A Radio Study of the Crab Nebula.

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I present VLA radio observations of the Crab Nebula at 1410, 1515, 4625 and 4885 MHz, with 1.8^ {''} resolution, and at 14 GHz with 6.5^{'' } resolution. In integrated emission, the Nebula seems to be mostly resolved at 1.8^ {''} resolution. In polarized emission, however, considerable small-scale structure is visible. Over the Nebula, the rotation measure (RM) is relatively uniform at -21 rad m ^{-2}, which is probably the interstellar value. The Nebula is weakly polarized (5% at 1.5 GHz; 8% at 5 GHz) in the center, while the periphery and the Crab Nebula 'jet' are at least 30% polarized. I show that the synchrotron emitting regions must be quite separate from the Faraday rotating regions. In the former, the scale size of the magnetic field is about 10^ {''}, and the density of thermal electrons is probably <0.01 cm^{-3}. The depolarization between 5 and 1.5 GHz is due to a network of Faraday rotating filaments of sizes <1^{ ''} which contain thermal gas. The projected field seems to be largely radial near the periphery of the Nebula, and shows little correlation with the total intensity structure. The Crab Nebula 'jet' is shown to have a projected field along its length. Its RM and spectral index (alpha) are indistinguishable from those of the rest of the Nebula. Over the rest of the Nebula, alpha is almost constant. In particular, it steepens by less than 0.05 near the edge of the Nebula. The filaments do not show steeper alpha than the body of the nebula even at 14 GHz. Using the 1982 VLA observations made by A. Wilson and D. Hogg, I show that the synchrotron nebula is expanding at about the same rate as the filaments. The outside edge of the Nebula has been post accelerated by about 10%. Features similar to, but not exactly coincident with Scargle's 'wisps' are detected in the radio. They have flatter alpha than the rest of the Nebula and display some motion between 1982 and 1987. Other changes are observed, but are difficult to characterize.

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