Validating Stellar Abundance Measurements from Multi-Resolution Spectroscopy

Large-scale surveys will provide spectroscopy for $\sim$50 million resolved stars in the Milky Way and Local Group. However, these data will have a high degree of heterogeneity and most will be low-resolution ($R<10000$), posing challenges to measuring consistent and reliable stellar labels. Here, we introduce a framework for identifying and remedying these issues. By simultaneously fitting the full spectrum and Gaia photometry with the Payne, we measure $\sim$40 abundances for 8 red giants in M15. From degraded quality Keck/HIRES spectra, we evaluate trends with resolution and S/N and find that (i) $\sim$20 abundances are recovered consistently within $\lesssim$0.1 dex agreement and with $\lesssim$0.05-0.15~dex systematic uncertainties from $10000\lesssim R\lesssim80000$; (ii) for 9 elements (C, Mg, Ca, Sc, Ti, Fe, Ni, Y, Nd), this systematic precision and accuracy extends down to $R\sim2500$; and (iii) while most elements do not exhibit strong S/N-dependent systematics, there are non-negligible biases for 4 elements (C, Mg, Ca, and Dy) below $\text{S/N}\sim10$ pixel$^{-1}$. We compare statistical uncertainties from MCMC sampling to the easier-to-compute Cram\'er-Rao bounds and find that they agree for $\sim$75% of elements, indicating the latter to be a reliable and faster way to estimate uncertainties. Our analysis illustrates the great promise of low-resolution spectroscopy for stellar chemical abundance work, and ongoing improvements to stellar models (e.g., 3D-NLTE physics) will only further extend its viability to more elements and to higher precision and accuracy.