The origin of the mass-metallicity relation: an analytical approach

Context. The mass-metallicity (MZ) relation in star-forming galaxies at all redshifts has been recently established. It is therefore important to understand the physical mechanisms underlying such a relation. Aims: We aim at studying some possible physical mechanisms contributing to the MZ relation by adopting analytical solutions of chemical evolution models, including infall and outflow. Methods: Analytical models assume the instantaneous recycling approximation, which is still an acceptable assumption for elements produced on short timescales such as oxygen, which is the measured abundance in the MZ relation.We explore the hypotheses of a variable galactic wind rate, infall rate, and yield per stellar generation (i.e. a variation in the IMF), as possible causes for the MZ relation. Results: By means of analytical models, we computed the expected O abundance for galaxies of a given total baryonic mass and gas mass.The stellar mass was derived observationally and the gas mass was derived by inverting the Kennicutt law of star formation, once its rate is known. Then we tested how the parameters describing the outflow, infall, and IMF should vary to reproduce the MZ relation, and we exclude the cases where such a variation leads to unrealistic situations. Conclusions: We find that a galactic wind rate increasing with decreasing galactic mass or a variable IMF are both viable solutions for the MZ relation. A variable infall rate instead is not acceptable. It is difficult to differentiate among the outflow and IMF solutions by only considering the MZ relation, and other observational constraints should be taken into account in selecting a specific solution. For example, a variable efficiency of star formation increasing with galactic mass can also reproduce the MZ relation and explain the downsizing in star formation suggested for ellipticals. The best solution could be a variable efficiency of star formation coupled with galactic winds, which are indeed observed in low-mass galaxies.