Analytical Approximations to the Evolution of Galaxies

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Abstract
Analytical expressions are derived for the evolution of the luminosity, mass of stars, mass of invisible remnants, rate of ejection of gas from stars, and yield of heavy elements in idealized model galaxies. The equations are based on simple assumptions concerning the mass function of star formation and stellar evolution, and they apply to an arbitrary time-dependence of the stellar birthrate. Especially simple and instructive forms are derived for the expressions in the cases where star formation occurs uniformly and where it occurs in an initial burst. These results are used to show how certain properties of elliptical galaxies, globular clusters, and late-type galaxies depend on parameters characterizing their rate of star formation and the initial mass function. In spite of the severe limitations of this approach to galactic evolution, it sheds light on the results obtained from detailed numerical models, and it predicts a number of useful general relationships among galactic properties. Subject headings: galaxies - star formation - stellar evolution - stellar statistics

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