The empirical star formation law on kpc scales is essentially one where star formation follows CO-emitting molecular gas with a constant rate per molecule, and the ratio of molecular to atomic gas scales nearly directly with the ISM pressure (Bigiel et al. 2008, Leroy et al. 2008). The rate per molecule corresponds to a consumption time of molecular gas equal to about 2 Gyr. The place in a galaxy where the transition occurs between HI dominance in the outer part to H2 dominance in the inner part is at a pressure of P = 2.3 ± 1.5 × 104 kB K cm-3. There also tend to be characteristic gas and stellar column densities at this place, and a characteristic galactic orbit time for all of the galaxies observed. Beyond this radius is the atomic-dominated outer disk. There, the SFR scales directly with HI, and the consumption time is about 100 Gyr.
Theoretical models of these empirical laws include the atomic-to-molecular transition in individual clouds and a sum over clouds to give the galactic scaling laws. Star formation occurs only in the densest parts of the clouds, as determined by a combination of turbulence-compression and self-gravity. Numerous simulations of star formation in galaxies can reproduce these empirical laws fairly well. The simulations usually show a sensitivity to the Toomre Q parameter, unlike the observations.