The origin of the galaxy mass-metallicity relation and implications for galactic outflows

Using cosmological hydrodynamic simulations that dynamically incorporate enriched galactic outflows together with analytical modelling, we study the origin of the stellar mass-gas-phase metallicity relation (MZR). We find that metallicities are driven by an equilibrium between the rate of enrichment owing to star formation and the rate of dilution owing to infall of unenriched gas. This equilibrium is in turn governed by the outflow strength. As such, the MZR provides valuable insights and strong constraints on galactic outflow properties across cosmic time. We compare three outflow models: no outflows, a 'constant-wind model that emulates the popular Dekel & Silk scenario, and a 'momentum-driven wind' model that best reproduces z ≳ 2 intergalactic medium metallicity data. Only the momentum-driven wind scaling simulation is able to reproduce the observed z ∼ 2 MZR's slope, amplitude, and scatter. In order to understand why, we construct a one-zone chemical evolution model guided by simulations. This model shows that the MZR in our outflow simulations can be understood in terms of three parameters: (i) the equilibrium metallicity Z_g,eq = yṀ_SFR/Ṁ_ACC (where y = net yield), reflecting the enrichment balance between star formation rate Ṁ_SFR and gas accretion rate Ṁ_ACC; (ii) the dilution time, representing the time-scale for a galaxy to return to Z _g,eq after a metallicity-perturbing interaction; and (iii) the blowout mass M_blowout, which is the galaxy stellar mass above which winds can escape its halo. Without outflows, galaxy metallicities exceed observations by approximately two to three times, although the slope of the MZR is roughly correct owing to greater star formation efficiencies in larger galaxies. When outflows with mass-loading factor η_W are present, galaxies below M_blowout obey Z_g,eq ≈ y/(1 + η_W), while above M_blowout, Z_g,eq → y. Our constant-wind model has M_blowout ∼ 10¹⁰ M _⊙, which yields a sharp upturn in the MZR above this scale and a flat MZR with large scatter below it, in strong disagreement with observations. Our momentum-driven wind model naturally reproduces the observed Z_g ∝ M^0.3_* because Z_g,eq ∝ η^-1_W ∝ M^1/3_* when η_W ≫ 1 (i.e. at low masses). The flattening of the MZR at M_* ≳ 10^10.5 M_⊙ observed by Tremonti et al. is reflective of the mass-scale where η_W ∼ 1 rather than a characteristic outflow speed; in fact, the outflow speed plays little role in the MZR except through M_blowout. The tight observed MZR scatter is ensured when t_d ≲ dynamical time, which is only satisfied at all masses in our momentum-driven wind model. We also discuss secondary effects on the MZR, such as baryonic stripping from neighbouring galaxies' outflows.