Abstract
Maps of the Crab Nebula at 2.7, 5 and 23 GHz, with resolution of a few arcseconds, are compared in detail. In this frequency range it is found that there are no variations in spectral index over the source greater than ±0.3. The synchrotron spectrum of the filaments does not differ systematically from that of the rest of the source, indicating that the relativistic electrons in the filaments and the surrounding material have the same origin – the pulsar. Consideration of the electron synchrotron lifetimes and the location of the filaments in the nebula shows that continuum emission from the filaments is probably detectable at frequencies up to several thousand GHz, but no higher. Polarization maps at 2.7 and 5 GHz are compared with new optical radial velocity data on the filaments, confirming that depolarization between these frequencies is caused chiefly by bright filaments on the near side of the nebula. The brightest filaments have enhanced polarization at their edges, irrespective of their position in the nebula. A new model for the magnetic field in the filaments, based on the properties of a thin slab of randomly-oriented field, is used to explain these observations.
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