The dispersion of E_ p,i-L_ iso correlation of long gamma-ray bursts is partially due to assembling different sources

Long gamma-ray burst (GRB) prompt emission shows a correlation between the intrinsic peak energy, E_p,i, of the time-average ν F_ν spectrum and the isotropic-equivalent peak gamma-ray luminosity, L_ p,iso, as well as the total released energy, E_ iso. The same correlation is found within individual bursts, when time-resolved E_ p,i and L_ iso are considered. These correlations are characterised by an intrinsic dispersion, whose origin is still unknown. Discovering the origin of the correlation and of its dispersion would shed light on the still poorly understood prompt emission and would propel GRBs to powerful standard candles. We studied the dispersion of both isotropic-equivalent and collimation-corrected time-resolved correlations. We also investigated whether the intrinsic dispersion computed within individual GRBs is different from that obtained including different bursts into a unique sample. We then searched for correlations between key features, like Lorentz factor and jet opening angle, and intrinsic dispersion, when the latter is treated as one of the characterising We performed a time-resolved spectral analysis of 20 long Type-II or collapsar-candidate GRBs detected by the Fermi Gamma-ray Burst Monitor with known redshift and estimates of jet opening angle and/or Lorentz factor. The collimation-corrected correlation appears to be no less dispersed than the isotropic-equivalent one. Also, individual GRBs are significantly less dispersed than the whole sample. We excluded (at 4.2 σ confidence level) the difference in samples' sizes as the possible reason, thus confirming that individual GRBs are intrinsically less dispersed than the whole sample. No correlation was found between intrinsic dispersion and other key properties for the few GRBs with available information.