XMM-Newton timing mode observations of Mrk 421

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) s. Individual spectra, resolved on time scales of similar to 100 s, can be quite well fitted by a broken power law and we find significant spectral variations on time scales as short as similar to 500 - 1000 s. 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 proportional to flux(-a) with a(hard) similar to 0.13 and a(soft) similar to 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 similar to 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.