Measuring star formation with resolved observations: the test case of
  M33
  Context. Measuring star formation at a local scale is important to constrain
star formation laws. Yet, it is not clear whether and how the measure of star
formation is affected by the spatial scale at which a galaxy is observed. Aims.
We want 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 have carried out a
multi-scale, pixel-by-pixel study of the nearby galaxy M33. Assembling FUV,
Halpha, 8, 24, 70, and 100 micron maps, we have systematically compared the
emission in individual bands with various SFR estimators from a resolution of
33 pc to 2084 pc. Results. We have found that there are strong,
scale-dependent, discrepancies up to a factor 3 between monochromatic SFR
estimators and Halpha+24 micron. 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 as the properties of these systems may be poorly known.
