Calibrating Extinction-Free Star Formation Rate Diagnostics with 33GHz Free-Free Emission in NGC6946

Abridged: Using free-free emission measured in the Ka-band (26-40GHz) for 10 star-forming regions in the nearby galaxy NGC6946, including its starbursting nucleus, we compare a number of SFR diagnostics that are typically considered to be unaffected by interstellar extinction: i.e., non-thermal radio (i.e., 1.4GHz), total infrared (IR; 8-1000um), and warm dust (i.e., 24um) emission, along with the hybrid (obscured + unobscured) indicators of H\alpha+24um and UV+IR. The 33GHz free-free emission is assumed to provide the most accurate measure of the current SFR. Among the extranuclear star-forming regions, the 24um, H\alpha+24um and UV+IR SFR calibrations are in good agreement with the 33GHz free-free SFRs. However, each of the SFR calibrations relying on some form of dust emission overestimate the nuclear SFR by a factor of ~2. This is more likely the result of excess dust heating through an accumulation of non-ionizing stars associated with an extended episode of star formation in the nucleus rather than increased competition for ionizing photons by dust. SFR calibrations using the non-thermal radio continuum yield values which only agree with the free-free SFRs for the nucleus, and underestimate the SFRs from the extranuclear star-forming regions by a factor of ~2. This result likely arises from the CR electrons decaying within the starburst region with negligible escape compared to the young extranuclear star-forming regions. Finally, we find that the SFRs estimated using the total 33GHz emission agree well with the free-free SFRs due to the large thermal fractions present at these frequencies even when local diffuse backgrounds are not removed. Thus, rest-frame 33GHz observations may act as a reliable method to measure the SFRs of galaxies at increasingly high redshift without the need of ancillary radio data to account for the non-thermal emission.