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We report results of a systematic study of the broad band (2--2000 keV) timeresolved prompt emission spectra of a sample of gamma-ray bursts (GRBs)detected with both Wide Field Cameras on board the \sax\ satellite and the\batse\ experiment on board CGRO. In this first paper, we study thetime-resolved dependence of the intrinsic peak energy $E_{p,i}$ of the $E F(E)$spectrum on the corresponding isotropic bolometric luminosity $L_{\rm iso}$.The $E_{p,i}$--$L_{\rm iso}$ relation or the equivalent relation between$E_{p,i}$ and the bolometric released energy $E_{iso}$, derived using the timeaveraged spectra of long GRBs with known redshift, is well established, but itsphysical origin is still a subject of discussion. In addition, some authorsmaintain that these relations are the result of instrumental selection effects.We find that not only a relation between the measured peak energy $E_p$ and thecorresponding energy flux, but also a strong $E_{p,i}$ versus $L_{\rm iso}$correlation are found within each burst and merging together the time resolveddata points from different GRBs. We do not expect significant instrumentalselection effects that can affect the obtained results, apart from the factthat the GRBs in our sample are sufficiently bright to perform a time-resolvedspectroscopy and that they have known redshift. If the fundamental physicalprocess that gives rise to the GRB phenomenon does not depend on itsbrightness, we conclude that the found $E_{p,i}$ versus $L_{\rm iso}$correlation within each GRB is intrinsic to the emission process, and that thecorrelations discovered by Amati et al. and Yonetoku et al. are likely not theresult of selection effects. We also discuss the properties of the correlationsfound.

Broad band time-resolved E_{p,i}--L_{iso} correlation in GRBs