Star Formation Rates in Resolved Galaxies: Calibrations with Near and Far Infrared Data for NGC5055 and NGC6946

We use the near--infrared Br\gamma hydrogen recombination line as a reference star formation rate (SFR) indicator to test the validity and establish the calibration of the {\it Herschel} PACS 70 \mu m emission as a SFR tracer for sub--galactic regions in external galaxies. Br\gamma offers the double advantage of directly tracing ionizing photons and of being relatively insensitive to the effects of dust attenuation. For our first experiment, we use archival CFHT Br\gamma and Ks images of two nearby galaxies: NGC\,5055 and NGC\,6946, which are also part of the {\it Herschel} program KINGFISH (Key Insights on Nearby Galaxies: a Far-Infrared Survey with Herschel). We use the extinction corrected Br\gamma emission to derive the SFR(70) calibration for H{\sc ii} regions in these two galaxies. A comparison of the SFR(70) calibrations at different spatial scales, from 200 pc to the size of the whole galaxy, reveals that about 50% of the total 70\mu m emission is due to dust heated by stellar populations that are unrelated to the current star formation. We use a simple model to qualitatively relate the increase of the SFR(70) calibration coefficient with decreasing region size to the star formation timescale. We provide a calibration for an unbiased SFR indicator that combines the observed H\alpha with the 70 \mu m emission, also for use in H{\sc ii} regions. We briefly analyze the PACS 100 and 160 \mu m maps and find that longer wavelengths are not as good SFR indicators as 70\mu m, in agreement with previous results. We find that the calibrations show about 50% difference between the two galaxies, possibly due to effects of inclination.