A statistical model for the gamma-ray variability and flare of the Crab nebula

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