Stochastic effects in the chemical evolution of galaxies

We use a simple of mixing processes to investigate how fluctuations in element abundance in the interstellar medium may affect the chemical evolution of galaxies. We present a complete solution for the abundance distribution in a schematic inhomogeneous steady-state model in which infalling gas replaces material consumed by star formation. In addition, we give differential equations which describe the evolution of certain moments of the abundance distribution in more general models, together with a Monte Carlo scheme which can be used to simulate this evolution. We compare results for inhomogeneous generalizations of the infall model of Lynden-Bell with data on the abundance distribution of stars and gas in the solar neighbourhood. The relatively small dispersion about the age metallicity relation presented by Twarog constrains mixing of infalling gas and stellar ejecta to be quite efficient. A major difference between homogeneous and moderately inhomogeneous chemical evolution models lies in the relative abundance distributions they predict for primary and secondary nucleosynthesis products. Provided the coherence length for metallicity variations in the interstellar medium is small, inhomogeneous models lead to secondary to primary abundance ratios which are weakly and only statistically related to absolute primary abundance. (author)