The star-formation law at GMC scales in M33, the Triangulum Galaxy

We present a high spatial resolution study, on scales of $\sim$100pc, 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 $0.17 \pm 0.06\,\rm{M}_\odot$/yr, somewhat lower than our other two measures of SFR -- combined FUV and 24$\mu$m SFR ($0.25^{+0.10}_{-0.07}\,\rm{M}_\odot$/yr) and SED-fitting tool MAGPHYS ($0.33^{+0.05}_{-0.06}\,\rm{M}_\odot$/yr). We trace the total gas using a combination of the 21cm HI line for atomic hydrogen, and CO($\textit{J}$=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$^{\prime\prime}$ to 500$^{\prime\prime}$ (100pc to 2kpc). 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 timescale is invariant with pixel scale.