THE SCALE DEPENDENCE OF THE MOLECULAR GAS DEPLETION TIME IN M33

We study the Local Group spiral galaxy M33 to investigate how the observed scaling between the (kpc-averaged) surface density of molecular gas (Sigma(H2)) and recent star formation rate (Sigma(SFR)) relates to individual star-forming regions. To do this, we measure the ratio of CO emission to extinction-corrected H alpha emission in apertures of varying sizes centered both on peaks of CO and H alpha emission. We parameterize this ratio as the molecular gas (H-2) depletion time (tau(dep)). On large (kpc) scales, our results are consistent with a molecular star formation law (Sigma(SFR) similar to Sigma(b)(H2)) with b similar to 1.1-1.5 and a median tau(dep) similar to 1 Gyr, with no dependence on type of region targeted. Below these scales, tau(dep) is a strong function of the adopted angular scale and the type of region that is targeted. Small (less than or similar to 300 pc) apertures centered on CO peaks have very long tau(dep) (i.e., high CO-to-H alpha flux ratio) and small apertures targeted toward H alpha peaks have very short tau(dep). This implies that the star formation law observed on kpc scales breaks down once one reaches aperture sizes of less than or similar to 300 pc. For our smallest apertures (75 pc), the difference in tau(dep) between the two types of regions is more than one order of magnitude. This scale behavior emerges from averaging over star-forming regions with a wide range of CO-to-H alpha ratios with the natural consequence that the breakdown in the star formation law is a function of the surface density of the regions studied. We consider the evolution of individual regions the most likely driver for region-to-region differences in tau(dep) (and thus the CO-to-H alpha ratio).