Constraints on electron acceleration in the Crab nebula

Using the radio through hard X-ray images of the Crab nebula to derive the spatial dependence of the electron spectrum and the magnetic field distribution from MHD flow models, we have rederived the high-energy spectrum of inverse Compton scattered gamma rays. We find agreement with the observed spectrum at TeV energies, but it is clear that the inverse Compton flux does not contribute significantly to the unpulsed nebular emission observed by COS-B from 50 to 500 MeV, which is consistent with a smooth continuation of the spectrum in hard X-rays. The emission at these energies must therefore be due to synchrotron radiation by electrons of at least PeV energies. It appears that the emission in the high-energy gamma-ray range, sensitive to the highest energy electrons in the nebula, can put interesting constraints on the acceleration mechanism.