CALIBRATING EXTINCTION-FREE STAR FORMATION RATE DIAGNOSTICS WITH 33 GHz FREE-FREE EMISSION IN NGC 6946
Using free-free emission measured in the Ka band (26-40 GHz) for 10 star-forming regions in the nearby galaxy NGC 6946, including its starbursting nucleus, we compare a number of star formation rate (SFR) diagnostics that are typically considered to be unaffected by interstellar extinction. These diagnostics include non-thermal radio (i.e., 1.4 GHz), total infrared (IR; 8-1000 {mu}m), and warm dust (i.e., 24 {mu}m) emission, along with hybrid indicators that attempt to account for obscured and unobscured emission from star-forming regions including H{alpha} + 24 {mu}m and UV + IR measurements. The assumption is made that the 33 GHz free-free emission provides the most accurate measure of the current SFR. Among the extranuclear star-forming regions, the 24 {mu}m, H{alpha} + 24 {mu}m, and UV + IR SFR calibrations are in good agreement with the 33 GHz free-free SFRs. However, each of the SFR calibrations relying on some form of dust emission overestimates the nuclear SFR by a factor of {approx}2 relative to the 33 GHz free-free SFR. 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 33 GHz free-free SFRs for the nucleus and underestimate the SFRs from the extranuclear star-forming regions by an average factor of {approx}2 and {approx}4-5 before and after subtracting local background emission, respectively. This result likely arises from the cosmic-ray (CR) electrons decaying within the starburst region with negligible escape, whereas the transient nature of star formation in the young extranuclear star-forming complexes allows for CR electrons to diffuse significantly further than dust-heating photons, resulting in an underestimate of the true SFR. Finally, we find that the SFRs estimated using the total 33 GHz flux density appear to agree well with those estimated using free-free emission due to the large thermal fractions present at these frequencies even when local diffuse backgrounds are not removed. Thus, rest-frame 33 GHz 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.