The star formation law at GMC scales in M33, the triangulum galaxy

We present a high spatial resolution study, on scales of ~100 pc, of the relationship between star formation rate (SFR) and gas content within Local Group galaxy M33. Combining deep SCUBA-2 observations with archival GALEX, SDSS, WISE, Spitzer, and submillimetre Herschel data, we are able to model the entire SED from UV to sub-mm wavelengths. We calculate the SFR on a pixel-by-pixel basis using the total infrared luminosity, and find a total SFR of 0.17 ± 0.06 M_⊙yr^-1, somewhat lower than our other twomeasures of SFR - combined FUV and 24μmSFR (0.25^+0.10 _-0.07 M_⊙yr^-1) and SED-fitting tool MAGPHYS (0.33^+0.05 _-0.06 M_⊙yr^-1). We trace the total gas using a combination of the 21cm HI line for atomic hydrogen, and CO(J=2-1) data for molecular hydrogen.We have also traced the total gas using dust masses. We study the star formation law in terms of molecular gas, total gas, and gas from dust. We perform an analysis of the star formation law on a variety of pixel scales, from 25 arcsec to 500 arcsec (100 pc to 2 kpc). At kpc scales, we find that a linear Schmidt-type power law index is suitable for molecular gas, but the index appears to be much higher with total gas, and gas from dust. Whilst we find a strong scale dependence on the Schmidt index, the gas depletion time-scale is invariant with pixel scale.