In the models presented here, metal-free gas accumulates in the galactic disc at a rate that decays exponentially on a time-scale tf. Stars then form with a constant initial mass function and a small velocity dispersion at a rate proportional to the nth power of the volume density of the gas layer. They are stochastically accelerated in such a way that the q th power of their velocity dispersion in the vertical direction increases at a rate proportional to the rate of star formation. Chemical enrichment is treated in the approximation of instantaneous recycling with no exchange of material between different galactocentric radii. The models are first compared with the observed dependence of metallicity and velocity dispersion on age and the distribution of metallicities for stars in the solar neighbourhood. These relations are satisfied by models with n = 1 and tf = 5.5 Gy or n = 3/2 and tf = 3.5 Gy and 1.5 ≲ q ≲ 2.5. This range of q brackets the values needed to explain the nearly constant scale-heights observed in the stellar discs of edge-on galaxies. The models that are successful in the solar neighbourhood also reproduce the observed variation of gas density and star formation rate between galactocentric radii of 4 and 14 kpc but they do not reproduce the observed gradient in metallicity.
Lacey, C., & Fall, S. (1983). Kinematical and chemical evolution of the galactic disc. Monthly Notices of the Royal Astronomical Society, 204(3), 791-810. https://doi.org/10.1093/mnras/204.3.791