GRAVITATIONAL-INSTABILITY AND DISK STAR-FORMATION

A self-consistent model based on gravitational instability is develope d for the rate of global star formation as a function of radius in gal actic disks. The star-formation timescale is assumed to be proportiona l 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 c louds, dissipating their kinetic energy within a time comparable to th at of the ensuing star formation. The derived star-formation rate in g alactic 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 Ga lactic radius. Our formulation naturally introduces a cutoff in the st ar-formation rate according to the condition of gravitational instabil ity for gaseous disks (the Q criterion). We compare our results with r elevant observations in the Galaxy. We take a conservative approach th at does not require gas infall or radial flows; an initial metallicity is adopted to resolve the G-dwarf problem. The model has two adjustab le parameters: the star-formation efficiency in the disk, and the init ial cloud covering factor of the disk. The time evolution of the disk formation and the heavy element abundance at various Galactocentric ra dii are calculated for a specified initial disk gas surface density, d ifferential rotation curve, and initial stellar mass function. Our mod el plausibly reproduces the observed star-formation rate, the metallic ity 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-fo rmation rate, and the heavy element abundance as a function of radius in the Galaxy. The success of our simple model emphasizes that gravita tional instability is principally responsible for star formation activ ity in galactic disks. Application of our results to galactic disks at early times may provide insight into understanding observations of di stant faint galaxies, and our simple analytical formulation of global star formation can be utilized in hydrodynamical simulations of large- scale galaxy formation and evolution.