Dwarf galaxy archaeology from chemical abundances and star formation histories

We model the stellar abundances and ages of two disrupted dwarf galaxies in the Milky Way stellar halo: Gaia-Sausage Enceladus (GSE) and Wukong/LMS-1. Using a statistically robust likelihood function, we fit one-zone models of galactic chemical evolution with exponential infall histories to both systems, deriving e-folding timescales of $\tau_\text{in} = 1.01 \pm 0.13$ Gyr for GSE and $\tau_\text{in} = 3.08^{+3.19}_{-1.16}$ Gyr for Wukong/LMS-1. GSE formed stars for $\tau_\text{tot} = 5.40^{+0.32}_{-0.31}$ Gyr, sustaining star formation for $\sim$$1.5 - 2$ Gyr after its first infall into the Milky Way $\sim$10 Gyr ago. Our fit suggests that star formation lasted for $\tau_\text{tot} = 3.36^{+0.55}_{-0.47}$ Gyr in Wukong/LMS-1, though our sample does not contain any age measurements. The differences in evolutionary parameters between the two are qualitatively consistent with trends with stellar mass $M_\star$ predicted by simulations and semi-analytic models of galaxy formation. Our fitting method is based only on poisson sampling from an evolutionary track and requires no binning of the data. We demonstrate its accuracy by testing against mock data, showing that it accurately recovers the input model across a broad range of sample sizes ($20 \leq N \leq 2000$) and measurement uncertainties ($0.01 \leq \sigma_\text{[$\alpha$/Fe]}, \sigma_\text{[Fe/H]} \leq 0.5$; $0.02 \leq \sigma_{\log_{10}(\text{age})} \leq 1$). Our inferred values of the outflow mass-loading factor reasonably match $\eta \propto M_\star^{-1/3}$ as predicted by galactic wind models. Due to the generic nature of our derivation, this likelihood function should be applicable to one-zone models of any parametrization and easily extensible to other astrophysical models which predict tracks in some observed space.