Galactic chemical evolution - Z versus ln(1/mu) relationship

The ways in which a radial abundance gradient in a disk galaxy may be interpreted are reexamined, asking how metallicity Z depends upon gas mass fraction mu in analytic models characterized by a temporally varying history of metal-poor infall. Six different such models are studied, and it is shown that the metallicity versus gas fraction relationship is well approximated by an expression which is the analog of the Z = y ln(1/mu) relation for closed evolution. The approximation appears valid when the infall rate is nonneglible, but not so great that it dominates the gas budget.