We study the origin and cosmic evolution of the mass-metallicity relation (MZR) in star-forming galaxies based on a full, numerical chemical evolution model. The model was designed to match the local MZRs for both gas and stars simultaneously. This is achieved by invoking a time-dependent metal enrichment process which assumes either a time-dependent metal outflow with larger metal loading factors in galactic winds at early times, or a time-dependent Initial Mass Function (IMF) with steeper slopes at early times. We compare the predictions from this model with data sets covering redshifts 0<z<3.5. The data suggests a two-phase evolution with a transition point around z ~ 1.5. Before that epoch the MZRgas has been evolving parallel with no evolution in the slope. After z ~ 1.5 the MZRgas started flattening until today. We show that the predictions of both the variable metal outflow and the variable IMF model match these observations very well. Our model also reproduces the evolution of the main sequence, hence the correlation between galaxy mass and star formation rate. We also compare the predicted redshift evolution of the MZRstar with data from the literature. As the latter mostly contains data of massive, quenched early-type galaxies, stellar metallicities at high redshifts tend to be higher in the data than predicted by our model. Data of stellar metallicities of lower-mass (< 10^11 solar mass), star-forming galaxies at high redshift is required to test our model.
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