We used the BIMA array to map the supernova remnant Cas A from 28 to 87 GHz with 2'' to 7'' angular resolution. Data from 75 to 87 GHz with 19 pointing centers were combined with single-dish data to form a completely sampled image. These new BIMA images were compared with VLA images at 1.5 and 5 GHz to look for spectral index variations across Cas A. The images were spatially filtered and convolved to a common sampled UV range corresponding to angular scales from 7'' to 95''. The images give direct evidence for a steeper spectral index in the knots outside the bright ring. Analysis of the 26 brightest peaks gives statistical evidence for spectral index variations throughout the remnant. The high-frequency spectra confirm and extend the spectral variations seen previously at lower frequencies. The spectra are largely consistent with different power laws and not curved spectra. This provides strong support for local variations in the acceleration of relativistic particles in Cas A.
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