Measuring star formation with resolved observations: the test case of M 33

Context. Measuring star formation on a local scale is important to constrain star formation laws. It is not clear yet, however, whether and how the measure of star formation is affected by the spatial scale at which a galaxy is observed. Aims. We wish to understand the impact of the resolution on the determination of the spatially resolved star formation rate (SFR) and other directly associated physical parameters such as the attenuation. Methods. We carried out a multi-scale, pixel-by-pixel study of the nearby galaxy M33. Assembling FUV, H alpha, 8 mu m, 24 mu m, 70 mu m, and 100 mu m maps, we have systematically compared the emission in individual bands with various SFR estimators from a resolution of 33 pc to 2084 pc. Results. There are strong, scale-dependent, discrepancies of up to a factor 3 between monochromatic SFR estimators and H alpha + 24 mu m. The scaling factors between individual IR bands and the SFR show a strong dependence on the spatial scale and on the intensity of star formation. Finally, strong variations of the differential reddening between the nebular emission and the stellar continuum are seen, depending on the specific SFR (sSFR) and on the resolution. At the finest spatial scales, there is little differential reddening at high sSFR. The differential reddening increases with decreasing sSFR. At the coarsest spatial scales the differential reddening is compatible with the canonical value found for starburst galaxies. Conclusions. Our results confirm that monochromatic estimators of the SFR are unreliable at scales smaller than 1 kpc. Furthermore, the extension of local calibrations to high-redshift galaxies presents non-trivial challenges because the properties of these systems may be poorly known.