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