New analytical solutions for chemical evolution models: characterizing the population of star-forming and passive galaxies

Analytical models of chemical evolution, including inflow and outflow of gas, are important tools to study how the metal content in galaxies evolves as a function of time. In this work, we present new analytical solutions for the evolution of the gas mass, total mass and metallicity of a galactic system, when a decaying exponential infall rate of gas and galactic winds are assumed. We apply our model to characterize a sample of local star-forming and passive galaxies from the Sloan Digital Sky Survey data, with the aim of reproducing their observed mass-metallicity relation; in this way, we can derive how the two populations of star-forming and passive galaxies differ in their particular distribution of ages, formation time scales, infall masses and mass loading factors. We find that the local passive galaxies are on average older and assembled on shorter typical time-scales than the local star-forming ones; on the other hand, the larger mass star-forming galaxies show generally older ages and longer typical formation time-scales compared with the smaller mass star-forming galaxies. Finally, we conclude that the local star-forming galaxies experience stronger galactic winds than the passive galaxy population. We explore the effect of assuming different initial mass functions in our model, showing that to reproduce the observed mass-metallicity relation stronger winds are requested if the initial mass function is top-heavy. Finally, our analytical models predict the assumed sample of local galaxies to lie on a tight surface in the 3D space defined by stellar metallicity, star formation rate and stellar mass, thus mimicking the well-known "fundamental relation".