The dispersion of the 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, Ep,i , of the time-average νFν spectrum and the isotropic-equivalent peak gamma-ray luminosity, Lp,iso , as well as the total released energy, Eiso . The same correlation is found within individual bursts, when time-resolved Ep,i and Liso 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 properties. 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. Time intervals were determined using Bayesian Blocks. Then we carried out a statistical analysis starting from distributions of simulated values of the intrinsic dispersion of each burst in the sample. 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 4.2σ 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. The contribution to the dispersion by the jet opening angle is not relevant. Moreover, our results prove that the intrinsic dispersion which affects the Ep,i –Liso correlation is partially, but not entirely due to assembling different GRBs. We therefore conclude that the presence of different GRBs significantly contributes to the observed dispersion of both time-average Ep,i –Lp,iso and Ep,i –Eiso correlations.