Chemical evolution in the solar neighborhood. IV - Some revised general equations and a specific model

It is usually assumed that one could extrapolate the initial mass function to very low (substellar) masses to account for any difference between the known and dynamically inferred amount of mass per square parsec in the disk. However, standard data on the present luminosity function make it clear that any plausible extrapolation below 0.1 solar mass will add only approximately 1 solar mass per sq pc. The conventional general equations for chemical evolution, which divide a system simply into 'stars' and 'gas', are revised to separate living stars explicitly from condensed remnants. The new equations facilitate the consistent use of constraints based on star counts, and the handling of predictions (or constraints) concerning remnants. A schematic, analytic model based on conceptually similar models by previous authors, is proposed for the solar neighborhood. An initial burst of (halo) star formation gives the initial disk gas a finite metallicity.