The Star Formation in Radio Survey: Jansky Very Large Array 33 GHz Observations of Nearby Galaxy Nuclei and Extranuclear Star-Forming Regions

We present 33GHz imaging for 112~pointings towards galaxy nuclei and extranuclear star-forming regions at $\approx$2\arcsec~resolution using the Karl~G. Jansky Very~Large~Array (VLA) as part of the Star Formation in Radio Survey. A comparison with 33GHz Robert C. Byrd~Green~Bank~Telescope single-dish observations indicates that the interferometric VLA observations recover $78\pm4\%$ of the total flux density over 25\arcsec~regions~($\approx$ kpc-scales) among all fields. On these scales, the emission being resolved out is most likely diffuse non-thermal synchrotron emission. Consequently, on the $\approx30-300$ pc scales sampled by our VLA observations, the bulk of the 33 GHz emission is recovered and primarily powered by free-free emission from discrete H{\sc ii} regions, making it an excellent tracer of massive star formation. Of the 225 discrete regions used for aperture photometry, 162 are extranuclear (i.e., having galactocentric radii $r_{\rm G} \geq 250$ pc) and detected at $>3\sigma$ significance at 33 GHz and in H$\alpha$. Assuming a typical 33 GHz thermal fraction of 90\%, the ratio of optically-thin 33 GHz-to-uncorrected H$\alpha$ star formation rates indicate a median extinction value on $\approx30-300$ pc scales of $A_{\rm H\alpha} \approx 1.26\pm0.09$ mag with an associated median absolute deviation of 0.87 mag. We find that 10\% of these sources are "highly embedded" (i.e., $A_{\rm H\alpha}\gtrsim3.3$ mag), suggesting that on average H{\sc ii} regions remain embedded for $\lesssim1$ Myr. Finally, we find the median 33 GHz continuum-to-H$\alpha$ line flux ratio to be statistically larger within $r_{\rm G}<250$ pc relative the outer-disk regions by a factor of $1.82\pm0.39$, while the ratio of 33 GHz-to-24 $\mu$m flux densities are lower by a factor of $0.45\pm0.08$, which may suggest increased extinction in the central regions.