We compare molecular gas traced by ^ { 12 } CO ( 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 \Sigma _ { mol } and \Sigma _ { SFR } but also find important second-order systematic variations in the apparent molecular gas depletion time , \tau _ { dep } ^ { mol } = \Sigma _ { mol } / \Sigma _ { 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 alpha _ { CO } equivalent to the Milky Way value , our data yield a molecular gas depletion time , \tau _ { dep } ^ { mol } = \Sigma _ { mol } / \Sigma _ { SFR } \approx 2.2 Gyr with 0.3 dex 1 \sigma 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 , \Sigma _ { SFR } \propto \Sigma _ { mol } ^ { N } .
We find N = 1 \pm 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 \tau _ { dep } ^ { mol } and other local and global quantities .
The strongest of these are a decreased \tau _ { dep } ^ { mol } in low-mass , low-metallicity galaxies and a correlation of the kpc-scale \tau _ { dep } ^ { mol } with dust-to-gas ratio , D/G .
These correlations can be explained by a CO-to-H _ { 2 } conversion factor ( \alpha _ { 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 observed \tau _ { dep } ^ { mol } trends .
After applying a D/G-dependent \alpha _ { CO } , some weak correlations between \tau _ { dep } ^ { mol } and local conditions persist .
In particular , we observe lower \tau _ { 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 \tau _ { dep } does not appear bimodal in galaxy centers , \tau _ { dep } does appear multivalued at fixed \Sigma _ { mol } , supporting the the idea of “ disk ” and “ starburst ” modes driven by other environmental parameters .