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We investigate the relationship between HI, H₂, and the star formation rate (SFR) using azimuthally averaged data for seven CO-bright spiral galaxies. Contrary to some earlier studies based on global fluxes, we find that the SFR surface density exhibits a much stronger correlation with the H₂ than with the HI, as the HI surface density saturates at a value of \10 Msol pc^-2 or even declines at large SFR surface densities. Hence the good correlation between the SFR surface density and the total (HI+H₂) gas surface density is driven by the molecular component in these galaxies. We find no clear evidence for a link between the gravitational instability parameter for the gas disk (Qg) and the SFR, and suggest that Qg be considered a measure of the gas fraction. This implies that for a state of marginal gravitational stability to exist in galaxies with low gas fractions, it must be due to instability of the stellar disk. In regions where we have both HI and CO measurements, the ratio of HI to H₂ surface density scales with radius R as roughly R^1. 5, and we suggest that the balance between HI and H₂ is determined primarily by the midplane interstellar pressure. These results favor a "law" of star formation in quiescent disks in which the ambient pressure and metallicity control the formation of molecular clouds from HI, with star formation then occurring at a roughly constant rate per unit H₂ mass. (abstract abridged)
Wong et al. (Mon,) studied this question.