Confirmed width-Eiso and width-Liso relations in GRB: comparison with the Amati and Yonetoku relations
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 Eiso as well as Liso. 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 Eiso as well as Liso for the long burst for both the F and P spectra. All of the short bursts are the outliers for width-Eiso relation and most of the short bursts are consistent with the long bursts for the width-Liso relation for both F and P spectra. Moreover, all of the location energy, E2 and E1, corresponding to various spectral widths are also positive correlated with Eiso as well as Liso. We compare all of the relations with the Amati and Yonetoku relations and find the width-Eiso and width-Liso relations when the widths are at about 90\% maximum of the EFE spectra almost overlap with Amati relation and Yonetoku relation, respectively. The correlations of E2-Eiso, E1-Eiso and E2-Liso, E1-Liso when the location energies are at 99\% maximum of the EFE spectra are very close to the Amati and Yonetoku relations, respectively. Therefore, we confirm the existence of tight width-Eiso and width-Liso relations for long bursts. We further show that the spectral shape is indeed related to Eiso and Liso. The Amati and Yonetoku relations are not necessarily the best relationships to relate the energy to the Eiso and Liso. They may be the special cases of the width-Eiso and width-Liso relations or the energy-Eiso and energy-Liso relations.