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

X-ray flares detected in nearly half of gamma-ray burst (GRB) afterglows are one of the most intriguing phenomena in high-energy astrophysics. All the observations indicate that the central engines of bursts, after the gamma-ray emission has ended, still have long periods of activity, during which energetic explosions eject relativistic materials, leading to late-time X-ray emission. It is thus expected that X-ray flares provide important clues to the nature of the central engines of GRBs, and more importantly, unveil the physical mechanism of the flares themselves, which has so far remained mysterious. Here we report statistical results of X-ray flares of GRBs with known redshifts, and show 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 framework of a self-organized criticality (SOC) system. The statistical properties of X-ray flares of GRBs are similar to solar flares, and thus can both be attributed to a SOC process. Both types of flares may be driven by a magnetic reconnection process, but X-ray flares of GRBs are produced in ultra-strongly magnetized millisecond pulsars or long-term hyperaccreting disks around stellar-mass black holes.