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.
