Open clusters in Gaia DR3
Stars born together share position, distance and motion. HDBSCAN finds them as dense clumps in Gaia DR3; the catalogue of Hunt & Reffert (2023) says which ones it should have found.
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Each star drifts along the sky at its proper motion, a million years a second, less the typical motion of the field at its distance: the Sun's own motion and the Galaxy's rotation shift every star there alike, and would hide the rest. Gaia has no radial velocity for most of these stars, so nothing moves in depth, and every path is a straight line.
HDBSCAN calls a clump a cluster only if it holds at least min_cluster_size stars. Small values cut the field into many small groups, most of which no catalogue lists; large ones merge neighbours and lose the poorer clusters. A cluster counts as recovered if any of the runs the protocol fixed recovers it; the other sizes were run afterwards, to explore, and are not part of the score.
Where it works
The share of the recoverable clusters (10 members or more in our sample) that at least one HDBSCAN run recovers, in both regions. Carina was clustered with its rule fixed in advance; Auriga's leaf runs are post hoc. Size matters more than distance: the biggest clusters all come back, the smallest about half the time.
One run at a time
Each HDBSCAN run alone, with min_cluster_size from 10 to 240, as on the slider under the map. These runs came after the score, to explore, and are not part of it. Smaller sizes recover more clusters, and find many more groups that no catalogue lists.
How to read it
Where things sit
Each grey star is at its distance from Bailer-Jones et al. (2021), not at one over its parallax, which is biased when the parallax is uncertain. The Sun is at the tip of the wedge, and the arcs mark every kiloparsec.
The members of a recovered cluster sit at the cluster's distance in Hunt & Reffert. In these regions, a member's own distance is uncertain by about 100 pc (median), while half of a cluster's members sit within about 3 pc of its centre (median). At their own distances, clusters would turn into needles pointing at the Sun. So a cluster's depth is not shown: seen side-on, it is flat.
What is drawn
A cluster is drawn at its catalogue position, as wide as its tidal radius in Hunt & Reffert, and never smaller than a few pixels: a sphere if HDBSCAN recovered it, a ring if not. Point at a sphere and it turns into its stars: the group of the HDBSCAN run that recovers it best, with the highest recovery × purity. A missed cluster's card shows the run that came closest.
The colour-magnitude diagram in each card shows the group's stars that Hunt & Reffert also list (blue), the group's other stars (red) and the members it misses (grey). Blue against red is purity; blue against grey, recovery.
Where a cluster was fitted, the diagram also draws two isochrones: our fit (solid) and the one for Hunt & Reffert's age, extinction and distance (dashed). Our ages agree with theirs within a factor of two for only 56 % of the clusters, so the colours by age stay theirs; the README says where the two part.
Beside it, the same stars by their motion on the sky (proper motion, in mas/yr), over the field stars that share the cluster's patch of sky and distance (light grey). A cluster's stars move alike, so they clump while the field spreads: with position and parallax, this is what HDBSCAN finds them by.
The groups that no Hunt & Reffert cluster owns are hidden unless you ask for them. Without a significance test they are not clusters.
Level of detail
The field is stored in random order and sent in nested levels: 65,536 stars, then twice as many each time. Every level is a uniform sample of the field, so the page shows the first one at once, adds the rest as they arrive, and draws fewer stars while the view moves.
This is not a discovery: Hunt & Reffert ran the same method on the same data. The score and how it was fixed in advance are in the README.