Star Formation in Isolated Disk Galaxies. Ii. Schmidt Laws and Efficiency of Gravitational Collapse

We model gravitational instability in a wide range of isolated disk galaxies, using GADGET, a three-dimensional, smoothed particle hydrodynamics code. The model galaxies include a dark matter halo and a disk of stars and isothermal gas. Absorbing sink particles are used to directly measure the mass of gravitationally collapsing gas. Below the density at which they are inserted, the collapsing gas is fully resolved. We make the assumption that stars and molecular gas form within the sink particle once it is created, and that the star formation rate is the gravitational collapse rate times a constant efficiency factor. In our models, the derived star formation rate declines exponentially with time, and radial profiles of atomic and molecular gas and star formation rate reproduce observed behavior. We derive from our models and discuss both the global and local Schmidt laws for star formation: power-law relations between surface densities of gas and star formation rate. The global Schmidt law observed in disk galaxies is quantitatively reproduced by our models. We find that the surface density of star formation rate directly correlates with the strength of local gravitational instability. The local Schmidt laws of individual galaxies in our models show clear evidence of star formation thresholds. The variations in both the slope and the normalization of the local Schmidt laws cover the observed range. The averaged values agree well with the observed average, and with the global law. Our results suggest that the non-linear development of gravitational instability determines the local and global Schmidt laws, and the star formation thresholds. We derive from our models the quantitative dependence of the global star formation efficiency on the initial gravitational instability of galaxies. The more unstable a galaxy is, the quicker and more efficiently its gas collapses gravitationally and forms stars. Subject headings: galaxy: evolution — galaxy: spiral — galaxy: kinematics and dynamics — galaxy: ISM — galaxy: star clusters — stars: formation