Elemental Abundances and Ages of $z\sim 0.7$ Quiescent Galaxies on the Mass-Size Plane: Implication for Chemical Enrichment and Star-Formation Quenching

We present elemental abundances and stellar population ages for 68 massive quiescent galaxies at $0.59\le z\le 0.75$ from the LEGA-C survey. The abundance patterns and ages, derived from full-spectrum modeling, are examined as a function of stellar mass ($M_{\ast }$) and size (i.e., half-light radius; $R_e$). We find that both [Mg/H] and [Fe/H] do not vary with stellar mass but are correlated with $M_{\ast }\mathrm{/}{R}_e$ for quiescent galaxies with $M_*>10^{10.5} M_\odot$. Thus, at fixed mass, compact quiescent galaxies are on average more metal rich. This result reinforces the picture that supernova feedback and gravitational potential regulate chemical enrichment. [Mg/Fe] does not vary with $M_{\ast }$ or $M_{\ast }\mathrm{/}{R}_e$, but there is a marginal positive relation between age and mass. Our results support low-redshift findings that more massive galaxies form their stars at earlier times. However, in contrast to low-redshift studies, star formation timescale does not appear to depend on mass or size. We also compare the mass-[Fe/H] and mass-[Mg/H] relations to stacks of quiescent galaxies at $z\sim 0$ and find that both relations increase by $\sim 0.2$ dex over the past 7 Gyr. Furthermore, at $z\sim 0.7$ we find a clear trend with age, such that older quiescent galaxies have lower metallicities. Both results can be explained by a chemical evolution model in which galaxies quench via gas removal. Future work, in particular with JWST/NIRSpec, will extend this analysis to higher redshifts, allowing us to fully exploit abundance patterns to study the formation histories of quiescent galaxies.