Confirmed width-Eiso and width-Liso relations in GRB: comparison with the Amati and Yonetoku relations

TL;DR

This study confirms strong correlations between spectral widths and isotropic energy and luminosity in GRBs, suggesting spectral shape is fundamentally linked to these energetic properties and relating to established Amati and Yonetoku relations.

Contribution

It introduces the width-$E_{iso}$ and width-$L_{iso}$ relations in GRBs, demonstrating their consistency and potential as fundamental indicators over traditional energy relations.

Findings

Strong positive correlation between spectral widths and $E_{iso}$, $L_{iso}$ in long GRBs.

Short GRBs are outliers in width-$E_{iso}$ but consistent in width-$L_{iso}.

Width-$E_{iso}$ and width-$L_{iso}$ relations overlap with Amati and Yonetoku relations at specific spectral maxima.

Abstract

In this paper, we select a sample including 141 BEST time-integrated F spectra and 145 BEST peak flux P spectra observed by the Konus-Wind with known redshift to recheck the connection between the spectral width and $E_{iso}$ as well as $L_{iso}$. We define six types of absolute spectral widths. It is found that all of the rest-frame absolute spectral widths are strongly positive correlated with $E_{iso}$ as well as $L_{iso}$ for the long burst for both the F and P spectra. All of the short bursts are the outliers for width-$E_{iso}$ relation and most of the short bursts are consistent with the long bursts for the width-$L_{iso}$ relation for both F and P spectra. Moreover, all of the location energy, $E_{2}$ and $E_{1}$, corresponding to various spectral widths are also positive correlated with $E_{iso}$ as well as $L_{iso}$. We compare all of the relations with the Amati and Yonetoku relations and find the width-$E_{iso}$ and width-$L_{iso}$ relations when the widths are at about 90\% maximum of the $EF_{E}$ spectra almost overlap with Amati relation and Yonetoku relation, respectively. The correlations of $E_{2}-E_{iso}$, $E_{1}-E_{iso}$ and $E_{2}-L_{iso}$, $E_{1}-L_{iso}$ when the location energies are at 99\% maximum of the $EF_{E}$ spectra are very close to the Amati and Yonetoku relations, respectively. Therefore, we confirm the existence of tight width-$E_{iso}$ and width-$L_{iso}$ relations for long bursts. We further show that the spectral shape is indeed related to $E_{iso}$ and $L_{iso}$. The Amati and Yonetoku relations are not necessarily the best relationships to relate the energy to the $E_{iso}$ and $L_{iso}$. They may be the special cases of the width-$E_{iso}$ and width-$L_{iso}$ relations or the energy-$E_{iso}$ and energy-$L_{iso}$ relations.