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Analytical models of chemical evolution, including inflow and outflow of gas,are important tools to study how the metal content in galaxies evolves as afunction of time. In this work, we present new analytical solutions for theevolution 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 passivegalaxies from the Sloan Digital Sky Survey data, with the aim of reproducingtheir observed mass-metallicity relation; in this way, we can derive how thetwo populations of star-forming and passive galaxies differ in their particulardistribution of ages, formation time scales, infall masses and mass loadingfactors. We find that the local passive galaxies are on average older andassembled on shorter typical time-scales than the local star-forming ones; onthe other hand, the larger mass star-forming galaxies show generally older agesand longer typical formation time-scales compared with the smaller massstar-forming galaxies. Finally, we conclude that the local star-forminggalaxies experience stronger galactic winds than the passive galaxy population.We explore the effect of assuming different initial mass functions in ourmodel, showing that to reproduce the observed mass-metallicity relationstronger winds are requested if the initial mass function is top-heavy.Finally, our analytical models predict the assumed sample of local galaxies tolie on a tight surface in the 3D space defined by stellar metallicity, starformation rate and stellar mass, thus mimicking the well-known "fundamentalrelation".

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