The bulk Lorentz factor of outflow powering X-ray flare in GRB afterglow

Abstract

We develop two methods to estimate the bulk Lorentz factor of X-ray flare outflow. In the first method the outflow is assumed to be baryonic and is accelerated by the thermal pressure, for which the final bulk Lorentz factor is limited by the outflow luminosity as well as the initial radius of the outflow getting accelerated. Such a method may be applied to a considerable fraction of flares. The second method, based on the curvature effect interpretation of the quick decline of the flare, can give a tightly constrained estimate of the bulk Lorentz factor but can only be applied to a few giant flares. The results obtained in these two different ways are consistent with each other. The obtained bulk Lorentz factor (or just upper limit) of the X-ray flare outflows, ranging from ten to a few hundred, is generally smaller than that of the Gamma-ray Burst (GRB) outflows.