In the last years, more and more interest has been devoted to analytical
solutions, including inflow and outflow, to study the metallicity enrichment in
galaxies. In this framework, we assume a star formation rate which follows a
linear Schmidt law, and we present new analytical solutions for the evolution
of the metallicity (Z) in galaxies. In particular, we take into account
environmental effects including primordial and enriched gas infall, outflow,
different star formation efficiencies, and galactic fountains. The enriched
infall is included to take into account galaxy-galaxy interactions. Our main
results can be summarized as: i) when a linear Schmidt law of star formation is
assumed, the resulting time evolution of the metallicity Z is the same either
for a closed-box model or for an outflow model. ii) The mass-metallicity
relation for galaxies which suffer a chemically enriched infall, originating
from another evolved galaxy with no pre-enriched gas, is shifted down in
parallel at lower Z values, if compared the closed box model. iii) When a
galaxy suffers at the same time a primordial infall and a chemically enriched
one, the primordial infall always dominates the chemical evolution. iv) We
present new solutions for the metallicity evolution in a galaxy which suffers
galactic fountains and an enriched infall from another galaxy at the same time.
The analytical solutions presented here can be very important to study the
metallicity (oxygen), which is measured in high-redshift objects. These
solutions can be very useful: a) in the context of cosmological semi-analytical
models for galaxy formation and evolution, and b) for the study of compact
groups of galaxies.Comment: Accepted for publication in MNRA
