Redshift Independence of the Amati and Yonetoku Relations for Gamma-Ray Bursts

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, E peak , in the v F v spectrum of a burst and its equivalent isotropic energy, E iso . The Yonetoku relation is a correlation between E peak and the isotropic peak luminosity, L iso . 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: log( E iso ) = A + B log( E peak /< E peak > ) for the Amati relation, and of the form: log( L iso ) = A + B log( E peak /< E peak >) for the Yonetoku relation, where < E peak > 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.