Context :

Aims : It has been suggested that X-ray observations of rapidly variable Seyfert galaxies may hold the key to probe the gas orbital motions in the innermost regions of accretion discs around black holes and , thus , trace flow patterns under the effect of the hole strong gravitational field .

Methods : We explore this possibility by re-analyzing the multiple XMM-Newton observations of the Seyfert 1 galaxy NGC 3783 .
A detailed time-resolved spectral analysis is performed down to the shortest possible time-scales ( few ks ) using “ excess maps ” and cross-correlating light curves in different energy bands .

Results : In addition to a constant core of the Fe K \alpha line , we detected a variable and redshifted Fe K \alpha emission feature between 5.3–6.1 keV .
The line exhibits a modulation on a time-scale of \sim 27 ks that is similar to and in phase with a modulation of the 0.3–10 keV source continuum .
The two components show a good correlation .

Conclusions : The time-scale of the correlated variability of the redshifted Fe line and continuum agrees with the local dynamical time-scale of the accretion disc at \sim 10 \mathrm { r _ { g } } around a black hole with the optical reverberation mass \sim 10 ^ { 7 } \mathrm { M _ { \odot } } .
Given the shape of the redshifted line emission and the overall X-ray variability pattern , the line is likely to arise from the relativistic region near the black hole , although the source of the few cycles of coherent variation remains unclear .