Star formation in isolated disk galaxies. I. Models and characteristics of nonlinear gravitational collapse

We model gravitational collapse leading to star formation in a wide range of isolated disk galaxies using 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. They reach masses characteristic of stellar clusters. In this paper we describe our galaxy models and numerical methods, followed by an investigation of the gravitational instability in these galaxies. Gravitational collapse forms star clusters with correlated positions and ages, as observed, for example, in the Large Magellanic Cloud. Gravitational instability alone acting in unperturbed galaxies appears sufficient to produce flocculent spiral arms, although not more organized patterns. Unstable galaxies show collapse in thin layers in the galactic plane; associated dust will form thin dust lanes in those galaxies, in agreement with observations. We find an exponential relationship between the global collapse timescale and the minimum value in a galaxy of the Toomre instability parameter for a combination of stars and gas Q_sg. Furthermore, collapse occurs only in regions with Q_sg < 1.6. Our results suggest that vigorous starbursts occur where Q_sg ≪ 1, while slow star formation takes place at higher values of Q_sg below 1.6. A massive, or gas-rich, galaxy has low initial Q_sg, giving it a high star formation rate, while a low-mass, or gas-poor, galaxy has a high initial Q_sg, giving it a low star formation rate.