International Journal of Astronomy and Astrophysics, 2013, 3, 372-375 Published Online December 2013 (http://www.scirp.org/journal/ijaa) http://dx.doi.org/10.4236/ijaa.2013.34042 Open Access IJAA Redshift Independence of the Amati and Yonetoku Relations for Gamma-Ray Bursts Walid J. Azzam, Mohamed J. Alothman Department of Physics, College of Science, University of Bahrain, Sakhir, Kingdom of Bahrain Email: wjazzam@uob.edu.bh, wjazzam@gmail.com Received August 28, 2013; revised September 24, 2013; accepted September 30, 2013 Copyright © 2013 Walid J. Azzam, Mohamed J. Alothman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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 F  spec- trum 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:     peak peak log log iso E A B E E   for the Amati relation, and of the form:     peak peak log log iso L A B E E   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 co- efficient, 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. Keywords: Gamma-Ray Bursts; Energy Correlations; Luminosity Indicators; Redshift Evolution 1. Introduction There are currently several energy and luminosity corre- lations for gamma-ray bursts (GRBs). Some were ob- tained 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 [3-6], 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 cosmo- logical probes that might help constrain cosmological models [11-15], and also as tools that might help probe the physics of GRBs. On the other hand, some studies have looked at possi- ble inherent problems that these relations might suffer from, like the circularity problem and selection effects [16-20]. However, less attention has been given to the possible redshift evolution of these correlations as evi- denced by the few studies dedicated specifically to this issue [21-26]. But since these relations are typically cali- brated 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. The purpose of this paper is to investigate the possible redshift evolution of two well-known GRB energy and luminosity correlations—namely, the Amati and Yone- toku relations. The Amati relation is a correlation be- tween the intrinsic (i.e., rest-frame) peak energy, E peak , in a burst’s F  spectrum and its equivalent isotropic energy, E iso . The Yonetoku relation, on the other hand, is a cor- relation between E peak and a burst’s isotropic peak lumi- nosity, L iso . 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 data, analysis, and results are presented in Section 2, which is followed by a discussion and summary in Section 3. 2. Data, Analysis, and Results The data sample used in this study is taken from Geng and Huang [27], who were able to fit the time-averaged