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 (Σ H2 ) and recent star formation rate (Σ SFR ) relates to individual star-forming regions. To do this, we measure the ratio of CO emission to extinction-corrected Hα emission in apertures of varying sizes centered both on peaks of CO and Hα emission. We parameterize this ratio as the molecular gas (H 2 ) depletion time (τ dep ). On large (kpc) scales, our results are consistent with a molecular star formation law ( Σ SFR ∼ Σ b H2 ) with b ∼ 1.1–1.5 and a median τ dep ∼ 1 Gyr, with no dependence on type of region targeted. Below these scales, τ dep is a strong function of the adopted angular scale and the type of region that is targeted. Small (≲300 pc) apertures centered on CO peaks have very long τ dep (i.e., high CO-to-Hα flux ratio) and small apertures targeted toward Hα peaks have very short τ dep . This implies that the star formation law observed on kpc scales breaks down once one reaches aperture sizes of ≲300 pc. For our smallest apertures (75 pc), the difference in τ 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-Hα 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 τ dep (and thus the CO-to-Hα ratio).