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We present time-resolved spectral analysis of the steep decay segments of 29bright X-ray flares of gamma-ray bursts (GRBs) observed with the Swift/X-raytelescope, and model their lightcurves and spectral index evolution behaviorswith the curvature effect model. Our results show that the observed rapid fluxdecay and strong spectral index evolution with time can be well fit with thismodel, and the derived characteristic timescales ($t_c$) are in the range of$33\sim 264$ seconds. Using an empirical relation between the peak luminosityand the Lorentz factor derived from the prompt gamma-rays, we estimate theLorentz factors of the flares ($\Gamma_{\rm X}$). We obtain $\Gamma_{\rmX}=17\sim 87$ with a median value of $52$, which is smaller than the initialLorentz 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 theradii of the afterglow fireballs at the peak times of the flares. A longevolution feature from prompt gamma-ray phase to the X-ray epoch is found byincorporating our results with a sample of GRBs whose initial Lorentz factorsare available in literatures, i.e., $\Gamma\propto [t_{p}/(1+z)]^{-0.69\pm0.06}$. These results may shed lights on the long term evolution of GRB centralengines.

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