On the origin of the mass-metallicity gradient relation in the local Universe

In addition to the well-known gas phase mass-metallicity relation (MZR), recent spatially resolved observations have shown that local galaxies also obey a mass-metallicity gradient relation (MZGR), whereby metallicity gradients can vary systematically with galaxy mass. In this work, we use our recently developed analytic model for metallicity distributions in galactic discs, which includes a wide range of physical processes - radial advection, metal diffusion, cosmological accretion, and metal-enriched outflows - to simultaneously analyse the MZR and MZGR. We show that the same physical principles govern the shape of both: centrally peaked metal production favours steeper gradients, and this steepening is diluted by the addition of metal-poor gas, which is supplied by inward advection for low-mass galaxies and by cosmological accretion for massive galaxies. The MZR and the MZGR both bend at galaxy stellar mass $\sim 10^{10}{-}10^{10.5}\, \rm {M_{\odot }}$, and we show that this feature corresponds to the transition of galaxies from the advection-dominated to the accretion-dominated regime. We also find that both the MZR and MZGR strongly suggest that low-mass galaxies preferentially lose metals entrained in their galactic winds. While this metal-enrichment of the galactic outflows is crucial for reproducing both the MZR and the MZGR at the low-mass end, we show that the flattening of gradients in massive galaxies is expected regardless of the nature of their winds.