A molecular star formation law in the atomic-gas-dominated regime in nearby galaxies

We use the IRAM HERACLES survey to study CO emission from 33 nearby spiral galaxies down to very low intensities. Using 21 cm line atomic hydrogen (H I) data, mostly from THINGS, we predict the local mean CO velocity based on the mean HI velocity. By re-normalizing the CO velocity axis so that zero corresponds to the local mean HI velocity we are able to stack spectra coherently over large regions. This enables us to measure CO intensities with high significance as low as I(CO) approximate to 0.3 K km s(-1) (Sigma(H2) approximate to 1 M(circle dot) pc(-2)), an improvement of about one order of magnitude over previous studies. We detect CO out to galactocentric radii r(gal) similar to r(25) and find the CO radial profile to follow a remarkably uniform exponential decline with a scale length of similar to 0.2 r(25). Here we focus on stacking as a function of radius, comparing our sensitive CO profiles to matched profiles of HI, H alpha, far-UV (FUV), and Infrared (IR) emission! at 24 mu m and 70 mu m. We observe a tight, roughly linear relationship between CO and IR intensity that does not show any notable break between regions that are dominated by molecular gas (Sigma(H2) > Sigma(HI)) and those dominated by atomic gas (Sigma(H2) < Sigma(HI)). We use combinations of FUV+ 24 mu m and H alpha + 24 mu m to estimate the recent star formation rate (SFR) surface density, Sigma(SFR), and find approximately linear relations between Sigma(SFR) and Sigma(H2). We interpret this as evidence of stars forming in molecular gas with little dependence on the local total gas surface density. While galaxies display small internal variations in the SFR-to-H(2) ratio, we do observe systematic galaxy-to-galaxy variations. These galaxy-to-galaxy variations dominate the scatter in relationships between CO and SFR tracers measured at large scales. The variations have the sense that less massive galaxies exhibit larger ratios of SFR-to-CO than massive galaxies. Unl! ike the SFR-to-CO ratio, the balance between atomic and molecu! lar gas depends strongly on the total gas surface density and galactocentric radius. It must also depend on additional parameters. Our results reinforce and extend to lower surface densities, a picture in which star formation in galaxies can be separated into two processes: the assembly of star-forming molecular clouds and the formation of stars from H(2). The interplay between these processes yields a total gas-SFR relation with a changing slope, which has previously been observed and identified as a star formation threshold.