Journal of Applied Mathematics and Physics, 2017, 5, 1515-1520 http://www.scirp.org/journal/jamp ISSN Online: 2327-4379 ISSN Print: 2327-4352 DOI: 10.4236/jamp.2017.58124 Aug. 4, 2017 1515 Journal of Applied Mathematics and Physics Peak Energy Correlations for Gamma-Ray Bursts Walid J. Azzam Department of Physics, College of Science, University of Bahrain, Sakhir, Bahrain Abstract Gamma-ray bursts (GRBs) are the most powerful explosions in the universe. Over the past two decades, several GRB energy and luminosity correlations were discovered. These correlations typically involve an observable parameter, like the observed peak energy, E p,obs , and a non-observable quantity, like the equivalent isotropic energy, E iso . This paper provides a brief review of GRB peak energy correlations. Specifically, it focuses on the Amati relation, which correlates E p,obs and E iso , and the Ghirlanda relation, which correlates E p,obs and E γ , the total energy corrected for beaming. The paper also discusses the physi- cal interpretation of these relations in the context of the internal shock model. Keywords Gamma-Ray Bursts, Peak Energy Correlations, Energy Indicators 1. Introduction Gamma-ray bursts (GRBs) are extremely powerful stellar explosions with an equivalent isotropic energy, E iso , that can exceed 10 54 erg [1]. Their light curves consist of intense irregular pulses that typically last for a few seconds and their spectra are nonthermal peaking between 10 and 10 4 keV. The radiation pro- duced by GRBs is believed to emanate from jets, but the precise mechanism be- hind the formation of these jets is still not fully understood [2]. Over the past two decades, several GRB energy and luminosity correlations were discovered. Some were obtained from the light curves, like the time-lag and variability relations [3] [4], while others were obtained from the spectra and in- clude the Amati relation [5] [6] [7] [8], the Ghirlanda relation [9], the Yonetoku relation [10] [11], and the Liang-Zhang relation [12]. These correlations are im- portant because they can potentially be used as cosmological probes to constrain How to cite this paper: Azzam, W.J. (2017) Peak Energy Correlations for Gam- ma-Ray Bursts. Journal of Applied Mathe- matics and Physics, 5, 1515-1520. https://doi.org/10.4236/jamp.2017.58124 Received: July 13, 2017 Accepted: July 31, 2017 Published: August 4, 2017 Copyright © 2017 by author and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access