Effects of galactic fountains and delayed mixing in the chemical evolution of the Milky Way

Context. The majority of galactic chemical evolution models assumes the instantaneous mixing approximation (IMA). This assumption is probably not realistic, as indicated by the existence of chemical inhomogeneities, although current chemical evolution models of the Milky Way can reproduce the majority of the observational constraints under the IMA. Aims. The aim of this paper is to test whether relaxing this approximation in a detailed chemical evolution model can improve or worsen the agreement with observations. To do that, we investigated two possible causes for relaxing of the instantaneous mixing: i) the "galactic fountain time delay effect" and ii) the "metal cooling time delay effect". Methods. We considered various galactic fountain time delays for the chemical enrichment from massive stars. We then tested a time delay in the enrichment from stars of all masses due to gas cooling in the range 0.5-1 Gyr. Results. We found that the effect of galactic fountains is negligible if an average time delay of 0.1 Gyr, as suggested in a previous paper, is assumed. Longer time delays produce differences in the results but they are not realistic. We also found that the O abundance gradient in the disk is not affected by galactic fountains. The metal cooling time delays produce strong effects on the evolution of the chemical abundances only if we adopt stellar yields depending on metallicity. If, instead, the yields computed for the solar chemical composition are adopted, negligible effects are produced, as in the case of the galactic fountain delay. Conclusions. The relaxation of the IMA by means of the galactic fountain model, where the delay is considered only for massive stars and only in the disk, does not affect the chemical evolution results. The combination of metal dependent yields and time delay in the chemical enrichment from all stars starting from the halo phase, instead, produces results at variance with observations.