Substructure in the stellar halo near the Sun. I.

To evaluate the statistical significance of the clusters, we compared the density within an ellipsoidal region centred on the cluster to that of random sets with similar global dynamical properties. By selecting the signal at the location of their maximum statistical significance in the hierarchical tree, we extracted a set of significant unique clusters. By describing these clusters with ellipsoids, we estimated the proximity of a star to the cluster centre using the Mahalanobis distance.

Additionally, we applied the HDBSCAN clustering algorithm in velocity space to each cluster to extract subgroups representing debris with different orbital phases. Our procedure identifies 67 highly significant clusters (>3{sigma}), containing 12% of the sources in our halo set, and 232 subgroups or individual streams in velocity space. In total, 13.8% of the stars in our data set can be confidently associated with a significant cluster based on their Mahalanobis distance.

Inspection of the hierarchical tree describing our data set reveals a complex web of relations between the significant clusters, suggesting that they can be tentatively grouped into at least six main large structures, many of which can be associated with previously identified halo substructures, and a number of independent substructures. This preliminary conclusion is further explored in a companion paper, in which we also characterise the substructures in terms of their stellar populations.

Our method allows us to systematically detect kinematic substructures in the Galactic stellar halo with a data-driven and interpretable algorithm. The list of the clusters and the associated star catalogue are provided in two tables in electronic format.