Previous attempts to explain the observed mass–metallicity relation of galaxies invoked selective outflows that need to be tuned to the particular cases.
Here we demonstrate that the simple concept of a star-formation history (SFH) dependent galaxy-wide integrated galactic initial stellar mass function (the IGIMF) can easily and naturally explain the mass–metallicity relation.
The idea relies on the simple fact that stars form in clusters. So to construct the IGIMF one needs to add all the stellar IMFs in the clusters formed in one epoch. The SFH enters because a galaxy with a high SFR can form more-massive clusters than a galaxy with a low SFR. Dwarf galaxies therefore have, per unit stellar mass formed, far fewer if any supernovae of type II than massive galaxies.
This work rests on the recent paper by Köppen, Weidner & Kroupa (2007).