Prospects for Measuring Abundances of >20 Elements with Low-resolution Stellar Spectra

Abstract: Understanding the evolution of the Milky Way calls for the precise abundance determination of many elements in many stars. A common perception is that deriving more than a few elemental abundances ([Fe/H], [$\alpha$/Fe], perhaps [C/H], [N/H]) requires medium-to-high spectral resolution, $R \gtrsim 10,000$, mostly to overcome the effects of line blending. In recent work (Rix et al. 2016; Ting et al. 2016) we presented an efficient and practical way to model the full stellar spectrum, even when fitting a large number of stellar labels simultaneously. In this paper we quantify to what precision the abundances of many different elements can be recovered, as a function of spectroscopic resolution and wavelength range. In the limit of perfect spectral models and spectral normalization, we show that the precision of elemental abundances is nearly independent of resolution, for a fixed exposure time and number of detector pixels; low-resolution spectra simply afford much higher S/N per pixel and generally larger wavelength range in a single setting. We also show that estimates of most stellar labels are not strongly correlated with one another once $R \gtrsim 1,000$. Modest errors in the line spread function, as well as small radial velocity errors, do not affect these conclusions, and data driven models indicate that spectral (continuum) normalization can be achieved well enough in practice. These results, to be confirmed with an analysis of observed low-resolution data, open up new possibilities for the design of large spectroscopic stellar surveys and for the re-analysis of archival low-resolution datasets.