The Relationship between Gas Content and Star Formation in Molecule-rich Spiral Galaxies

We investigate the relationship between H I, 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 Σ_SFR exhibits a much stronger correlation with Σ than with Σ, as Σ saturates at a value of ~ 10 M_☉ pc^-2 or even declines for large Σ_SFR. Hence, the good correlation between Σ_SFR and the total (H I+H₂) gas surface density Σ_gas is driven by the molecular component in these galaxies, with the observed relation between Σ_SFR and Σ following a Schmidt-type law of index n_mol ≈ 0.8 if a uniform extinction correction is applied or n_mol ≈ 1.4 for a radially varying correction dependent on gas density. The corresponding Schmidt law indices for Σ_gas versus Σ_SFR are 1.1 and 1.7 for the two extinction models, in rough agreement with previous studies of the disk-averaged star formation law. An alternative to the Schmidt law, in which the gas depletion timescale is proportional to the orbital timescale, is also consistent with the data if radially varying extinction corrections are applied. We find no clear evidence for a link between the gravitational instability parameter for the gas disk (Q_g) and the SFR, and we suggest that Q_g 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 enforced by the stellar component. In regions where we have both H I and CO measurements, the ratio of H I to H₂ surface density scales with radius as roughly R^1.5, and we suggest that the balance between H I 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 H I, with star formation then occurring at a roughly constant rate per unit H₂ mass.