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It is generally accepted that astrophysical sources cannot emit synchrotronradiation above 160 MeV in their rest frame. This limit is given by the balancebetween the accelerating electric force and the radiation reaction force actingon the electrons. The discovery of synchrotron gamma-ray flares in the CrabNebula, well above this limit, challenges this classical picture of particleacceleration. To overcome this limit, particles must accelerate in a region ofhigh electric field and low magnetic field. This is possible only with anon-ideal magnetohydrodynamic process, like magnetic reconnection. We presentthe first numerical evidence of particle acceleration beyond the synchrotronburnoff limit, using a set of 2D particle-in-cell simulations ofultra-relativistic pair plasma reconnection. We use a new code, Zeltron, thatincludes self-consistently the radiation reaction force in the equation ofmotion of the particles. We demonstrate that the most energetic particles moveback and forth across the reconnection layer, following relativistic Speiserorbits. These particles then radiate >160 MeV synchrotron radiation rapidly,within a fraction of a full gyration, after they exit the layer. Our analysisshows that the high-energy synchrotron flux is highly variable in time becauseof the strong anisotropy and inhomogeneity of the energetic particles. Wediscover a robust positive correlation between the flux and the cut-off energyof the emitted radiation, mimicking the effect of relativistic Doppleramplification. A strong guide field quenches the emission of >160 MeVsynchrotron radiation. Our results are consistent with the observed propertiesof the Crab flares, supporting the reconnection scenario.

Simulations of particle acceleration beyond the classical synchrotron burnoff limit in magnetic reconnection: An explanation of the Crab flares