On the variability of the GeV and multi-TeV gamma-ray emission from the Crab Nebula

Recently the AGILE $\gamma$-ray telescope has reported the enhanced $\gamma$-ray emission above 100 MeV from the direction of the Crab Nebula during a period of a few days. This intriguing observation has been confirmed by the Fermi-LAT telescope. This emission does not show evidences of pulsations with the Crab pulsar. It seems that it originates at the shock region created as a result of the interaction of the pulsar wind with the nebula. We propose that such variable $\gamma$-ray emission originate in the region behind the shock when the electrons can be accelerated as a result of the reconnection of the magnetic field compressed by the decelerating pulsar wind. The natural consequence of such interpretation is the prediction that the Crab Nebula $\gamma$-ray spectrum produced by electrons as a result of the inverse Compton scattering of soft radiation to multi-TeV energies should also show synchronous variability on the time scales as observed at GeV energies by the AGILE and Fermi-LAT telescopes. We calculate how the end of the IC component of the Crab Nebula $\gamma$-ray spectrum should look like during the quiescent and the flare GeV $\gamma$-ray emission. We conclude that the variability of the multi-TeV $\gamma$-ray spectrum from the Crab Nebula might in principle be responsible for the differences between the spectral features reported by the HEGRA and HESS Collaborations at the multi-TeV energies.