Correlated Spectral And Temporal Behaviour Of Late-Time Afterglows Of Gamma Ray Bursts

TL;DR

This study analyzes the spectral and temporal behavior of late-time X-ray afterglows of 315 Swift GRBs, confirming the CB model's prediction that the difference between temporal and spectral indices clusters around 0, 1/2, and 1.

Contribution

It provides the first comprehensive distribution analysis of spectral and temporal indices in GRB afterglows, supporting the CB model's predictions with observational data.

Findings

Distribution of index differences peaks at 0, 1/2, and 1

Measurement errors are consistent with the narrow peaks

Supports the CB model's predictions for afterglow behavior

Abstract

The cannonball (CB) model of gamma ray bursts (GRBs) predicts that the asymptotic behaviour of the spectral energy density of the X-ray afterglow of GRBs is a power-law in time and in frequency where the difference between the temporal and spectral power-law indexes, $\alpha_X-\beta_X$, is restricted to the values 0, 1/2 and 1. Here we report the distributions of the values $\alpha_X$, $\beta_X$ and their difference for a sample of 315 Swift GRBs. This sample includes all Swift GRBs that were detected before August 1, 2012, whose X-ray afterglow extended well beyond 1 day and the estimated error in $\alpha_X-\beta_X$ was $\leq 0.25$. The values of $\alpha_X$ were extracted from the CB model fits to the entire light curves of their X-ray afterglow while the spectral index was extracted by the Swift team from the time integrated X-ray afterglow of these GRBs. We found that the distribution of the difference $\alpha_X-\beta_X$ for these 315 Swift GRBs has three narrow peaks around 0, 1/2 and 1 whose widths are consistent with being due to the measurement errors, in agreement with the CB model prediction.