2013AJ....146...19L

We compare molecular gas traced by ¹²CO (2-1) maps from the HERACLES survey, with tracers of the recent star formation rate (SFR) across 30 nearby disk galaxies. We demonstrate a first-order linear correspondence between Σ_mol and Σ_SFRbut also find important second-order systematic variations in the apparent molecular gas depletion time, τ_dep^mol = Σ_mol/Σ_SFR. At the 1 kpc common resolution of HERACLES, CO emission correlates closely with many tracers of the recent SFR. Weighting each line of sight equally, using a fixed α_CO equivalent to the Milky Way value, our data yield a molecular gas depletion time, τ_dep^mol = Σ_mol/Σ_SFR ≈ 2.2 Gyr with 0.3 dex 1σ scatter, in very good agreement with recent literature data. We apply a forward-modeling approach to constrain the power-law index, N, that relates the SFR surface density and the molecular gas surface density, Σ_SFR ∝ Σ_mol^N. We find N = 1±0.15 for our full data set with some scatter from galaxy to galaxy. This also agrees with recent work, but we caution that a power-law treatment oversimplifies the topic given that we observe correlations between τ_dep^mol and other local and global quantities. The strongest of these are a decreased τ_dep^mol in low-mass, low-metallicity galaxies and a correlation of the kpc-scale τ_dep^mol with dust-to-gas ratio, D/G. These correlations can be explained by a CO-to-H₂ conversion factor (α_CO) that depends on dust shielding, and thus D/G, in the theoretically expected way. This is not a unique interpretation, but external evidence of conversion factor variations makes this the most conservative explanation of the strongest observedτ_dep^mol trends. After applying a D/G-dependent α_CO, some weak correlations between τ_dep^mol and local conditions persist. In particular, we observe lower τ_dep^mol and enhanced CO excitation associated with nuclear gas concentrations in a subset of our targets. These appear to reflect real enhancements in the rate of star formation per unit gas, and although the distribution of τ_dep does not appear bimodal in galaxy centers, τ_depdoes appear multivalued at fixed Σ_H2, supporting the idea of "disk" and "starburst" modes driven by other environmental parameters.