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The completeness of the open cluster census towards the Galactic anticentre

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read After correcting for selection effects, old open clusters are $2.97\pm0.11$ times more common at a Galactocentric radius of 13 kpc than in the solar neighbourhood, and this excess is physical rather than a bias of the census.

desk verdict Impressive injection-recovery selection function; the old-cluster excess is likely real, but the headline 2.97 ratio carries unquantified systematics from using true parameters for completeness and measured ones for real clusters. read the letter →

arxiv 2506.18708 v1 pith:MTZIX4CH submitted 2025-06-23 astro-ph.GA astro-ph.SR

Emily L. Hunt , Tristan Cantat-Gaudin , Friedrich Anders , Lorenzo Spina , Lorenzo Cavallo , Alfred Castro-Ginard , Vasily Belokurov , Anthony G. A. Brown
show 4 more authors
Andrew R. Casey Ronald Drimmel Morgan Fouesneau Sabine Reffert
This is my paper · ORCID
classification astro-ph.GAastro-ph.SR
keywords openclustersGalacticanticentreselectionfunctioncompletenessGaiaDR3HDBSCANstructureclusterformation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper builds an empirical selection function for the HR24 open-cluster catalogue and uses it to ask whether the outer Milky Way really contains a different mix of old and young star clusters than the solar neighbourhood. The authors generate 192,318 realistic mock clusters, inject them into Gaia DR3 data, and try to recover them with the same blind HDBSCAN-based search that produced the catalogue. They find that cluster mass, distance, extinction, and age control detectability, with old clusters much harder to recover because they contain few bright stars. After correcting for these biases, they conclude that clusters older than $\log t = 8.5$ are $2.97 \pm 0.11$ times more common at a Galactocentric radius of 13 kpc than near the Sun, and that this excess cannot be explained by observational bias. If true, the result means the outer disc is not forming young clusters massive enough to be seen in Gaia, while a population of old clusters remains hidden there.

What carries the argument

The load-bearing object is an empirical selection function built by injecting realistic mock open clusters into Gaia DR3 and attempting to recover them with the same HDBSCAN blind search used to construct the catalogue. A gradient-boosted classifier converts the injection-recovery outcomes into a detection probability $f_{\rm detected}$ as a function of longitude, latitude, distance, mass, age, and proper motion; cluster core and tidal radii are dropped after showing negligible effect. This function is then used to correct the observed cluster counts in mass, distance, and age bins, and to forward-model what a kinematically 'warm' versus 'hot' outer-disc cluster population would look like.

What would settle it

Run a deeper, independent blind cluster search in the anticentre and count young ($\log t<8.5$) clusters of mass 250 to 2000 $M_\odot$ at $R_{\rm GC}\approx13$ kpc: if the completeness-corrected young fraction comes out well above $27.5\%\pm5.7\%$, the claimed $2.97\pm0.11$ excess of old clusters is wrong.

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Extended reading notes

Core claim

The central claim is that the observed excess of old open clusters in the Galactic anticentre is a real property of the Milky Way, not a selection artefact. Using 147,639 recovered mock clusters out of 192,318 injected, the paper builds a completeness model and finds that the fraction of clusters younger than $\log t = 8.5$ drops from $81.7\%\pm9.2\%$ in the solar neighbourhood to $27.5\%\pm5.7\%$ at $R_{\rm GC}=13$ kpc, equivalent to old clusters being $2.97\pm0.11$ times more common there. The paper further argues that this deficit of young outer-disc clusters is best interpreted as a limit on the mass of clusters that can form in the outer Galaxy, that many low-mass old clusters remain undiscovered, and that the two most distant known clusters, Berkeley 29 and Saurer 1, are likely the high-latitude tip of that hidden population.

Load-bearing premise

The result rests on the assumption that the simulated cluster population and the catalogue's mass and age estimates reproduce the true outer-disc population, so that the correction bins are not systematically mis-scaled.

Editorial extensions

If this is right

  • Completeness-corrected counts place the young-cluster fraction at $27.5\%\pm5.7\%$ at $R_{\rm GC}=13$ kpc, versus $81.7\%\pm9.2\%$ near the Sun, so old clusters are $2.97\pm0.11$ times more common in the outer disc.
  • The outer Galaxy is not forming young clusters massive enough to be identified in Gaia DR3, so $R_{\rm GC}\sim13$ kpc is likely a limit for massive cluster formation rather than for star formation itself.
  • The old-cluster census in the anticentre is probably very incomplete, with many low-mass or low-latitude old clusters still undiscovered; Berkeley 29 and Saurer 1 are likely the visible high-latitude part of that population.
  • The observed asymmetry of the cluster warp, with more old clusters below the disc than above it, survives selection correction at the $3.7\sigma$ level and would appear roughly twice as strong in a complete census.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Inference: applying the same injection-recovery machinery to the whole sky would separate algorithm-specific detection biases from physical gradients, allowing a direct test of whether the $2.97$ ratio persists beyond the anticentre.
  • Inference: the migration explanation carries a testable chemical signature: old clusters in the outer disc should show inner-disc metallicities and abundance patterns if they migrated outward, whereas a lower destruction rate predicts a shallower age gradient in the anticentre.
  • Inference: the selection function predicts specific dust-obscured low-latitude zones between $R_{\rm GC}=14$ and $19$ kpc where dozens of hidden low-mass old clusters should reside, a prediction that deeper astrometric or co-added ground-based surveys could check directly.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper constructs an empirical selection function for the open cluster census in the Galactic anticentre (140° ≤ ℓ ≤ 240°, |b| ≤ 10°, d ≥ 2 kpc), based on the HR23/HR24 HDBSCAN cluster search in Gaia DR3. The authors generate 194,752 realistic mock clusters spanning broad ranges in mass, age, distance, position, proper motion, and internal structure; inject them into Gaia DR3 data; and attempt blind recovery with the same HDBSCAN pipeline used for HR23. A gradient-boosting (XGBoost) model is trained on the resulting 147,639 recovered clusters to predict detection probability as a function of cluster parameters, yielding a smooth selection function. The main detectability drivers are found to be mass, extinction, distance, and age, with secondary effects from proper motion. Applying this selection function to HR24 clusters through a forward-modelled 'warm' kinematic correction, the paper reports that old clusters (log t > 8.5) are 2.97 ± 0.11 times more common at Galactocentric radius 13 kpc than in the solar neighbourhood, and interprets this as a physical property of the Milky Way rather than an observational bias. Additional applications address the Galactic warp in the old cluster population and the detectability of the distant clusters Berkeley 29 and Saurer 1.

Significance. If the central claim holds, the paper provides a strong, quantitative demonstration that the old-to-young open cluster ratio increases toward the outer Milky Way, with consequences for cluster formation thresholds, radial migration, and cluster destruction rates. The methodological contribution — an empirical, injection-based selection function for a full Gaia cluster catalogue — is important and likely to be reused for other surveys and regions. The paper has notable strengths: the injection-recovery experiment is large and closely replicates the original detection pipeline; the selection function is derived independently of the observed catalogue, so the central conclusion is not circular; and the CST predictor is validated against real clusters with an RMSE of 3.75, comparable to its simulated validation RMSE of 3.17. The principal weakness is that the size and direction of systematic errors in the headline 2.97 ratio, particularly those arising from the use of measured (rather than true) cluster parameters in the correction, are not quantified.

major comments (3)
  1. [§5.1, Fig. 8; §4.2]
  2. [§5.1]
  3. [§4.3]
minor comments (4)
  1. [Abstract and §5.1] The abstract states the 2.97 ± 0.11 ratio without noting that the analysis in Fig. 8 is restricted to clusters with masses between 250 and 2000 M☉ and to the adopted anticentre region and binning; please state this restriction in the abstract or results summary.
  2. [Fig. 7 caption] The caption says 'clusters in HR23 are shown by the blue points', while the text in §4.3 refers to HR24 clusters; please check which catalogue is plotted and make the caption consistent.
  3. [§5.2] When the below-disk cluster population is flipped in Z to estimate detection probabilities above the disk, the text should clarify how extinction and line-of-sight quantities are handled, since the selection function depends on l, b, d and therefore implicitly on the dust column at the new position.
  4. [§3.1.2] The assumption of virial equilibrium (η = 10) is stated to have negligible impact at the distances considered, but the text could note the expected maximum effect on the internal velocity dispersion for the nearest simulated clusters, to make this assertion easier to verify.

Circularity Check

0 steps flagged · score 0.0 of 10

No material circularity: the selection function is measured by an injection-recovery experiment, and the corrected 2.97 ratio is not an input to the fit.

full rationale

The derivation chain is not circular. The selection function is measured rather than assumed: mock clusters with known input parameters are injected into Gaia DR3 and recovered with the same HDBSCAN+CST pipeline used to build HR24 (Sects. 3.2 and 4.2), and the resulting XGBoost f_detected model is validated against real HR24 clusters in Sect. 4.3, with a CST RMSE of 3.75 on real clusters versus 3.17 on simulated validation data. The headline ratio of 2.97 is obtained by binning observed HR24 clusters by mass, distance, and age and scaling each bin by the measured inverse detection probability (Sect. 5.1); no equation defines the ratio as an input to the correction, and the warm and hot kinematic models are used only to evaluate how detectability would vary under alternative assumptions, not to impose the result. The Sect. 6 caveat that the correction is limited by the quality of cluster parameters is a legitimate calibration concern, not a circular step: a mismatch between measured and true masses or ages could bias the correction, but this is explicitly acknowledged and does not reduce the 2.97 claim to an assumed input. Self-citations to HR23, HR24, and Cavallo et al. (2024) are the catalogue under study and independent published products, and the paper's conclusion is not forced by a self-citation chain.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The ledger lists hand-set parameters and domain assumptions that the central claim depends on. None of these are fitted to the headline result, so the circularity burden stays low. The most load-bearing choices are the uniform simulation ranges and the warm kinematic model used in the forward-model correction; the latter directly affects the 2.97 factor. No new physical entities are introduced.

free parameters (6)
  • Fixed mock metallicity [M/H] = -0.2 dex
    Chosen in Table 2 as a fair average for the anticentre; metallicity has minimal impact on cluster CMDs for detectability, but the choice is hand-set.
  • Virial equilibrium assumption eta = 10
    Set in Sect. 3.2.2; clusters are assumed virialised. At the distances considered, internal dispersion is below Gaia proper-motion uncertainties, so the impact is small.
  • Uniform sampling ranges for mock cluster parameters = l 140-240 deg, b -10 to +10 deg, d 2-15 kpc, M 50-5000 Msun, logt 6.4-10.0, rc 1-5 pc
    Table 2; the selection function is computed from recovery fractions over this chosen grid, and the uniform weighting sets the effective prior for detection probabilities.
  • Warm model scale-height growth index = 1.3 (h_z ~ t^1.3)
    Sect. 5.1; adopted from Cantat-Gaudin et al. (2020) to represent a Milky-Way-like population in the forward model that produces the corrected ratio.
  • Warm model age-velocity relation = Tarricq et al. (2021) relation
    Sect. 5.1; used to generate proper motions of the simulated underlying population, which affects detectability corrections.
  • XGBoost hyperparameters = 200 estimators, max depth 7, learning rate 0.2
    Sect. 4.2; chosen by the authors after tuning and used for the smooth selection function.
assumptions (7)
  • domain assumption HR23/HR24 catalogue classifications and parameters are correct enough for binning and comparison.
    Stated in Sect. 2 and as a caveat in Sect. 6: the selection function is built for HR24 and assumes bound clusters are not systematically misclassified as moving groups.
  • domain assumption The Gaia selection function and HR23 quality-cut subsample selection function are accurately modelled.
    Sect. 3.1.1; uses the Cantat-Gaudin et al. (2023) selection function and Castro-Ginard et al. (2023) subsample method.
  • domain assumption Stellar population models (Kroupa IMF, PARSEC isochrones, Moe and Di Stefano binary fractions) describe cluster members.
    Sect. 3.1.1; mock photometry is generated from these models and drives the simulated cluster luminosity functions.
  • domain assumption Green et al. (2019) dust map gives correct extinction at the cluster distances.
    Sect. 3.1.1; extinction for each simulated cluster is drawn from this map, and the map strongly shapes the detectability patterns in Fig. 5.
  • domain assumption MWPotential2014 and the Jacobi radius formula give correct cluster tidal radii.
    Sect. 3.1.2; used to set cluster tidal radii, which the paper finds has little effect on detectability.
  • domain assumption HDBSCAN recovery with quality cuts reproduces the HR23 blind search.
    Sect. 3.2.1; the same algorithm, min_cluster_size values, and CST threshold are used, which is necessary for the selection function to apply to HR24.
  • domain assumption Cavallo et al. (2024) ages and extinctions are accurate for old clusters.
    Sect. 2; these ages define the old/young split used throughout the analysis.

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Cite this review

Pith. "Pith review of The completeness of the open cluster census towards the Galactic anticentre." pith.science (2026). https://pith.science/paper/MTZIX4CH

@misc{pith2026250618708,
  author       = {Pith},
  title        = {Pith review of: The completeness of the open cluster census towards the Galactic anticentre},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MTZIX4CH}},
  note         = {Machine review of arXiv:2506.18708}
}
abstract

Open clusters have long been used as tracers of Galactic structure. However, without a selection function to describe the completeness of the cluster census, it is difficult to quantitatively interpret their distribution. We create a method to empirically determine the selection function of a Galactic cluster catalogue. We test it by investigating the completeness of the cluster census in the outer Milky Way, where old and young clusters exhibit different spatial distributions. We develop a method to generate realistic mock clusters as a function of their parameters, in addition to accounting for Gaia's selection function and astrometric errors. We then inject mock clusters into Gaia DR3 data, and attempt to recover them in a blind search using HDBSCAN. We find that the main parameters influencing cluster detectability are mass, extinction, and distance. Age also plays an important role, making older clusters harder to detect due to their fainter luminosity function. High proper motions also improve detectability. After correcting for these selection effects, we find that old clusters are $2.97\pm0.11$ times more common at a Galactocentric radius of 13~kpc than in the solar neighbourhood -- despite positive detection biases in their favour, such as hotter orbits or a higher scale height. The larger fraction of older clusters in the outer Galaxy cannot be explained by an observational bias, and must be a physical property of the Milky Way: young outer-disc clusters are not forming in the outer Galaxy, or at least not with sufficient masses to be identified as clusters in Gaia DR3. We predict that in this region, more old clusters than young ones remain to be discovered. The current presence of old, massive outer-disc clusters could be explained by radial heating and migration, or alternatively by a lower cluster destruction rate in the anticentre.

Figures

Figures reproduced from arXiv: 2506.18708 by the authors.

Figure 1
Figure 1. Spatial distribution of high-certainty clusters (CST>4) from Hunt & Reffert (2023). Ages are taken from Cavallo et al. (2024) as they are more accurate for old clusters (see Sect. 2 for discussion). Top left: Histogram of cluster galactocentric radii divided into young (log t < 8.5, blue) and old (log t > 8.5, red) clusters and with a 200 pc bin width. Bottom left: Distribution of the same young and old clusters but… view at source ↗
Figure 2
Figure 2. Example result of the injection-recovery procedure for a simulated OC, in the typical projections used in cluster discovery studies. Top row: Original simulated cluster (including realistic Gaia DR3-like astrometric errors), shown in position (far left), proper motion (centre left), position versus parallax (centre right), and the colour-magnitude diagram of the cluster (far right). This simulated cluster was then i… view at source ↗
Figure 3
Figure 3. Trends in cluster detectability as a function of ten cluster parameters for the simulated cluster injection and retrievals in this work. In each subplot, the black line shows the fraction of clusters detected, fdetected, while marginalising over all other parameters. For comparison, the grey line shows the distribution of injected clusters in this work, normalised to have a maximum at one. The top row of plots and t… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Comparison between the impact of extinction AV and distance modulus µ on cluster detectability, for clusters with a mass below 800 M⊙. The blue curve shows fdetected as a function of distance modu￾lus µ for simulated clusters with negligible extinction (AV < 0.5), whil…
Figure 5
Figure 5. Figure 5: Fraction of simulated clusters recovered compared to the input dust distribution in this study. Top: Fraction of all simulated clusters recovered in this work as a function of l and b. Clusters were binned in bins of size 1◦ × 1 ◦ . Grey circles show the distribution o…
Figure 6
Figure 6. Figure 6: Fraction of simulated clusters recovered as a function of RGC and Z divided into multiple different mass and ages ranges, and compared against the distribution of OCs in HR24 within those ranges. Each row shows clusters in a different mass range, indicated by the label…
Figure 7
Figure 7. Figure 7: Comparison between the CST of simulated and real clusters in a restricted parameter range as a function of cluster mass. Simulated clusters are shown by the heatmap in the background, while clusters in HR23 are shown by the blue points, plotted as a function of their m…
Figure 9
Figure 9. Figure 9: Top: Fraction of detectable clusters as a function of Galactocentric radius at three different masses and five different ages, for the simulated kinematically warm cluster population (see text). Middle: Same as above, for the kinematically hot cluster population. Botto…
Figure 10
Figure 10. Figure 10: Fraction of simulated clusters recovered at young and old ages compared to the location of old distant clusters Berkeley 29 and Saurer 1. Top: Sky distribution of simulated cluster recoveries for young clusters log t < 7.5, at distances greater than 10 kpc, and with m…

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