Evolution of the Mass-Metallicity Relation from Redshift $z\approx8$ to the Local Universe

A tight positive correlation between the stellar mass and the gas-phase metallicity of galaxies has been observed at low redshifts, with only $\sim 0.1$ dex scatter in metallicity. The shape and normalization of this correlation can set strong constraints on theories of galaxy evolution. In particular, its redshift evolution is thought to be determined by stellar and active galactic nucleus feedback-driven outflows, the redshift evolution of the stellar initial mass function or stellar yields, and broadly the star-formation histories of galaxies. The advent of \jwst\ allows probing the mass--metallicity relation at redshifts far beyond what was previously accessible. Here we report the discovery of two emission-line galaxies at redshift $z = 8.15$ and $z = 8.16$ in \jwst\ NIRCam imaging and NIRSpec spectroscopy of galaxies gravitationally lensed by the cluster RX\,J2129.4$+$0009. We measure their metallicities using the strong-line method and their stellar masses through spectral-energy-distribution fitting with a nonparametric star-formation history. We combine these with nine similarly re-analysed galaxies at $7.2 < z < 9.5$ to compile a sample of eleven galaxies at $z \approx 8$ (six with \jwst\ metallicities and five with ALMA metallicities). Based on this sample, we report the first quantitative statistical inference of the mass--metallicity relation at $z\approx8$ (median $z = 8.15$). We measure a $\sim 1.0$ dex redshift evolution in the normalization of the mass--metallicity relation from $z \approx 8$ to the local Universe; at fixed stellar mass, galaxies are 10 times less metal enriched at $z \approx 8$ compared to the present day (abridged).