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The Milky Way has accreted many ultra-faint dwarf galaxies (UFDs), and starsfrom these galaxies can be found throughout our Galaxy today. Studying thesestars provides insight into galaxy formation and early chemical enrichment, butidentifying them is difficult. Clustering stellar dynamics in 4D phase space($E$, $L_z$, $J_r$, $J_z$) is one method of identifying accreted structurewhich is currently being utilized in the search for accreted UFDs. We produce32 simulated stellar halos using particle tagging with the \textit{Caterpillar}simulation suite and thoroughly test the abilities of different clusteringalgorithms to recover tidally disrupted UFD remnants. We perform over 10,000clustering runs, testing seven clustering algorithms, roughly twentyhyperparameter choices per algorithm, and six different types of data sets eachwith up to 32 simulated samples. Of the seven algorithms, HDBSCAN mostconsistently balances UFD recovery rates and cluster realness rates. We findthat even in highly idealized cases, the vast majority of clusters found byclustering algorithms do not correspond to real accreted UFD remnants and wecan generally only recover $6\%$ of UFDs remnants at best. These results focusexclusively on groups of stars from UFDs, which have weak dynamic signaturescompared to the background of other stars. The recoverable UFD remnants arethose that accreted recently, $z_{\text{accretion}}\lesssim 0.5$. Based onthese results, we make recommendations to help guide the search fordynamically-linked clusters of UFD stars in observational data. We find thatreal clusters generally have higher median energy and $J_r$, providing a way tohelp identify real vs. fake clusters. We also recommend incorporating chemicaltagging as a way to improve clustering results.

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