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".
