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 [ { Mg / Fe } ] = 0.51 \pm 0.05 , [ Fe / H ] = 0.26 \pm 0.04 , 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 \sim 2 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 .