We report on our analysis of the 1 Ms Chandra observation of the supernova remnant Cas A in order to localize, characterize, and quantify the nonthermal X-ray emission. More specifically, we investigated whether the X-ray synchrotron emission from the inside of the remnant is from the outward shock, but projected toward the inner ring, or from the inner shell. We tackled this problem by employing a Lucy-Richardson deconvolution technique and measuring spectral indices in the 4.2-6 keV band. We show that most of the continuum emission is coming from an inner ring that coincides with the previously reported location of the reverse shock. This inner ring also includes filaments whose X-ray emission has been found to be dominated by X-ray synchrotron emission. The X-ray emission from these filaments, both at the forward shock and from the inner ring, have relatively hard spectra with spectral index >–3.1. The regions emitting hard X-ray continuum contribute about 54% of the total X-ray emission in the 4.2-6 keV. This is lower than that suggested by extrapolating the hard X-ray spectrum as measured by BeppoSAX PDS and INTEGRAL. This can be reconciled by assuming a gradual steepening of the spectrum toward higher energies. We argue that the X-ray synchrotron emission is mainly coming from the western part of the reverse shock. The reverse shock in the west is almost at rest in our observation frame, corresponding to a relatively high reverse shock velocity of ~6000 km s−1 in the frame of the freely expanding ejecta
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