Two Chandra observations have been used to search for thermal X-ray emission from within and around the Crab Nebula. Dead-time was minimized by excluding the brightest part of the Nebula from the field of view. A dust-scattered halo comprising 5% of the strength of the Crab is clearly detected with surface brightness measured out to a radial distance of 18 arcminutes. Coverage is 100% at 4 arcminutes, 50% at 12 arcminutes, and 25% at 18 arcminutes. The observed halo is compared with predictions based on 3 different interstellar grain models and one can be adjusted to fit the observation. This dust halo and mirror scattering form a high background region which has been searched for emission from shock-heated material in an outer shell. We find no evidence for such emission. We can set upper limits a factor of 10-1000 less than the surface brightness observed from outer shells around similar remnants. The upper limit for X-ray luminosity of an outer shell is about 10e34 erg/s. Although it is possible to reconcile our observation with an 8-13 solar mass progenitor, we argue that this is unlikely.
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