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The gamma-ray space telescopes AGILE and Fermi detected short and brightsynchrotron gamma-ray flares at photon energies above 100 MeV in the CrabNebula. This discovery suggests that electron-positron pairs in the nebula areaccelerated to PeV energies in a milliGauss magnetic field, which is difficultto explain with classical models of particle acceleration and pulsar windnebulae. We investigate whether particle acceleration in a magneticreconnection layer can account for the puzzling properties of the flares. Wenumerically integrate relativistic test-particle orbits in the vicinity of thelayer, including the radiation reaction force, and using analytical expressionsfor the large-scale electromagnetic fields. As they get accelerated by thereconnection electric field, the particles are focused deep inside the currentlayer where the magnetic field is small. The electrons suffer less fromsynchrotron losses and are accelerated to extremely high energies. Populationstudies show that, at the end of the layer, the particle distribution piles upat the maximum energy given by the electric potential drop and is focused intoa thin fan beam. Applying this model to the Crab Nebula, we find that theemerging synchrotron emission spectrum peaks above 100 MeV and is close to thespectral shape of a single electron. The flare inverse Compton emission isnegligible and no detectable emission is expected at other wavelengths. Thismechanism provides a plausible explanation for the gamma-ray flares in the CrabNebula and could be at work in other astrophysical objects such as relativisticjets in active galactic nuclei.

Extreme particle acceleration in magnetic reconnection layers. Application to the gamma-ray flares in the Crab Nebula