Recover known open star clusters from Gaia DR3 with HDBSCAN, and measure how many come back.
Stars born in the same cloud share position, distance and motion. On the sky they blend into the field; in five dimensions (position, parallax, proper motion) they form dense clumps. HDBSCAN finds those clumps without being told how many there are and leaves the field as noise.
This is not a discovery project. Hunt & Reffert (2023) already ran HDBSCAN over Gaia DR3 and catalogued about 7,000 clusters. Their catalogue is used here as the reference: the score is the share of their members we recover, and the share of what we find that they also list.
Open the 3D viewer: Auriga and Carina in the browser.
Carina, 2.5 million Gaia DR3 stars, looking along the Galactic plane about 2.4 kpc from the Sun. Grey: field stars at their Bailer-Jones distance. Blue: the members of each recovered cluster, at the cluster's distance, lighter for younger (Hunt & Reffert's age). Red rings: clusters HDBSCAN missed. Rendered in Blender from the viewer's data (scripts/render.py); points and rings are sized to be seen, not to scale.
A 6° cone around the Pleiades with parallax > 1 mas, RUWE < 1.4 and parallax/error > 5
(118,080 stars), clustered with min_cluster_size=40, min_samples=10, untuned:
| Clusters found | 2: the field and the Pleiades |
| Pleiades cluster | 1,497 stars |
| Recovery (Hunt & Reffert members passing our cuts that we find) | 96.9 % (1,424 of 1,470) |
| Purity (our members that Hunt & Reffert also list) | 95.1 % |
These numbers come from the hdbscan library, which the project uses because it scales to millions
of stars. The first run used scikit-learn's HDBSCAN and gave 96.3 % and 96.3 %.
The Pleiades are the easy case: close, rich and far from the field in proper motion. The number that matters is the all-sky one, with distant and sparse clusters. Also, this is the same method on the same data as the reference, so it measures agreement with it, not truth.
Galactic longitude 170–180°, latitude −5° to +5°, towards the Galactic anticentre:
576,442 Gaia DR3 stars with RUWE < 1.4 and parallax/error > 5, and 121 Hunt & Reffert clusters
centred in the box, from 350 pc to 5.4 kpc. 104 of them keep at least 10 members after our cuts;
those are the ones scored. Region, cuts, parameters and matching rule were fixed in
docs/protocol-auriga.md and committed before the first run (e2a63a1).
A cluster counts as recovered when one of our groups holds more than half of its members and more than half of that group are its members. HDBSCAN runs four times, with min_cluster_size 10, 20, 40 and 80 as Hunt & Reffert did, and a cluster recovered by any run counts.
Under the protocol: 3 of 104 clusters recovered (3 %). HDBSCAN's default cluster selection, excess of mass, put most of the field into a single group in every run (545,214 of the 576,442 stars with min_cluster_size 10), and the clusters stayed inside it. The protocol missed that Hunt & Reffert's first paper (2021), whose parameter choices the catalogue paper reuses, found leaf selection "almost always superior" to excess of mass and much better at recovering small clusters, which hold very few stars next to their field.
Post hoc, switching to leaf selection and changing nothing else: 84 of 104 recovered (81 %), and 62 of the 70 that Hunt & Reffert rate highly reliable (89 %). This number was obtained after seeing the first one, so a second region with leaf selection fixed in advance had to confirm it: Carina, below.
| Protocol (excess of mass) | Post hoc (leaf) | |
|---|---|---|
| Under 1 kpc | 3 of 18 | 17 of 18 |
| 1–2 kpc | 0 of 46 | 37 of 46 |
| 2–3 kpc | 0 of 22 | 18 of 22 |
| 3 kpc and beyond | 0 of 18 | 12 of 18 |
| 10–29 members in our sample | 1 of 45 | 27 of 45 |
| 30–99 members | 1 of 49 | 47 of 49 |
| 100 members or more | 1 of 10 | 10 of 10 |
Both expectations written in the protocol hold in the leaf runs: recovery falls with distance (94, 80, 82 and 67 %, not strictly), and highly reliable clusters come back more often than the rest (89 % against 65 %). Beyond 3 kpc the cuts weigh as much as the clustering: 13 of the 31 clusters there keep fewer than 10 members once parallax/error > 5 is applied.
Of the 20 misses, 11 sit inside a bigger group of ours (more than half of their members are there, but they are less than half of the group), 7 are not found at all (12 members in our sample, median) and 2 are only partly found. The leaf run with min_cluster_size 10 also finds 494 groups that no Hunt & Reffert cluster owns. They are not discoveries: Hunt & Reffert discard groups like these with a significance test and a colour-magnitude classifier, which this project does not have yet.
Full tables in results/auriga.md, one row per cluster in results/auriga_scores_*.csv.
Galactic longitude 285–295°, latitude −5° to +5°, along the Carina arm: 2,521,944 stars after the
same cuts, 4.4 times Auriga's field, and 224 Hunt & Reffert clusters, the most of any 10° window
along the plane. That rule picked the region, from the catalogue alone. 202 of its clusters keep at
least 10 members after our cuts. The protocol, docs/protocol-carina.md,
is Auriga's with leaf selection instead of excess of mass, and was committed before the first run
(f8d1d03).
The protocol also said when Auriga's result would count as replicated. Auriga's leaf rates by members in our sample (60 % for 10–29, 96 % for 30–99, 100 % for 100 or more), applied to Carina's clusters, predict 81.5 %, with a 95 % range of 73.3 % to 89.1 %. The bar was the bottom of that range: at least 148 of the 202.
Result: 149 of 202 recovered (73.8 %). Auriga's result replicates, with one cluster to spare. It lands at the bottom of the predicted range, 8 points under the prediction: the denser field costs something, and Auriga, with the thinnest field, is the easier case.
| Auriga, post hoc | Carina, fixed in advance | |
|---|---|---|
| Stars after the cuts | 576,442 | 2,521,944 |
| All recoverable | 84 of 104 (81 %) | 149 of 202 (74 %) |
| Highly reliable | 62 of 70 (89 %) | 107 of 132 (81 %) |
| Under 1 kpc | 17 of 18 | 14 of 20 |
| 1–2 kpc | 37 of 46 | 34 of 37 |
| 2–3 kpc | 18 of 22 | 57 of 78 |
| 3 kpc and beyond | 12 of 18 | 44 of 67 |
| 10–29 members in our sample | 27 of 45 (60 %) | 43 of 78 (55 %) |
| 30–99 members | 47 of 49 (96 %) | 76 of 94 (81 %) |
| 100 members or more | 10 of 10 | 30 of 30 |
Against the expectations in the protocol:
- Excess of mass fails again: 2 of 202 (1 %). With min_cluster_size 10 it puts 2,520,594 of the 2,521,944 stars into one group.
- Highly reliable clusters come back more often than the rest: 81 % against 60 %.
- Recovery does not fall steadily with distance: 70, 92, 73 and 66 %. The nearest bin breaks the pattern. Four of its six misses have only 10 to 15 members in our sample, and the other two hold most of their members in a group where they fall just short of half (purity 0.48 and 0.49).
- Recovery is lower than Auriga's for clusters with fewer than 100 members in our sample (55 against 60 %, 81 against 96 %). Those with 100 or more are all recovered in both regions.
Most misses are close calls, and that is where the denser field shows. Post hoc, as a description and not a new result: in 28 of the 53 misses, the closest run scores above 0.4 on both recovery and purity, against 6 of 20 in Auriga. In 21 of them it holds most of the cluster's members, but they are only 40–50 % of the group, which also takes in field stars.
The leaf run with min_cluster_size 10 finds 2,281 groups, and in 2,109 of them no Hunt & Reffert cluster holds the majority. As in Auriga, they are not discoveries.
The diagrams show the three richest clusters in the reference and the farthest recovered one with at least 30 members. NGC 3532 even shows its white dwarfs, bottom left, and Trumpler 19 its red giants. Majaess 133, at 6.8 kpc, draws no clear sequence: Hunt & Reffert's own classifier gives its diagram 0.04 out of 1. Matching their members is not the same as being a cluster.
Full tables in results/carina.md, one row per cluster in results/carina_scores_*.csv.
The viewer colours clusters by Hunt & Reffert's age, which a neural network gives from each cluster's diagram. To check those ages with a plainer method, PARSEC isochrones (solar metallicity) are fitted to each recovered group's colour-magnitude diagram: age, extinction and distance modulus, with a parallax prior. Each isochrone point is weighted by the share of stars the IMF puts there, so an isochrone pays for predicting stars the group does not have. The rule, the clusters and the bar were fixed in docs/protocol-ages.md before any fit; the fit's settings were frozen on three calibration clusters (NGC 3532, Trumpler 19, M37) before the test run.
The bar is not met. Of 170 test clusters with at least 30 stars, 141 get an age; 79 of them (56 %) are within 0.3 dex of Hunt & Reffert's, with a Spearman correlation of 0.64, against a bar of two thirds and 0.8. The median difference is 0.00 dex, but the misses are not noise:
- One failure mode makes most of the large misses. 23 clusters come out more than 0.8 dex younger than Hunt & Reffert's, at a median 3.7 kpc: groups whose stars stop around G = 16.5 get ages of a few million years (median 7 Myr) where Hunt & Reffert give a median 210 Myr. Our parallax cut (parallax_over_error > 5) empties the faint end at that distance, the model still expects stars down to G = 18, and a very young isochrone, whose pre-main sequence bends away there, explains the sudden edge best. The protocol named this risk and cut at G = 18; that was not enough.
- Post hoc, cutting each cluster at its own 90th percentile in G, chosen once and not tuned: 134 get an age, 80 (60 %) within 0.3 dex, Spearman 0.82. The young misfits mostly go, and the bar is still not met (results/ages_posthoc.md).
- What remains is a stretch. Between 0.1 and 1 Gyr ours are older by a median 0.19 dex (post hoc); between 10 and 100 Myr, younger by 0.14. The three calibration clusters were already 0.16 to 0.27 dex older. Whether our fits overshoot or theirs pull towards the middle, this test cannot say.
- The rich clusters agree: 9 of the 10 with 300 stars or more are within 0.3 dex, and our extinctions follow theirs closely (Spearman 0.95, ours 0.18 mag higher).
So the age colouring in the viewer stays Hunt & Reffert's, as a catalogue value, not as something this project reproduces. Each card shows both ages and draws both isochrones over the diagram, so a miss like the ones above can be seen. Full tables in results/ages.md.
The Hyades, 47 pc away, lose stars into two tidal tails that Röser et al. (2019) traced over a few hundred parsecs and Jerabkova et al. (2021) out to about 800 pc end to end. Across that much sky a tail star's proper motion changes with its position, so the regions' method cannot see them. The test, fixed in docs/protocol-hyades.md before the download: a convergent-point cut (tangential velocity within 3 km/s of the Hyades' space velocity projected at each star, widened by the parallax error), then HDBSCAN with excess of mass on 3D position, over all stars within 500 pc.
The bar is not met. The velocity cut keeps 165,536 of 913,737 stars, and excess of mass puts 152,904 of them in one group, the whole volume. So it "recovers" 283 of Jerabkova et al.'s 439 tail stars in our sample (64 %), and 88 % of Röser et al.'s, but only because it takes everything: under 1 % of our tail stars are theirs. Excess of mass fails as it did in Auriga.
The diagnostic after the run says why no velocity cut would have saved it. Jerabkova et al.'s tail stars stop sharing the cluster's tangential velocity with distance: a median of 1.1 km/s off within 100 pc of the Sun, 3.0 at 100–200 pc, 6.7 at 200–300 and 8.8 beyond. Tail stars drift away from the cluster's velocity as they go, which their method models with N-body simulations. Beyond 200 pc, 77 of their tail stars sit among 70,000 field stars closer to the cluster's velocity than they are. The near tails, within 200 pc, are where a plain velocity cut has a chance; the 800 pc tails are a model-based selection, not something this cut can check (results/hyades.md).
The viewer (source) shows both regions in space, seen from above the wedge that each one fills from the Sun: the field, the recovered clusters and the missed ones. Each cluster has a card with its distance, recovery, purity and colour-magnitude diagram.
- Field stars sit at their own distance, the geometric one of
Bailer-Jones et al. (2021), not at one over the
parallax, which is biased when the parallax is uncertain. It comes from the same GAVO service
(
gedr3dist.litewithdist), with the polygon and cuts of the star download. - The members of a recovered cluster sit at the cluster's distance in Hunt & Reffert
(
dist50), each at its own place on the sky. A member's own distance is uncertain by 87 pc in Carina and 85 pc in Auriga (median), while half of a cluster's members sit within 3.2 and 3.6 pc of its centre (medianr50pc). At their own distances, clusters would be needles some 25 times longer than wide, pointing at the Sun. The cost: depth is not shown, and seen side-on a cluster is flat. So a cluster's members only show when you point at it. - A cluster is drawn at its catalogue position, as wide as its tidal radius in Hunt & Reffert
(
rtpc) and never smaller than a few pixels: a sphere if it was recovered, a ring if it was missed. Pointing at a sphere swaps it for the group of the run that recovers it best (highest recovery × purity). In the colour-magnitude diagram, blue stars are in both our group and Hunt & Reffert, red only in our group and grey only in Hunt & Reffert: blue against red is purity, blue against grey is recovery. - Beside it, a proper-motion diagram of the same stars, over up to 400 field stars that share the cluster's patch of sky (three tidal radii, 0.3° to 3°) and distance (a quarter either way). A cluster's stars move alike, so they clump while the field spreads. A 3D view of the whole region in distance and proper motion was tried and set aside: at that scale the clusters sit inside the field's band and do not stand out.
- Colour by age recolours spheres and rings by Hunt & Reffert's median age (
logAge50) in four bands, lighter for younger: under 10 Myr, 10–100 Myr, 0.1–1 Gyr, over 1 Gyr. Shape still tells recovered from missed. Each card gives the age with its 16th–84th percentile range. - Tour (top right of the map) walks through six or seven clusters per region, from the nearest and richest to misses on purity and the farthest. The stops and their text are in viewer/tour.js; every number in them comes from the region's data.
- Under the map, Where it works charts the recovery rate by distance and by members in our
sample, both regions side by side, with the counts. The export writes them into each region's
meta.json(rates) from the scores, with the binsscore_region.pyreports in. - The groups that no Hunt & Reffert cluster owns (2,109 in Carina's min_cluster_size 10 run, 494 in Auriga's) stay hidden behind a toggle labelled unverified.
- One run at a time: a slider under the map shows a single leaf run, with min_cluster_size from
10 to 240: its recovered clusters, its misses, its groups and its unverified groups. These runs came
after the score, to explore, and are not part of it; the score stays the four runs the protocols fix.
Smaller sizes recover more clusters and find far more groups that no catalogue lists: in Carina,
143 of 202 recovered with 2,109 unverified groups at 10, against 13 of 202 with 15 at 240. Two charts
under Where it works follow both counts in both regions (also in
results/<region>_sweep.csv). - Level of detail: the field is stored in random order and sent in nested levels of 65,536 stars, doubling each time, so every level is a uniform sample of the field. The page shows the first at once, adds the rest as they arrive (on a phone, up to 524,288 unless asked) and draws fewer while the view moves. Like the sky maps above, it shows the field as a density on a log scale.
- Time: a slider and a play button move every star along the sky at its proper motion, up to 5 Myr either way. By default, the field's median motion at the star's distance (in 250 pc bins) is taken off: the Sun's own motion and the Galaxy's rotation shift every star at a distance alike, by about 6 to 11 mas/yr in Carina against a spread of 1 to 5. A toggle leaves it in. A cluster's members keep together while the field around them spreads. Most of these stars have no radial velocity in Gaia, so nothing moves in depth, and the paths are straight lines: a picture of the motions, not an orbit.
uv run scripts/export_viewer.py <region> writes the page's data into viewer/data/<region>/
(6.1 MB for Auriga, 26.1 MB for Carina, of which the proper motions, loaded only when time moves, are
2.3 and 10.1 MB) from what the scoring produces, and, if scripts/sweep_region.py has run, the
slider's runs (4.9 and 6.7 MB more, each run fetched when the slider reaches it). Then
python3 -m http.server -d viewer serves the page locally.
uv sync
uv run pytest
uv run scripts/pleiades.py # downloads into data/ on first run (~15 min from VizieR)
uv run scripts/fetch_region.py auriga # stars and distances from GAVO, Hunt & Reffert members from VizieR
uv run scripts/score_region.py auriga # HDBSCAN runs, scores, figures (same for carina)
uv run scripts/sweep_region.py auriga # optional: leaf runs from 10 to 240 for the viewer's slider
uv run scripts/fit_ages.py auriga # isochrone ages (also --calibration, --post-hoc); then compare_ages.py
uv run scripts/export_viewer.py auriga # the viewer's data
uv run scripts/fetch_hyades.py # the Hyades: all-sky sample within 500 pc (~15 min) and the references
uv run scripts/hyades.py # convergent point + HDBSCAN, scored against the published tails
blender -b -P scripts/render.py -- auriga # a still from the viewer's data, figures/render-auriga.jpg