We study gravitational instability and consequent star formation in a wide range of isolated disk galaxies , using three-dimensional , smoothed particle hydrodynamics simulations at resolution sufficient to fully resolve gravitational collapse .
Stellar feedback is represented by an isothermal equation of state .
Absorbing sink particles are inserted in dynamically bound , converging regions with number density n > 10 ^ { 3 } cm ^ { -3 } to directly measure the mass of gravitationally collapsing gas available for star formation .
Our models quantitatively reproduce not only the observed Schmidt law , but also the observed star formation threshold in disk galaxies .
Our results suggest that the dominant physical mechanism determining the star formation rate is just the strength of gravitational instability , with feedback primarily functioning to maintain a roughly constant effective sound speed .