Mapping the radio to mid-infrared spectral index of Cas A: evidence for flattening and a cooling break

Non-linear shock acceleration models predict a flattening of synchrotron radiation spectrum at higher frequencies. For Cassiopeia A a synchrotron spectral flattening was previously reported for a small part of the remnant in the mid-infrared regime. Here we present new measurements for spectral flattening using the archival radio (4.72~GHz) and mid-infrared (3.6~$\mu$m) data, and produce a complete spectral index map to investigate the spatial variations within the remnant. Our result shows overall spectral flattening across the remnant ($\alpha \sim -0.5$ to $-0.7$), with the flattest values coinciding with the locations of most recent particle acceleration. In addition to overall flattening, we also detect a relatively steeper region in the Southeast of the remnant ($\alpha \sim -0.67$). We argue that this could be a signature of a cooling break, and estimate the lower limit of magnetic field to be $B \sim 420$~$\mu$G, consistent with other magnetic-field strength estimates.