The mass-metallicity relation as a ruler for galaxy evolution: insights from the James Webb Space Telescope

Galaxy evolution emerges from the balance between cosmic gas accretion, fueling star formation, and supernova (SN) feedback, regulating the metal enrichment. Hence, the stellar mass ($M_*$) - gas metallicity relation (MZR) is key to understanding the physics of galaxies. High-quality JWST data enable accurate measurements of the MZR up to redshift z=10. Our aims are to understand the observed MZR, its connection with the star formation rate (SFR), the role played by SFR stochasticity, and how it is regulated by SN feedback. We compare the MZR from the JADES, CEERS, and UNCOVER surveys, which comprise about 180 galaxies at $z=3-10$ with $10^6<M_*/M_\odot<10^{10}$, with 200 galaxies from the SERRA cosmological simulations. To interpret the MZR, we develop a minimal model for galaxy evolution that includes: cosmic accretion modulated with an amplitude $A_{100}$ on 100 Myr; a time delay $t_d$ between SFR and SN; SN-driven outflows with a varying mass loading factor $\epsilon_{SN}$. Using our minimal model, we find the observed mean MZR is reproduced by weak outflows ($\epsilon_{SN}=1/4$), in line with findings from JADES. Matching the observed MZR dispersion requires $t_d=20$ Myr and a $A_{100}=1/3$ modulation of the accretion rate. Successful models have low stochasticity ($\sigma_{SFR}=0.2$), yielding a MZR dispersion of $\sigma_{Z}=0.2$. Such values are close but lower than SERRA predictions ($\sigma_{SFR}=0.24$, $\sigma_{Z}=0.3$), clarifying why SERRA shows flatter trend and some tension with the observations. As the MZR is very sensitive to SFR stochasticity, models predicting high r.m.s. values ($\sigma_{SFR}=0.5$) result in a ``chemical chaos'' (i.e. $\sigma_{Z}=1.4$), virtually destroying the MZR. As a consequence, invoking a highly stochastic SFR ($\sigma_{SFR}=0.8$) to explain the overabundance of bright, super-early galaxies leads to inconsistencies with the observed MZR.