Spectral-Luminosity relation within individual Fermi GRBs

We study the spectra of all long Gamma Ray Bursts (GRBs) of known redshift detected by the Fermi satellite. Their fluxes and fluences are large enough to allow a time dependent study of their spectral characteristics in the 8 keV-1 MeV energy range. We find that the peak energy Ep of their EL(E) spectrum correlates with the luminosity in a remarkable tight way within individual bursts. This time resolved Ep-Liso correlation is very similar for all the considered bursts, and has a slope and normalisation similar to the analogous Ep-Liso correlation defined by the time integrated spectra of different bursts detected by several different satellites. For a few of the considered GRBs, we could also study the behaviour of the Ep-Liso correlation during the rising and decaying phases of individual pulses within each burst, finding no differences. Our results indicate the presence of a similar physical mechanism, operating for the duration of different GRBs, linking tightly the burst luminosity with the peak energy of the spectrum emitted at different times. Such a physical mechanism is the same during the rise and decay phase of individual pulses composing a GRB. These results, while calling for a robust physical interpretation, strongly indicate that the Ep-Liso spectral energy correlation found considering the time integrated spectra of different bursts is real, and not the result of instrumental selection effects.