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Recently the AGILE and Fermi/LAT detectors uncovered giant $\gamma$-rayflares from the Crab nebula. The duration of these flares is a few days. TheFermi/LAT data with monthly time binning further showed significant variabilityof the synchrotron tail of the emission, while the inverse Compton componentwas stable. The simultaneous or follow-up observations in X-ray, optical,infrared and radio bands did not find significant flux variation. Based onthese observations, we propose that the $\gamma$-ray variability and flares aredue to statistical fluctuations of knots that can accelerate electrons to$\sim$PeV energies. The maximum achievable energy of electrons is adopted to beproportional to the size of the knot, which is assumed to follow a power-lawdistribution. Thus the low energy electron flux will be stable due to the largenumber of small knots, while the high energy electron flux may experience largefluctuations. Monte Carlo realization of such a picture can reproduce theobservational data quite well given proper model parameters.

A statistical model to explain the gamma-ray variability and flares of the Crab nebula