Galactic-scale star formation by gravitational instability

I review the dependence of star formation on the nonlinear development of gravitational instability in galaxies. In the last several years, high-resolution numerical models of star cluster formation in disk galaxies using both grid and particle techniques have been done. Models of both isolated galaxies and galaxies embedded in the cosmological context reproduce observed global and local Schmidt laws (relationships between gas surface density and star formation rate). Isolated models also reproduce star formation thresholds in disk galaxies, and correlations between star cluster positions and ages. Globular cluster formation also appears to be explainable with similar principles. I discuss the assumptions made in the models, including the different feedback prescriptions used, and the question of how star formation occurs in collapsing regions. Models of molecular cloud formation show that it can occur in a few megayears. However, star formation cannot follow immediately, or star formation rates in our own galaxy would be too high, given the amount of molecular gas present, suggesting that the conversion from molecular gas to stars may be extended over 10-20 Myr. I conclude by comparing and contrasting models that derive the star formation rate primarily from global gravitational instability to those that rely primarily on the local behaviour of the molecular clouds.