Starfold on 9,242 Milky Way stars

Each star carries eight numbers. [Fe/H] is its iron abundance relative to the Sun, in dex, a base-10 logarithm, and [α/M] and [Mg/Fe] say how rich it is in alpha elements such as magnesium; all three come from APOGEE spectra through the ASPCAP pipeline. The other five describe its orbit, integrated with galpy in the McMillan17 model of the Galaxy from Gaia DR3 astrometry: the radial and vertical actions J_R and J_z, the angular momentum L_z, the eccentricity and the energy E.

Starfold tried 48 settings of UMAP and HDBSCAN, scored each without labels against a structureless copy of the table, and fitted the selected one on all stars. The map shows that fit. UMAP placed the stars so that neighbours in the eight standardised columns stay close, and HDBSCAN marked the two dense regions as groups and left 1,068 stars around and between them unassigned. Positions on the map have no units; only which stars sit near which counts.

The chemistry panel is the classic test. The Milky Way disc holds two chemical sequences: a high-alpha one of older, metal-poorer stars on hotter orbits, and a low-alpha one that reaches solar [Fe/H] and above (Bensby et al. 2014; Hayden et al. 2015). Starfold was told none of this. Group 0 has the high-alpha pattern and group 1 the reverse, in chemistry and in orbits. That passes a sanity check of the method; it is not a finding about the Galaxy.

To see how far the split holds, Starfold refitted the same setting 32 times, each on a random 80 per cent of the stars with new seeds. A star's support for a group is the share of its refit group that belongs to that group, averaged over the refits that drew it, and dots fade where support for their own group is low. Refit groups carry arbitrary numbers, so the replay colours each one by the group it matches by Jaccard index, as Starfold does for recurrence.

Recurrence is that matched overlap, averaged over the refits: 0.914 for group 0 and 0.918 for group 1, both above the 0.85 that the clusterboot documentation gives for a highly stable cluster. Refit 10 found a third group of 124 stars, 119 of them from group 1; the other 31 refits found two, so the count interval is 2 to 2. The unresolved mass, 0.154, is the average share of a star's refit outcomes that were no group.

The co-association contrast measures how much more often the refits put two stars of one group together than two stars of different groups; on a seeded subset of 4,096 stars it is 0.976. A second clustering of that matrix left every one of those stars unassigned and raised consensus_disagrees; the tutorial records its cause as not diagnosed. The calibration test ran separately on the same run: one of 19 structureless copies scored at or above the table, so p = 0.10, with a 95 per cent Monte Carlo interval of 0.001 to 0.260.

So the run supports two reproducible groups, and no more. With p above 0.05 the split is not shown to exceed a single correlated population, so the panel shows the flag no_structure_supported. The test was run separately and is not attached to the saved run. The run gives no membership probabilities, models no selection function and carries no measurement errors. The table's provenance note calls it a convenience for tutorials, not a source for scientific work.

The star panel follows the star under the pointer, or the one you clicked or chose. Its 32 cells are the refits in order: a coloured cell means the refit put the star with that group, an outline means it left the star unassigned, and a dot means it did not draw the star.

Each line below spans the 1st to 99th percentile of all stars, the ticks mark the two group medians and the dot marks the star; a square means the star lies beyond the line. The source_id links to the star's row in the Gaia DR3 catalogue at VizieR.

Hover over a star to read it in the star panel, click to keep it, and drag across any panel to select a set of stars, which the other panels then show. Replay steps through the refits, cross-fading between them unless your device asks for reduced motion. On ten labelled tables Starfold matched or beat the library defaults on six of six development tables and on two of four held-out ones; the benchmark lists every table.