Confirmed Width–Eiso and Width–Liso Relations in Gamma-Ray Bursts: Comparison with the Amati and Yonetoku Relations

Abstract

Abstract The well-known Amati and Yonetoku relations in gamma-ray bursts show strong correlations between the rest-frame νf ν spectrum peak energy, E p,i , and the isotropic energy, E iso, as well as isotropic peak luminosity, L iso. Recently, Peng et al. showed that the cosmological rest-frame spectral widths are also correlated with E iso and with L iso. In this paper, we select a sample including 141 BEST time-integrated F spectra and 145 BEST peak flux P spectra observed by 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 as the differences between the upper (E 2) and lower energy bounds (E 1) of the full width at 50%, 75%, 85%, 90%, 95%, and 99% of maximum of the EF E versus E spectra. It is found that all of the rest-frame absolute spectral widths are strongly positively 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 outliers for the 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 energies, E 2 and E 1, corresponding to various spectral widths, are also positively correlated with E iso as well as L iso. We compare all of the relations with the Amati and Yonetoku relations and find that 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 the Amati relation and the 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% of 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 for relating the energy to the E iso and L iso. They may be special cases of the width–E iso and width–L iso relations or the energy–E iso and energy–L iso relations.