The History of GRB Outflows: Ejection Lorentz Factor and Radiation Location of X-Ray Flares

TL;DR

This study analyzes the spectral and temporal evolution of X-ray flares in gamma-ray bursts, estimating Lorentz factors and emission regions, revealing insights into the long-term evolution of GRB central engines.

Contribution

It provides the first detailed time-resolved spectral analysis of X-ray flare decay segments and constrains their emission regions and Lorentz factors, linking prompt and flare phases.

Findings

Rapid flux decay fits curvature effect model

Derived Lorentz factors range from 17 to 87

Radiating regions are smaller than afterglow fireballs

Abstract

We present time-resolved spectral analysis of the steep decay segments of 29 bright X-ray flares of gamma-ray bursts (GRBs) observed with the Swift/X-ray telescope, and model their lightcurves and spectral index evolution behaviors with the curvature effect model. Our results show that the observed rapid flux decay and strong spectral index evolution with time can be well fit with this model, and the derived characteristic timescales ($t_c$) are in the range of $33\sim 264$ seconds. Using an empirical relation between the peak luminosity and the Lorentz factor derived from the prompt gamma-rays, we estimate the Lorentz factors of the flares ($\Gamma_{\rm X}$). We obtain $\Gamma_{\rm X}=17\sim 87$ with a median value of $52$, which is smaller than the initial Lorentz factors of prompt gamma-ray fireballs. With the derived $t_c$ and $\Gamma_{\rm X}$, we constrain the radiating regions of 13 X-ray flares, yielding $R_{\rm X}=(0.2\sim 1.1)\times 10^{16}$ cm, which are smaller than the radii of the afterglow fireballs at the peak times of the flares. A long evolution feature from prompt gamma-ray phase to the X-ray epoch is found by incorporating our results with a sample of GRBs whose initial Lorentz factors are available in literatures, i.e., $\Gamma\propto [t_{p}/(1+z)]^{-0.69\pm 0.06}$. These results may shed lights on the long term evolution of GRB central engines.