The updated Bulk Lorentz Factors of Gamma-Ray Burst X-Ray Flares

Abstract

X-ray flares are the most common phenomena in the afterglow phase of gamma-ray bursts (GRBs) in the Swift era, and are known as a canonical component in X-ray afterglows. In this work, we constrain the Lorentz factor of X-ray flares with an updated sample. We extensively search for X-ray light curves showing flare and jet break simultaneously. A smooth broken power law function is used to fit the jet breaks in 11 GRBs. We also use a smooth broken power law function to fit the profile of X-ray flares, and the total number of the flares is 20. We obtain the lower and upper limits of Lorentz factor () with the timescale, half-opening angle and mean luminosity of the X-ray flares for interstellar medium (ISM) and wind cases. The lower limits on range from tens to a few hundred, and the upper limits are mainly about a few hundred. We also apply the limited Lorentz factor to test correlations of and for GRBs, and find X-ray flares in the ISM case are much more consistent with those of prompt emission than the wind case in a statistical sense for both correlations. X-ray flares are almost consistent with the trend in the correlations of for prompt GRBs, indicating X-ray flares and prompt bursts may have the same physical origin.