_{1}

Gamma-ray bursts (GRBs) are the most powerful explosions in the universe. Alt-hough the exact mechanism behind these explosions remains elusive, GRBs hold great promise as cosmological probes for two main reasons: they have been observed up to very high redshift (z > 9), and their gamma-ray emission is unencumbered by any intervening dust. Several GRB energy and luminosity indicators have been discovered. These indicators correlate an observable quantity, like the intrinsic peak energy, E
* _{p}*,

*, in the spectrum of a burst to an unobservable parameter like the equivalent isotropic energy, E*

_{i}_{iso}, or the isotropic peak luminosity, L

_{p,iso}. This paper provides a brief review of one of these energy and luminosity indicators, the Amati relation, and discusses its potential use as a cosmological probe.

There are currently several energy and luminosity correlations for gamma-ray bursts (GRBs). Some, like the lag-luminosity and variability relations [

Some studies have looked at possible inherent problems that these relations might suffer from, like the circularity problem and selection effects [

The purpose of this paper is to provide a brief review of a well-known GRB energy and luminosity correlation―namely, the Amati relation, and to discuss its potential use as a cosmological probe.

The Amati relation is a correlation between a GRB’s equivalent isotropic energy, _{n} spectrum. It was first discovered by Amati et al. in 2002 and confirmed by later studies [

The Amati relation is given by:

where K and m are constants, and

Alternatively, the Amati relation can be expressed logarithmically as:

where the normalization, A, and the slope, B, are constants, and where

Before we can utilize the Amati relation as a cosmological probe, we need to check its robustness. One of the central issues concerning the Amati relation is whether the fitting parameters are constant. A recent study [

Another problem that arises when we try to employ the Amati relation as a cosmological probe is the circularity problem, which refers to the fact that in order to calibrate the relation, one must assume a cosmological model in the first place. Two recent studies [

Early attempts to constrain cosmological parameters, like the matter density parameter W_{M}, had limited success due to the paucity of data points [

Gamma-ray bursts hold great promise as cosmological probes since they can be observed to huge distances (z > 9) and their radiation is unencumbered by any intervening dust. The most effective way of using them as cosmological probes is by utilizing one of the currently available energy and luminosity correlations.

In this brief review we focused on one of these correlations―namely, the Amati relation. It is a correlation between the equivalent isotropic energy and the intrinsic peak energy. Early attempts to employ the Amati relation as a cosmological probe faced several hurdles, like the circularity problem, the extrinsic scatter, and the paucity of data points. However, as high quality data samples have become available, the scatter in the correlation has diminished and the Amati relation has become more robust. In the near future, the Amati relation will be an effective cosmological tool that will shed light on many cosmological issues, like the density parameters and the star formation rate.

The author would like to thank the anonymous referee for the useful remarks that helped improve the paper.

Azzam, W.J. (2016) A Brief Review of the Amati Relation for GRBs. International Journal of Astronomy and Astrophysics, 6, 378-383. http://dx.doi.org/10.4236/ijaa.2016.64030