Forecasting Chemical Abundance Precision for Extragalactic Stellar Archaeology

Abstract: Increasingly powerful and multiplexed spectroscopic facilities promise detailed chemical abundance patterns for millions of resolved stars in galaxies beyond the Milky Way (MW). Here, we employ the Cram\'er-Rao Lower Bound (CRLB) to forecast the precision to which stellar abundances for metal-poor, low-mass stars outside the MW can be measured for 41 current (e.g., Keck, MMT, VLT, DESI) and planned (e.g., MSE, JWST, ELTs) spectrograph configurations. We show that moderate resolution ($R\lesssim5000$) spectroscopy at blue-optical wavelengths ($\lambda\lesssim4500$ \AA) (i) enables the recovery of 2-4 times as many elements as red-optical spectroscopy ($5000\lesssim\lambda\lesssim10000$ \AA) at similar or higher resolutions ($R\sim 10000$) and (ii) can constrain the abundances of several neutron capture elements to $\lesssim$0.3 dex. We further show that high-resolution ($R\gtrsim 20000$), low S/N ($\sim$10 pixel$^{-1}$) spectra contain rich abundance information when modeled with full spectral fitting techniques. We demonstrate that JWST/NIRSpec and ELTs can recover (i) $\sim$10 and 30 elements, respectively, for metal-poor red giants throughout the Local Group and (ii) [Fe/H] and [$\alpha$/Fe] for resolved stars in galaxies out to several Mpc with modest integration times. We show that select literature abundances are within a factor of $\sim$2 (or better) of our CRLBs. We suggest that, like ETCs, CRLBs should be used when planning stellar spectroscopic observations. We include an open source python package, \texttt{Chem-I-Calc}, that allows users to compute CRLBs for spectrographs of their choosing.