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.
