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X-ray flares detected in nearly half of gamma-ray burst (GRB) afterglows areone of the most intriguing phenomena in high-energy astrophysics. All theobservations indicate that the central engines of bursts, after the gamma-rayemission has ended, still have long periods of activity, during which energeticexplosions eject relativistic materials, leading to late-time X-ray emission.It is thus expected that X-ray flares provide important clues to the nature ofthe central engines of GRBs, and more importantly, unveil the physicalmechanism of the flares themselves, which has so far remained mysterious. Herewe report statistical results of X-ray flares of GRBs with known redshifts, andshow that X-ray flares and solar flares share three statistical properties:power-law frequency distributions for energies, durations, and waiting times.All of the distributions can be well understood within the physical frameworkof a self-organized criticality (SOC) system. The statistical properties ofX-ray flares of GRBs are similar to solar flares, and thus can both beattributed to a SOC process. Both types of flares may be driven by a magneticreconnection process, but X-ray flares of GRBs are produced in ultra-stronglymagnetized millisecond pulsars or long-term hyperaccreting disks aroundstellar-mass black holes.

Self-organized criticality in X-ray flares of gamma-ray burst afterglows