination of the jet ’ s physical parameters from ‘ simple ’ emission models must be regarded with caution : at any time we are seeing the emission from several emission regions distinct in space and time , which are connected by the complex hydrodynamic evolution of the non-uniform jet .