Statistical Analysis of the Parameters of Gamma-Ray Bursts with Known Redshifts and Peaked Optical Light Curves

TL;DR

This paper statistically analyzes gamma-ray bursts with known redshifts and peaked optical light curves, revealing new empirical correlations between optical luminosity, redshift, and gamma-ray energy, enhancing understanding of GRB properties.

Contribution

It introduces the first empirical relations linking optical luminosity with redshift and peak time, and compares optical luminosity correlations for afterglows and prompt emissions.

Findings

Optical luminosity correlates with redshift as L_R ∝ (z+1)^5.39.

Peak optical luminosity inversely correlates with peak time as L_R ∝ T_peak^{-3.85}.

Optical luminosity shows a strong correlation with gamma-ray energy for both afterglows and prompt emissions.

Abstract

We present the statistical analysis of the properties of gamma-ray bursts with measured host galaxy redshifts and peaked optical light curves in proper frames of reference. The optical transients are classified by comparing the time lag of the optical peak relative to the GRB trigger with the duration of the gamma-ray emission itself. The results of the correlation analysis of all possible pairs of energy, spectral, and temporal characteristics of both gamma-ray and optical emissions are given. We specify the pairs of the parameters with correlation coefficients greater than 50 % at significance levels better than 1 %. The following empirical relations, obtained for the first time, are specifically discussed: a correlation between the peak optical afterglow $R$ band luminosity and redshift $L_{R} \propto (z+1)^{5.39 \pm 0.74}$ and a correlation between the peak luminosity of the prompt optical emissions and the time of the peak $L_{R} \propto T_{\rm peak}^{-3.85 \pm 1.22}$. We also analyze the similarity of the relationships between the peak optical luminosity and the isotropic equivalent of the total energy of gamma-ray bursts for afterglows ($L_{R} \propto E_{\rm iso}^{1.06 \pm 0.22}$) and for prompt optical emissions ($L_{R} \propto E_{\rm iso}^{1.59 \pm 0.21}$).