Is there Evidence of alpha-Enhancement in Massive Quiescent Galaxies at z > 3?

We propose NIRSpec MOS spectroscopy of three massive quiescent galaxies at 3< z< 5. We have confirmed their quiescent nature and redshifts via the detection of Balmer absorption lines in deep Keck/MOSFIRE spectroscopy. Our robust sample selection and analysis reveals that two them are uncomfortably massive (log M/M_sun>11), placing them in tension with predictions from LCDM. The missing piece in resolving this tension is a direct observational constraint on their formation timescales and hence stellar mass assembly histories via fossil records imprinted in their stellar populations (i.e. their [alpha/Fe] ratios). The largest factor limiting progress on this front is the lack of high SNR spectroscopic data with continuous wavelength coverage (1.6-5.3 microns) that includes these key features. This is a Herculean task to attempt from the ground, where atmospheric absorption and emission make continuum observations far more challenging, thereby requiring 50+ hours on the most sensitive ground-based spectrographs to make marginally constraining measurements of elemental ratios. In this proposal, we demonstrate that we achieve the requisite SNR for all our candidates with only 8 hours of JWST/NIRSpec time enabling us to constrain [alpha/Fe] to within 0.12 dex. This will allow us to trace stellar population properties as close to their formation epoch as possible and make practical recommendations for stellar population synthesis codes and cosmological simulations, which will address this tension with theory. Our modest proposal is a proof of concept that this transformative science can only be done at these early epochs with JWST and will motivate future, deeper observations.