On the Correlation of Low-energy Spectral Indices and Redshifts of Gamma-ray Bursts

TL;DR

This study confirms a correlation between the low-energy spectral index and redshift in gamma-ray bursts, expanding previous findings with a larger sample and exploring related spectral parameter correlations to inform GRB physics.

Contribution

It provides a larger sample analysis confirming the spectral index-redshift correlation and explores its relation with other spectral parameters, offering new insights into GRB physics.

Findings

Confirmed correlation between low-energy index and redshift.

Found correlations between spectral index and peak energy, isotropic energy, and luminosity.

Indicated these parameters are interconnected, constraining GRB models.

Abstract

It was found by Amati et al. in 2002 that for a small sample of 9 gamma-ray bursts, more distant events appear to be systematically harder in the soft gamma-ray band. Here, we have collected a larger sample of 65 gamma-ray bursts, whose time integrated spectra are well established and can be well fitted with the so called Band function. It is confirmed that a correlation between the redshifts ($z$) and the low-energy indices ($\alpha$) of the Band function does exist, though it is a bit more scattered than the result of Amati et al. This correlation can not be simply attributed to the effect of photon reddening. Furthermore, correlations between $\alpha$ and $E_{\rm peak}$ (the peak energy in the $\nu F_{\nu}$ spectrum in the rest frame), $\alpha$ and $E_{\rm iso}$ (the isotropic energy release), $\alpha$ and $L_{\rm iso}$ (the isotropic luminosity) are also found, which indicate that these parameters are somehow connected. The results may give useful constraints on the physics of gamma-ray bursts.