THE X-FACTOR IN GALAXIES. II. THE MOLECULAR-HYDROGEN-STAR-FORMATION RELATION

There is ample observational evidence that the star formation rate (SFR) surface density, Sigma(SFR), is closely correlated with the surface density of molecular hydrogen, Sigma(H2). This empirical relation holds both for galaxy-wide averages and for individual greater than or similar to kpc sized patches of the interstellar medium, but appears to degrade substantially at a sub-kpc scale. Identifying the physical mechanisms that determine the scale-dependent properties of the observed Sigma(H2)-Sigma(SFR) relation remains a challenge from a theoretical perspective. To address this question, we analyze the slope and scatter of the Sigma(H2)-Sigma(SFR) relation using a set of cosmological, galaxy formation simulations with a peak resolution of similar to 100 pc. These simulations include a chemical network for molecular hydrogen, a model for the CO emission, and a simple, stochastic prescription for star formation that operates on similar to 100 pc scales. Specifically, star formation is modeled as a Poisson process in which the average SFR is directly proportional to the present mass of H-2. The predictions of our numerical model are in good agreement with the observed Kennicutt-Schmidt and Sigma(H2)-Sigma(SFR) relations. We show that observations based on CO emission are ill suited to reliably measure the slope of the latter relation at low (less than or similar to 20 M-circle dot pc(-2)) H-2 surface densities on sub-kpc scales. Our models also predict that the inferred Sigma(H2)-Sigma(SFR) relation steepens at high H-2 surface densities as a result of the surface density dependence of the CO/H-2 conversion factor. Finally, we show that on sub-kpc scales most of the scatter of the relation is a consequence of discreteness effects of the star formation process. In contrast, variations of the CO/H-2 conversion factor are responsible for most of the scatter measured on super-kpc scales.