Control of Star Formation in Galaxies by Gravitational Instability
  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. 
Yuexing Li, Mordecai-Mark Mac Low, and Ralf S. Klessen