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

TL;DR

The study tackles the dispersion of the time-resolved $E_{p,i}$-$L_{iso}$ correlation in long GRBs, investigating whether dispersion arises primarily from intrinsic burst physics or from assembling heterogeneous sources. It analyzes 20 long GRBs with known redshift and jet properties using time-resolved GBM spectroscopy, Bayesian Blocks intervaling, and a D'Agostini likelihood to jointly fit slope, intercept, and intrinsic dispersion for isotropic and collimation-corrected luminosities. The authors show that the intrinsic dispersion within individual GRBs is smaller than the dispersion of the combined sample, and that jet opening angle does not explain the dispersion; a 4.2 sigma rejection of the null hypothesis indicates that sample assembly contributes significantly to the observed scatter. They conclude that the dispersion of both time-average and time-resolved $E_{p,i}$-$L$ correlations is partially, but not wholly, due to assembling different bursts, implying that GRB prompt emission physics and viewing-angle effects must be further clarified with larger, upcoming samples from missions like SVOM and THESEUS.

Abstract

Long gamma-ray burst (GRB) prompt emission shows a correlation between the intrinsic peak energy, $E_{\mathrm{p,i}}$, of the time-average $νF_ν$ spectrum and the isotropic-equivalent peak gamma-ray luminosity, $L_{\rm p,iso}$, as well as the total released energy, $E_{\rm iso}$. The same correlation is found within individual bursts, when time-resolved $E_{\rm p,i}$ and $L_{\rm iso}$ 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 {\em 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.

Figures (1)

• Figure 1: Top panel: time-resolved $E_{\rm p,i}$--$L_{\rm iso}$ relation for the overall sample $\mathcal{S}$. Bottom panel: collimation-corrected $E_{\rm p,i}$--$L_{\rm coll}$ relation for the subset $\mathcal{S}^{\rm (ISM)}$ of GRBs with available information on $\theta_{\rm j}^{\rm (ISM)}$. In both panels the best-fit model along with the 1-$\sigma_{\mathrm{int, t}}$ region a (shaded-area) is shown, while median uncertainties along both axes are shown in the top left.