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We present new observations and photoionization calculations for investigating gaseous regions that represent expected nuclear processing in the Crab Nebula supernova remnant. High helium abundance is shown to cause a very efficient [N II] ¸¸6548,6583 emitting zone which can account for some strong nitrogen emission. This high helium abundance causes strong emission of [C I] ¸¸9823,9850. When emission line measurements are compared with model simulations, most of the nebular gas appears to have depleted or solar nitrogen and enhanced carbon. This argues for a precursor star that had a mass greater than 9.5M¯. We also use images of selected emission lines along with photoionization calculations to investigate the overall spatial distribution of elements in the Crab Nebula. We introduce new methods of calibrating direct images, including using existing Fabry-Perot data to take into account the different line-of-sight velocities of each individual filament. After processing, we compare these flux distributions with a large number of numerical model simulations to produce abundance maps of helium, nitrogen, oxygen, and sulfur in the Crab Nebula. These maps show evidence of gas that has undergone Carbon-Nitrogen-Oxygen processing, helium-burning, and oxygen-burning. High sulfur abundances mixed with gas representative of CNO processing were most likely generated from an off-center oxygen flash and then repositioned north and southeast from the pulsar by a relativistic wind. Clear evidence of oxygen burning material in the remnant gives strong support for a precursor star mass near 10M¯.

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