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A self-consistent model based on gravitational instability is developed for the rate of global star formation as a function of radius in galactic disks. The star-formation timescale is assumed to be proportional to the growth time of gravitational instability in a disk consisting of stars and gas, and the stellar contribution to the instability is included. We postulate that small clouds agglomerate to form massive clouds, dissipating their kinetic energy within a time comparable to that of the ensuing star formation. The derived star-formation rate in galactic disks may be compared to a Schmidt law with a power-law index of about 2 in the dependence on the total gas surface density, but the star formation rate is also proportional to the epicyclic frequency, resulting in a steep radial decline of the star formation rate with Galactic radius. Our formulation naturally introduces a cutoff in the star-formation rate according to the condition of gravitational instability for gaseous disks (the Q criterion). We compare our results with relevant observations in the Galaxy. We take a conservative approach that does not require gas infall or radial flows; an initial metallicity is adopted to resolve the G-dwarf problem. The model has two adjustable parameters: the star-formation efficiency in the disk, and the initial cloud covering factor of the disk. The time evolution of the disk formation and the heavy element abundance at various Galactocentric radii are calculated for a specified disk gas surface density, differential rotation curve, and initial stellar mass function. Our model plausibly reproduces the observed star-formation rate, the metallicity distribution among G-dwarf stars, and the age-metallicity relation for F-dwarfs in the solar neighborhood. Our calculations also account approximately for the observed total gas surface density, the star-formation rate, and the heavy element abundance as a function of radius in the Galaxy. The success of our simple model emphasizes that gravitational instability is principally responsible for star formation activity in galactic disks. Application of our results to galactic disks at early times may provide insight into understanding observations of distant faint galaxies, and our simple analytical formulation of global star formation can be utilized in hydrodynamical simulations of large-scale galaxy formation and evolution.
Wang et al. (Wed,) studied this question.