Scale invariance in x-ray flares of gamma-ray bursts

X-ray flares are generally believed to be produced by the reactivation of central engine, and may have same energy dissipation mechanism as prompt emission gamma-ray bursts (GRBs). can therefore provide important clues understanding nature engines GRBs. In this work, we study for first time physical connection between differential size return distributions GRBs with known redshifts. We find that duration, energy, waiting well fitted a power-law function. particular, differences durations, energies, times at different (i.e., distributions) follow $q$-Gaussian form. The $q$ values in remain nearly steady temporal interval scales, implying scale-invariant structure GRB flares. Moreover, verify parameters related indices $\alpha$ distributions, characterized $q=(\alpha+2)/\alpha$. These statistical features explained within framework self-organizing criticality system.