Effect of GRB spectra on the empirical luminosity correlations and the GRB Hubble diagram

TL;DR

This study examines how different spectral models of GRBs, specifically the Band function and cut-off power law, influence the empirical luminosity correlations and the resulting GRB Hubble diagram, finding minimal dependence.

Contribution

It provides an analysis of the impact of spectral model choice on luminosity correlations and the GRB Hubble diagram using the latest Swift-BAT data.

Findings

Luminosity correlations are only moderately affected by spectral model choice.

The Amati relation is insensitive to the high-energy power-law index.

The GRB Hubble diagram is nearly independent of the spectral model used.

Abstract

The spectra of gamma-ray bursts (GRBs) in a wide energy range can usually be well described by the Band function, which is a two smoothly jointed power laws cutting at a breaking energy. Below the breaking energy, the Band function reduces to a cut-off power law, while above the breaking energy it is a simple power law. However, for some detectors (such as the Swift-BAT) whose working energy is well below or just near the breaking energy, the observed spectra can be fitted to cut-off power law with enough precision. Besides, since the energy band of Swift-BAT is very narrow, the spectra of most GRBs can be fitted well even using a simple power law. In this paper, with the most up-to-date sample of Swift-BAT GRBs, we study the effect of different spectral models on the empirical luminosity correlations, and further investigate the effect on the reconstruction of GRB Hubble diagram. We mainly focus on two luminosity correlations, i.e., the Amati relation and Yonetoku relation. We calculate these two luminosity correlations on both the case that the GRB spectra are modeled by Band function and cut-off power law. It is found that both luminosity correlations only moderately depend on the choice of GRB spectra. Monte Carlo simulations show that Amati relation is insensitive to the high-energy power-law index of the Band function. As a result, the GRB Hubble diagram calibrated using luminosity correlations is almost independent on the GRB spectra.