Possibilities and Limitations of Kinematically Identifying Stars from Accreted Ultra-Faint Dwarf Galaxies

The Milky Way has accreted many ultra-faint dwarf galaxies (UFDs), and stars from these galaxies can be found throughout our Galaxy today. Studying these stars provides insight into galaxy formation and early chemical enrichment, but identifying them is difficult. Clustering stellar dynamics in 4D phase space ($E$, $L_z$, $J_r$, $J_z$) is one method of identifying accreted structure which is currently being utilized in the search for accreted UFDs. We produce 32 simulated stellar halos using particle tagging with the \textit{Caterpillar} simulation suite and thoroughly test the abilities of different clustering algorithms to recover tidally disrupted UFD remnants. We perform over 10,000 clustering runs, testing seven clustering algorithms, roughly twenty hyperparameter choices per algorithm, and six different types of data sets each with up to 32 simulated samples. Of the seven algorithms, HDBSCAN most consistently balances UFD recovery rates and cluster realness rates. We find that even in highly idealized cases, the vast majority of clusters found by clustering algorithms do not correspond to real accreted UFD remnants and we can generally only recover $6\%$ of UFDs remnants at best. These results focus exclusively on groups of stars from UFDs, which have weak dynamic signatures compared to the background of other stars. The recoverable UFD remnants are those that accreted recently, $z_{\text{accretion}}\lesssim 0.5$. Based on these results, we make recommendations to help guide the search for dynamically-linked clusters of UFD stars in observational data. We find that real clusters generally have higher median energy and $J_r$, providing a way to help identify real vs. fake clusters. We also recommend incorporating chemical tagging as a way to improve clustering results.