Elemental Abundances and Ages of $z\sim0.7$ 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 $0.59\leq z\leq0.75$ from the LEGA-C survey. The
abundance patterns and ages, derived from full-spectrum modeling, are examined
as a function of stellar mass ($M_*$) 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 $M_*/R_e$ 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 $M_*$ or $M_*/R_e$, 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 $z\sim0$ and find that both relations increase by $\sim0.2$ dex
over the past 7 Gyr. Furthermore, at $z\sim0.7$ 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.
