The Star Formation in Radio Survey: GBT 33 GHz Observations of Nearby Galaxy Nuclei and Extranuclear Star-Forming Regions

We present 33\,GHz photometry of 103 galaxy nuclei and extranuclear star-forming complexes taken with the Green Bank Telescope (GBT) as part of the Star Formation in Radio Survey (SFRS). Among the sources without evidence for an AGN, and also having lower frequency radio data, we find a median thermal fraction at 33GHz of ~76% with a dispersion of ~24%. For all sources resolved on scales <0.5kpc, the thermal fraction is even larger, being >90%. This suggests that the rest-frame 33GHz emission provides a sensitive measure of the ionizing photon rate from young star-forming regions, thus making it a robust star formation rate indicator. Taking the 33GHz star formation rates as a reference, we investigate other empirical calibrations relying on different combinations of warm 24\mu m dust, total infrared (IR; 8-1000\mu m), H\alpha\ line, and far-UV continuum emission. The recipes derived here generally agree with others found in the literature, albeit with a large dispersion that most likely stems from a combination of effects. Comparing the 33GHz to total IR flux ratios as a function of the radio spectral index, measured between 1.7 and 33GHz, we find that the ratio increases as the radio spectral index flattens which does not appear to be a distance effect. Consequently, the ratio of non-thermal to total IR emission appears relatively constant, suggesting only moderate variations in the cosmic-ray electron injection spectrum and ratio of synchrotron to total cooling processes among star-forming complexes. Assuming that this trend solely arises from an increase in the thermal fraction sets a maximum on the scatter of the non-thermal spectral indices among the star-forming regions of \sigma_\alpha^{NT} < 0.13.