  We present a 1.4 GHz Karl G. Jansky Very Large Array (VLA) study of a sample
of early-type galaxies (ETGs) from the volume- and magnitude-limited ATLAS-3D
survey. The radio morphologies of these ETGs at a resolution of 5" are diverse
and include sources that are compact on sub-kpc scales, resolved structures
similar to those seen in star-forming spiral galaxies, and kpc-scale radio
jets/lobes associated with active nuclei. We compare the 1.4 GHz, molecular
gas, and infrared (IR) properties of these ETGs. The most CO-rich ATLAS-3D ETGs
have radio luminosities consistent with extrapolations from H_2-mass-derived
star formation rates from studies of late-type galaxies. These ETGs also follow
the radio-IR correlation. However, ETGs with lower molecular gas masses tend to
have less radio emission relative to their CO and IR emission compared to
spirals. The fraction of galaxies in our sample with high IR-radio ratios is
much higher than in previous studies, and cannot be explained by a systematic
underestimation of the radio luminosity due to the presence extended,
low-surface-brightness emission that was resolved-out in our VLA observations.
In addition, we find that the high IR-radio ratios tend to occur at low IR
luminosities, but are not associated with low dynamical mass or metallicity.
Thus, we have identified a population of ETGs that have a genuine shortfall of
radio emission relative to both their IR and molecular gas emission. A number
of mechanisms may conspire to cause this radio deficiency, including a
bottom-heavy stellar initial mass function, weak magnetic fields, a higher
prevalence of environmental effects compared to spirals and enhanced cosmic ray
losses.
