Abstract
The Amati and Yonetoku relations are two of the main energy and luminosity correlations that currently exist for gamma-ray bursts (GRBs). The Amati relation is a correlation between the intrinsic peak energy, Epeak, in the F spectrum of a burst and its equivalent isotropic energy, Eiso. The Yonetoku relation is a correlation between Epeak and the isotropic peak luminosity, Liso. In this paper, we use a recent data sample of 65 GRBs to investigate whether these two relations evolve with redshift, z. The z-correction and the k-correction are both taken into account. Our method consists of binning the data in redshift, z, then applying (for each bin) a fit of the form: peak peak log log iso EA B E E for the Amati relation, and of the form: peak peak log log iso LA B E E for the Yonetoku relation, where Epeak is the mean value of the peak energy for the entire sample. The objective is to see whether the two fitting parameters, A and B, evolve systematically with z. Good least-squares fits were obtained with reasonable values for the linear regression coefficient, r. Our results indicate that the normalization, A, and the slope, B, do not evolve with redshift, and hence the Amati and Yonetoku relations seem to be redshift independent.
Highlights
There are currently several energy and luminosity correlations for gamma-ray bursts (GRBs)
In this paper we study the possible redshift evolution of these two relations by making use of a recent data sample consisting of 65 GRBs
The entire data sample consists of 65 GRBs, only 53 bursts have both Epeak and Eiso values available and so these are the bursts that we used in our analysis of the Amati relation; only 47 bursts have both Epeak and Liso values available and these are the bursts that we used in our analysis of the Yonetoku relation
Summary
There are currently several energy and luminosity correlations for gamma-ray bursts (GRBs). Some were obtained from the light curves, like the lag-luminosity and variability relations [1,2], while others were obtained from the spectra and included the Amati relation [3,4,5,6], the Ghirlanda relation [7], the Yonetoku relation [8,9], and the Liang-Zhang relation [10] The importance of these correlations resides in their potential use as cosmological probes that might help constrain cosmological models [11,12,13,14,15], and as tools that might help probe the physics of GRBs. On the other hand, some studies have looked at possible inherent problems that these relations might suffer from, like the circularity problem and selection effects [16,17,18,19,20]. Since these relations are typically calibrated over a wide range in redshift (roughly 0.1 < z < 8), it becomes incumbent to study their possible dependence on z, if they are to be utilized as cosmological probes
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