Mapping the spectral index of Cassiopeia A: evidence for flattening from radio to infrared

Synchrotron radiation from supernova remnants is caused by electrons accelerated through diffusive shock acceleration (DSA). The standard DSA theory predicts an electron spectral index of p = 2, corresponding to a radio spectral index of α = −0.5. An extension of DSA theory predicts that the accelerated particles change the shock structure, resulting in a spectrum that is steeper than p > 2 (α < −0.5) at low energies and flattens with energy. 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 archival radio (4.72 GHz) and mid-infrared (3.6 μm) data, and we produce a complete spectral index map to investigate the spatial variations within the remnant. We compare this to measurements of the radio spectral index from L-band (1.285 GHz) and C-band (4.64 GHz) maps. Our result shows overall spectral flattening across the remnant (α_R-IR ∼ −0.5 to −0.7), to be compared with the radio spectral index of α_R = −0.77. The flattest values coincide with the locations of most recent particle acceleration. In addition to overall flattening, we detect a relatively steeper region in the south-east of the remnant (α_R-IR ∼ −0.67). We explore whether these locally steeper spectra could be the result of synchrotron cooling, which provides constraints on the local magnetic field strengths and the age of the plasma, suggesting B ≲ 2 mG for an age of 100 yr, and even B ≲ 1 mG using the age of Cas A, in agreement with other estimates.