Cool and Data-Driven: An Exploration of Optical Cool Dwarf Chemistry with Both Data-Driven and Physical Models

Detailed chemical studies of F/G/K -- or Solar-type -- stars have long been routine in stellar astrophysics, enabling studies in both Galactic chemodynamics, and exoplanet demographics. However, similar understanding of the chemistry of M and late-K dwarfs -- the most common stars in the Galaxy -- has been greatly hampered both observationally and theoretically by the complex molecular chemistry of their atmospheres. Here we present a new implementation of the data-driven \textit{Cannon} model, modelling $T_{\rm eff}$, $\log g$, [Fe/H], and [Ti/Fe] trained on low-medium resolution optical spectra ($4\,000-7\,000\,$\SI{}{\angstrom}) from 103 cool dwarf benchmarks. Alongside this, we also investigate the sensitivity of optical wavelengths to various atomic and molecular species using both data-driven and theoretical means via a custom grid of MARCS synthetic spectra, and make recommendations for where MARCS struggles to reproduce cool dwarf fluxes. Under leave-one-out cross-validation, our \textit{Cannon} model is capable of recovering $T_{\rm eff}$, $\log g$, [Fe/H], and [Ti/Fe] with precisions of 1.4\%, $\pm0.04\,$dex, $\pm0.10\,$dex, and $\pm0.06\,$dex respectively, with the recovery of [Ti/Fe] pointing to the as-yet mostly untapped potential of exploiting the abundant -- but complex -- chemical information within optical spectra of cool stars.