Luminosity--time and luminosity--luminosity correlations for GRB prompt and afterglow plateau emissions

TL;DR

This study analyzes correlations between luminosity and time in GRB prompt and afterglow phases, revealing differences in their slopes, energy distributions, and intrinsic correlations after accounting for cosmological evolution.

Contribution

It provides the first detailed comparison of luminosity-time correlations between GRB prompt emission and afterglow plateau phases, including the intrinsic nature of these correlations.

Findings

The $L_a-T^{*}_a$ slope differs from the prompt $L_{f}-T^{*}_{f}$ slope by over 2 sigma.

Afterglow energy is approximately 10% of prompt emission energy.

The $L_{peak}-L_a$ correlation is stronger and more intrinsic than the $L_{prompt}-L_a$ correlation.

Abstract

We present an analysis of 123 Gamma-ray bursts (GRBs) with known redshifts possessing an afterglow plateau phase. We reveal that $L_a-T^{*}_a$ correlation between the X-ray luminosity $L_a$ at the end of the plateau phase and the plateau duration, $T^*_a$, in the GRB rest frame has a power law slope different, within more than 2 $\sigma$, from the slope of the prompt $L_{f}-T^{*}_{f}$ correlation between the isotropic pulse peak luminosity, $L_{f}$, and the pulse duration, $T^{*}_{f}$, from the time since the GRB ejection. Analogously, we show differences between the prompt and plateau phases in the energy-duration distributions with the afterglow emitted energy being on average $10\%$ of the prompt emission. Moreover, the distribution of prompt pulse versus afterglow spectral indexes do not show any correlation. In the further analysis we demonstrate that the $L_{peak}-L_a$ distribution, where $L_{peak}$ is the peak luminosity from the start of the burst, is characterized with a considerably higher Spearman correlation coefficient, $\rho=0.79$, than the one involving the averaged prompt luminosity, $L_{prompt}-L_a$, for the same GRB sample, yielding $\rho=0.60$. Since some of this correlation could result from the redshift dependences of the luminosities, namely from their cosmological evolution we use the Efron-Petrosian method to reveal the intrinsic nature of this correlation. We find that a substantial part of the correlation is intrinsic. We apply a partial correlation coefficient to the new de-evolved luminosities showing that the intrinsic correlation exists.