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We investigate the relationship between 8.44\,GHz brightness temperatures and1.4 to 8.44\,GHz radio spectral indices with 6.2\,$\mu$m polycyclic aromatichydrocarbon (PAH) emission and 9.7\,$\mu$m silicate absorption features for asample of 36 local luminous and ultra-luminous infrared galaxies. We find thatgalaxies having small 6.2\,$\mu$m PAH equivalent widths (EQWs), which signalthe presence of weak PAH emission and/or an excess of very hot dust, also haveflat spectral indices. The three active galactic nuclei (AGN) identifiedthrough their excessively large 8.44\,GHz brightness temperatures are alsoidentified as AGN via their small 6.2\,$\mu$m PAH EQWs. We also find that theflattening of the radio spectrum increases with increasing silicate opticaldepth, 8.44\,GHz brightness temperature, and decreasing size of the radiosource even after removing potential AGN, supporting the idea that compactstarbursts show spectral flattening as the result of increased free-freeabsorption. These correlations additionally suggest that the dust obscurationin these galaxies must largely be coming from the vicinity of the compactstarburst itself, and is not distributed throughout the (foreground) disk ofthe galaxy. Finally, we investigate the location of these infrared-brightsystems relative to the main sequence (star formation rate vs. stellar mass) ofstar-forming galaxies in the local universe. We find that the radio spectralindices of galaxies flattens with increasing distance above the main sequence,or in other words, with increasing specific star formation rate. This indicatesthat galaxies located above the main sequence, having high specific starformation rates, are typically compact starbursts hosting deeply embedded starformation that becomes more optically thick in the radio and infrared withincreased distance above the main sequence.

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