2010ApJ...716L.131M

We offer a simple parameterization of the rate of star formation in galaxies. In this new approach, we make explicit and decouple the timescales associated (1) with disruptive effects of the star formation event itself from (2) the timescales associated with the cloud assembly and collapse mechanisms leading up to star formation. The star formation law in near-by galaxies, as measured on sub-kiloparsec scales, has recently been shown by Bigiel et al. to be distinctly nonlinear in its dependence on total gas density. Our parameterization of the spatially resolved Schmidt-Sanduleak relation naturally accommodates that dependence. The parameterized form of the relation is ρ_* ∼ ερ_g/(τ_s+ ρ^–n _g), where ρ_gis the gas density, ε is the efficiency of converting gas into stars, and ρ^–n _g captures the physics of cloud collapse. Accordingly at high gas densities, quiescent star formation is predicted to progress as ρ_*∼ ρ_g, while at low gas densities ρ_*∼ ρ¹⁺ⁿ _g, as is now generally observed. A variable efficiency in locally converting gas into stars as well as the unknown plane thickness variations from galaxy to galaxy, and radially within a given galaxy, can readily account for the empirical scatter in the observed (surface density rather than volume density) relations, and also plausibly account for the noted upturn in the relation at very high apparent projected column densities.