Resolved Multi-element Stellar Chemical Abundances in the Brightest
  Quiescent Galaxy at z $\sim$ 2
  Measuring the chemical composition of galaxies is crucial to our
understanding of galaxy formation and evolution models. However, such
measurements are extremely challenging for quiescent galaxies at high
redshifts, which have faint stellar continua and compact sizes, making it
difficult to detect absorption lines and nearly impossible to spatially resolve
them. Gravitational lensing offers the opportunity to study these galaxies with
detailed spectroscopy that can be spatially resolved. In this work, we analyze
deep spectra of MRG-M0138, a lensed quiescent galaxy at z = 1.98 which is the
brightest of its kind, with an H-band magnitude of 17.1. Taking advantage of
full spectral fitting, we measure $[{\rm Mg/Fe}]=0.51\pm0.05$,
$[\rm{Fe/H}]=0.26\pm0.04$, and, for the first time, the stellar abundances of 6
other elements in this galaxy. We further constrained, also for the first time
in a $z\sim2$ galaxy, radial gradients in stellar age, [Fe/H], and [Mg/Fe]. We
detect no gradient in age or [Mg/Fe] and a slightly negative gradient in
[Fe/H], which has a slope comparable to that seen in local early-type galaxies.
Our measurements show that not only is MRG-M0138 very Mg-enhanced compared to
the centers of local massive early-type galaxies, it is also very iron rich.
These dissimilar abundances suggest that even the inner regions of massive
galaxies have experienced significant mixing of stars in mergers, in contrast
to a purely inside-out growth model. The abundance pattern observed in
MRG-M0138 challenges simple galactic chemical evolution models that vary only
the star formation timescale and shows the need for more elaborate models.
