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

We report results of a systematic study of the broad band (2--2000 keV) time resolved 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 the time-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 time averaged spectra of long GRBs with known redshift, is well established, but its physical origin is still a subject of discussion. In addition, some authors maintain 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 the corresponding energy flux, but also a strong $E_{p,i}$ versus $L_{\rm iso}$ correlation are found within each burst and merging together the time resolved data points from different GRBs. We do not expect significant instrumental selection effects that can affect the obtained results, apart from the fact that the GRBs in our sample are sufficiently bright to perform a time-resolved spectroscopy and that they have known redshift. If the fundamental physical process that gives rise to the GRB phenomenon does not depend on its brightness, we conclude that the found $E_{p,i}$ versus $L_{\rm iso}$ correlation within each GRB is intrinsic to the emission process, and that the correlations discovered by Amati et al. and Yonetoku et al. are likely not the result of selection effects. We also discuss the properties of the correlations found.