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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.