Physics of the saturation of particle acceleration in relativistic magnetic reconnection

We investigate the saturation of particle acceleration in relativistic reconnection using two-dimensional particle-in-cell simulations at various magnetizations sigma. We find that the particle energy spectrum produced in reconnection quickly saturates as a hard power law that cuts off at gamma approximate to 4 sigma, confirming previous work. Using particle tracing, we find that particle acceleration by the reconnection electric field in X-points determines the shape of the particle energy spectrum. By analysing the current sheet structure, we show that physical cause of saturation is the spontaneous formation of secondary magnetic islands that can disrupt particle acceleration. By comparing the size of acceleration regions to the typical distance between disruptive islands, we show that the maximum Lorentz factor produced in reconnection is gamma approximate to 5 sigma, which is very close to what we find in our particle energy spectra. We also show that the dynamic range in Lorentz factor of the power-law spectrum in reconnection is <= 40. The hardness of the power law combined with its narrow dynamic range implies that relativistic reconnection is capable of producing the hard narrow-band flares observed in the Crab nebula but has difficulty producing the softer broad-band prompt gamma-ray burst emission.