Radio and Mid-Infrared Properties of Compact Starbursts: Distancing Themselves from the Main Sequence

We investigate the relationship between 8.44\,GHz brightness temperatures and 1.4 to 8.44\,GHz radio spectral indices with 6.2\,$\mu$m polycyclic aromatic hydrocarbon (PAH) emission and 9.7\,$\mu$m silicate absorption features for a sample of 36 local luminous and ultra-luminous infrared galaxies. We find that galaxies having small 6.2\,$\mu$m PAH equivalent widths (EQWs), which signal the presence of weak PAH emission and/or an excess of very hot dust, also have flat spectral indices. The three active galactic nuclei (AGN) identified through their excessively large 8.44\,GHz brightness temperatures are also identified as AGN via their small 6.2\,$\mu$m PAH EQWs. We also find that the flattening of the radio spectrum increases with increasing silicate optical depth, 8.44\,GHz brightness temperature, and decreasing size of the radio source even after removing potential AGN, supporting the idea that compact starbursts show spectral flattening as the result of increased free-free absorption. These correlations additionally suggest that the dust obscuration in these galaxies must largely be coming from the vicinity of the compact starburst itself, and is not distributed throughout the (foreground) disk of the galaxy. Finally, we investigate the location of these infrared-bright systems relative to the main sequence (star formation rate vs. stellar mass) of star-forming galaxies in the local universe. We find that the radio spectral indices of galaxies flattens with increasing distance above the main sequence, or in other words, with increasing specific star formation rate. This indicates that galaxies located above the main sequence, having high specific star formation rates, are typically compact starbursts hosting deeply embedded star formation that becomes more optically thick in the radio and infrared with increased distance above the main sequence.