The peak luminosity-peak energy correlation in gamma-ray bursts

We derive the correlation between the peak luminosity L_iso and the peak energy of the νF_ν spectrum E_peak using 25 long gamma-ray bursts (GRBs) with firm redshift measurements. We find that its slope is similar to that of the correlation between the time-integrated isotropic emitted energy E_iso and E_peak. For the 16 GRBs in our sample with estimated jet opening angle, we compute the collimation-corrected peak luminosity L_γ, and find that it correlates with E_peak. This correlation has, however, a scatter larger than that of the correlation between E_peak and E_γ (the time-integrated emitted energy, corrected for collimation), which we ascribe to the fact that the opening angle is estimated through the global energetics. We have then selected a large sample of 442 GRBs with pseudo-redshifts, derived through the lag-luminosity relation, to test the existence of the L_iso-E_peak correlation. With this sample we also explore the possibility of a correlation between time-resolved quantities, namely L^p_iso and the peak energy at the peak of emission E^p_peak.