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Open cluster members in APOGEE DR17 I. Dynamics and star members

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Adding APOGEE radial velocities and iron abundances to Gaia astrometry in an HDBSCAN analysis yields 1,987 member stars across 49 open clusters, and the authors find that clusters younger than 2 Gyr trace a shallower Milky Way metallicity…

desk verdict A useful APOGEE+Gaia membership catalog for 49 open clusters, but the age-dependent gradient headline is a sub-2σ effect that the paper overstates. read the letter →

arxiv 2506.19936 v2 pith:6K4P6MM3 submitted 2025-06-24 astro-ph.GA astro-ph.SR

R. Guerço , D. Souto , J. G. Fernández-Trincado , S. Daflon , K. Cunha , J. V. Sales-Silva , V. Loaiza-Tacuri , V. V. Smith
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M. Ortigoza-Urdaneta M. P. Roriz
This is my paper · ORCID
classification astro-ph.GAastro-ph.SR
keywords openclustersHDBSCANGaiaEDR3APOGEEDR17metallicitygradientGalacticdiskevolutionclustermembershipprobabilitiesbarresonance
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

The paper tries to establish that combining Gaia EDR3 astrometry with APOGEE DR17 radial velocities and iron abundances in a single HDBSCAN clustering recovers open-cluster members more reliably than astrometry alone. Using that method, the authors identify 1,987 tentative member stars across 49 open clusters, 941 of them with membership probability above 80%. From the cluster means, they recover a two-slope metallicity gradient with Galactocentric radius and guiding-center radius, and they report the central new result: clusters younger than 2 Gyr trace a shallower $[\mathrm{Fe/H}]$ gradient (about $-0.066$ to $-0.067$ dex/kpc) than clusters older than 2 Gyr (about $-0.074$ to $-0.088$ dex/kpc). If this age split is real, open clusters record a chemical flattening of the outer Galactic disk over roughly the last 2 Gyr, and the new membership catalog becomes a tool for further chemical and dynamical studies.

What carries the argument

The machine at the center is HDBSCAN, a hierarchical density-based clustering algorithm that builds a persistence dendrogram over the combined feature space and assigns each point a membership probability from the stability of the branch it belongs to. Its two control parameters are the minimum number of points ($m_{pts}$) and the minimum cluster size ($m_{clSize}$); the authors set $m_{pts}=m_{clSize}$ and choose $m_{clSize}$ between 2 and 10 per cluster by minimizing the standard deviation of $[\mathrm{Fe/H}]$ among members with probability above 80%. Radial velocity and $[\mathrm{Fe/H}]$ are the extra dimensions that distinguish this run from earlier astrometry-only HDBSCAN membership catalogs, and they do the work of suppressing interloping field stars with discrepant line-of-sight motion. A second piece of machinery is GravPot16, a steady-state Galactic potential with a boxy/peanut bar, used with Monte Carlo resampling to integrate half a million orbits per cluster and to identify corotation resonance and Lagrange-point trapping.

What would settle it

Re-run the membership analysis with $[\mathrm{Fe/H}]$ removed from the HDBSCAN features and with the minimum cluster size chosen by a criterion unrelated to metallicity scatter, then recompute the age-split gradients; if clusters older than 2 Gyr no longer show a steeper slope than younger clusters, the central gradient claim fails. A second decisive check is to measure intra-cluster element scatter from high-resolution spectra: finding real $\sigma([\mathrm{Fe/H}])$ or other abundance scatter above the roughly 0.02 dex homogeneity floor would show that the tuning step selects against genuine chemical variation.

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Extended reading notes

Core claim

Open clusters are chemically homogeneous by assumption, so the authors run HDBSCAN over six input dimensions—right ascension, declination, parallax, proper motions, radial velocity, and $[\mathrm{Fe/H}]$—and tune the minimum cluster size per cluster to minimize the metallicity scatter of its high-probability members. The resulting catalog contains 1,987 stars in 49 clusters, with 941 stars above 80% membership probability; stars within $2\sigma$ of the cluster mean radial velocity receive higher probabilities, whereas stars $2$–$3\sigma$ away drop below 50%. The cluster means define a $[\mathrm{Fe/H}]$ gradient that steepens with age: young clusters (age below 2 Gyr) show a single shallow slope of $-0.066\pm0.004$ dex/kpc in projected Galactocentric distance and $-0.067\pm0.005$ dex/kpc in guiding-center radius, while clusters older than 2 Gyr show $-0.074\pm0.018$ and $-0.088\pm0.010$ dex/kpc. The full sample also shows the previously reported two-slope shape, with a steep inner decline of $-0.085\pm0.011$ dex/kpc inside about 11.5 kpc and a flatter outer slope of $-0.032\pm0.004$ dex/kpc beyond it. Orbit integrations with a barred Galactic potential place all 49 clusters on prograde, disk-like, low-eccentricity orbits, with a few clusters, notably NGC 6705, trapped in resonant motion around the bar's Lagrange points $L_4$ and $L_5$.

Load-bearing premise

The load-bearing premise is that each open cluster is chemically homogeneous in $[\mathrm{Fe/H}]$, so choosing the clustering parameter that minimizes metallicity scatter among high-probability members is a valid way to find true members; if real intra-cluster scatter exists or APOGEE metallicities carry systematics that track position or distance, the memberships, mean metallicities, and the age-split gradient slopes are all biased in the same direction.

Editorial extensions

If this is right

  • Membership catalogs built from Gaia astrometry alone can be sharpened by adding spectroscopic radial velocities and metallicities; stars near the cluster velocity mean gain confidence while outliers fall below 50% probability.
  • The Milky Way's outer-disk chemical gradient stops flattening at small radii only when clusters older than 2 Gyr are included; the under-2-Gyr sample alone shows no break in slope from 6 to 16 kpc.
  • If the age split is real, the Galactic disk's chemical enrichment has been more spatially uniform in the last 2 Gyr than before, constraining models of radial migration and gas accretion.
  • The two-slope gradient changes its break location depending on whether radius is measured as projected Galactocentric distance (break near 11.5 kpc) or guiding-center radius (break near 10.5 kpc), so the flattening is tied to orbital angular momentum, not just present position.
  • Bar-resonant open clusters such as NGC 6705 provide a population-level test of whether the Galactic bar traps clusters near corotation, connecting cluster dynamics to moving groups in the solar neighborhood.

Reading between the lines

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

  • A test the authors do not run is to remove $[\mathrm{Fe/H}]$ from the HDBSCAN inputs and re-derive the gradients; if the age split persists, the result is not an artifact of tuning the cluster size to metallicity scatter, and if it vanishes, the circularity in the tuning criterion is implicated.
  • The homogeneity assumption could be checked directly with the same APOGEE spectra by measuring the scatter in other elements, since the paper only validates low scatter in $[\mathrm{Fe/H}]$; real scatter in, say, carbon or magnesium would show that the tuning step is conflating chemical homogeneity with selection.
  • The bar-resonance interpretation depends on the adopted bar pattern speed; varying it from 31 to 51 km s$^{-1}$ kpc$^{-1}$ changes which clusters appear trapped, so an independent measurement of the bar speed would be needed before using these orbits as evidence for the Hercules stream's origin.
  • The catalog is limited to APOGEE-observed stars, mostly red giants, so the member lists are incomplete at the low-mass end; completeness-corrected samples would be needed before interpreting the 1,987-star count as a census of cluster population.
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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

4 major / 5 minor

Summary. This paper applies the HDBSCAN clustering algorithm to Gaia EDR3 astrometry (RA, Dec, parallax, proper motions) and APOGEE DR17 spectroscopy (radial velocity and [Fe/H]) to identify open cluster (OC) members in 49 clusters, yielding 1,987 tentative members, of which 941 have membership probabilities above 80%. The authors then compute orbital elements using the GravPot16 potential, find that the clusters are on prograde disk-like orbits with a few showing bar-resonant behavior, and derive metallicity gradients as a function of projected Galactocentric distance and guiding-center radius. They report a two-slope gradient, consistent with earlier work, and claim that clusters younger than 2 Gyr have a shallower gradient than older clusters.

Significance. If the membership catalog is reliable, it is a useful resource: it adds APOGEE radial velocities and metallicities to Gaia-based cluster memberships and provides orbital parameters for 49 clusters. The reported overlap with Cantat-Gaudin & Anders (2020) and Hunt & Reffert (2023) for M67 and NGC 2158 is encouraging, and the two-slope metallicity gradient with an inner slope near -0.085 dex/kpc and an outer slope near -0.03 dex/kpc is consistent with several previous studies. However, the paper's headline physical claim, an age-dependent gradient steepening for clusters older than 2 Gyr, is not supported by the quoted slopes, which differ by less than 2σ. In addition, the membership method uses metallicity scatter both as a tuning criterion and as a validation metric, which is circular and may bias the cluster mean metallicities that feed into the gradient analysis. The age-gradient claim therefore needs a proper statistical test, and the membership validation needs to be extended to all clusters before the conclusions can be accepted.

major comments (4)
  1. [Section 4.2, Fig. 8(e)-(h)] The claim that clusters older than 2 Gyr show 'significantly steeper' metallicity gradients is not supported by the quoted numbers. For RGC, the slopes are -0.066±0.004 dex/kpc for age<2 Gyr and -0.074±0.018 dex/kpc for age>2 Gyr, a difference of 0.008±0.018 dex/kpc (~0.4σ). For RGuide, the difference is 0.021±0.011 dex/kpc (~1.9σ). A sub-2σ difference in an unweighted fit of 30 versus 19 clusters is not a 'clear distinction,' as the Conclusions state. Moreover, the fits use sklearn LinearRegression on cluster means without weights and without propagating cluster-level uncertainties or the covariance between [Fe/H] and RGuide, both of which depend on the same distance and orbit inputs. The authors should either perform a proper statistical test (e.g., bootstrap with cluster resampling, or a weighted fit that includes the distance-metallicity covariance) or temper the conclusion to reflect that the evidence is marginal.
  2. [Section 3.1 and 3.2] The membership procedure is circular with respect to the metallicity-scatter claim. In Section 3.1, mclSize is chosen per cluster as the value that minimizes the standard deviation of [Fe/H] among stars with membership probabilities above 80%, explicitly assuming that OCs are chemically homogeneous. Section 3.2 then reports that the selected members have low σ([Fe/H]) (~0.04 dex) and cites this as evidence supporting the membership assignments. The low scatter is partly guaranteed by construction, so it cannot be used as independent validation. More importantly, selecting members to minimize metallicity scatter can bias the cluster mean [Fe/H] used in the gradient analysis, especially if APOGEE metallicity uncertainties or systematics correlate with sky position or distance. The authors should validate memberships using the cross-match with Cantat-Gaudin & Anders (2020) and Hunt & Reffert (2023) for all clusters, and should assess how the gradient slopes change when mclSize is selected by a criterion that does not involve [Fe/H].
  3. [Section 3.2] The cross-validation of the membership catalog is anecdotal: only two clusters (M67 and NGC 2158) are compared quantitatively with previous catalogs. For a paper whose main product is a membership catalog, the authors should report agreement statistics for all 49 clusters, including the number of common members, the fraction of our high-probability members found in Cantat-Gaudin & Anders (2020) and Hunt & Reffert (2023), and the level of contamination. Without such global metrics, the membership probabilities are not calibrated and the reliability of the catalog is not established.
  4. [Section 4.2, Fig. 8(c,d,g,h)] The two-slope gradient and the 'no break' statement for the young-cluster subsample are not backed by statistical tests. The breakpoint for the two-slope fit (11.5 kpc in RGC, 10.5 kpc in RGuide) is stated without justification or uncertainty, and no test is presented to show that a two-slope model is preferred over a single slope. Similarly, the statement that there is 'no break' for clusters younger than 2 Gyr is not quantified; the reader cannot tell whether the single-slope fit is actually a good description of the inner and outer parts. The authors should add model-comparison statistics (e.g., F-test, BIC, or bootstrap) and should discuss the sensitivity of the age-gradient conclusion to the choice of breakpoint and age split.
minor comments (5)
  1. [Abstract and Section 4.2] The abstract is internally inconsistent: it says 'we observe no significant difference in the metallicity gradient slope beyond a certain distance' and then immediately says 'Our results show a shallower gradient for clusters younger than 2 Gyr.' The body text (Section 4.2) also uses 'significantly steeper' for the >2 Gyr slopes, which the quoted uncertainties do not support. Please rephrase to be consistent and to reflect the actual significance.
  2. [Figure 3 caption] The word 'Probability' is misspelled as 'Probaility' in the color-bar label of the upper panel.
  3. [Section 4.2] The text says 'Milk Way map' instead of 'Milky Way map' in the description of Figure 7.
  4. [Section 4.2, Fig. 8 caption] The caption and text state that the ages 'from 0.02 to 4.00 Gyr,' but Table B.1 lists several clusters with ages greater than 4 Gyr (e.g., Berkeley 17 at 7.24 Gyr, NGC 188 at 7.08 Gyr, Collinder 261 at 6.31 Gyr, NGC 6791 at 6.31 Gyr). Please correct the stated age range or clarify that it refers to a subset.
  5. [Section 4.1] The characterization of some orbits as 'chaotic' appears to be based on visual inspection of the orbital projections rather than a quantitative chaos indicator (e.g., Lyapunov exponents or frequency analysis); please clarify the criterion used.

Circularity Check

1 steps flagged · score 4.0 of 10

The mclSize tuning minimizes σ([Fe/H]) among high-probability members, so the reported low metallicity scatter is partly guaranteed by construction; the membership catalog and gradient claims are not directly circular.

  1. fitted input called prediction [Section 3.1 (mclSize selection, Fig. 2, Table B.1) and Section 3.2 (low-σ report)]
    "The optimal mclSize value for each OC was determined by selecting the value that led to the smallest standard deviation of the mean metallicity of stars with membership probabilities greater than 80%. ... Regarding metallicities, we find that OCs exhibit [Fe/H] values with lowσfor their stars that have probabilities greater than 80%. For the 49 OCs included here, the typical value ofσ([Fe/H])∼0.04 dex, using the [Fe/H] values from DR17. These standard deviations were used as a criterion in HDBSCAN to determine the value of mclSize for each OC."

    Section 3.1 tunes mclSize to minimize σ([Fe/H]) among P>80% members, under an assumption of chemical homogeneity that the passage explicitly acknowledges. Section 3.2 then reports the resulting low σ([Fe/H]) (typical 0.04 dex) as a validation of homogeneity, explicitly stating that these standard deviations were the criterion for choosing mclSize. The reported low scatter is thus partly guaranteed by the selection rule: the cluster definition and the validation metric are the same quantity. External comparisons (Bovy 2016; Sinha et al. 2024) provide independent support, so the circularity is partial, not total. The membership and gradient claims are not directly optimized by this criterion and are cross-checked against external catalogs, so they retain independent content.

full rationale

The main circular step is in the homogeneity validation: mclSize is fitted to minimize σ([Fe/H]) among high-probability members, and that same σ([Fe/H]) is then reported as an empirical finding of low scatter. This is a fitted input presented as a result, but it supports a secondary validation claim rather than the paper's central catalog or gradient results. The HDBSCAN memberships are checked against Hunt & Reffert (2023) and Cantat-Gaudin & Anders (2020), and the gradient slopes are compared with Spina et al. (2022), Myers et al. (2022), and Magrini et al. (2023); those comparisons are external and not circular. Use of the author-developed GravPot16 for orbit calculations is a self-citation but not a load-bearing circularity: the potential is constructed from the Besançon model and external parameters, and RGuide is not defined in terms of the gradient result. The skeptic's statistical critique of the age-gradient significance is a robustness/correctness concern, not a circularity, and does not increase the score beyond the partial construction of the low-scatter claim. Overall score 4 reflects one concrete partial circularity while the central claims retain independent content.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claims rest on per-cluster mclSize tuning, an empirical window ratio, and hand-selected breakpoints, together with assumptions that cluster chemistry is homogeneous, survey calibrations are accurate, and the GravPot16 barred potential describes the Milky Way. No new physical entities are introduced.

free parameters (3)
  • mclSize per cluster = 2 to 10, listed per cluster in Table B.1
    Chosen per open cluster to minimize the [Fe/H] scatter of high-probability members; this controls which stars are called members and affects the mean metallicities used for gradients.
  • HDBSCAN window size ratio = 6, with 8 and 10 for four clusters
    The ratio between the angular search window and the Gaia parallax is described as empirically chosen in Section 3, and a few clusters use different values for better HDBSCAN operation.
  • Two-slope breakpoints = RGC = 11.5 kpc and RGuide = 10.5 kpc
    The piecewise regressions in Figure 8 use breakpoints selected by inspection or comparison with prior work; no uncertainty or automated breakpoint fit is reported, and the outer slope depends on this choice.
assumptions (6)
  • domain assumption Open clusters are chemically homogeneous in [Fe/H].
    Used in Section 3.1 to choose mclSize by minimizing metallicity scatter and in the interpretation of the low sigma([Fe/H]) values in Section 3.2. The paper states this assumption explicitly.
  • domain assumption APOGEE DR17 radial velocities and metallicities are accurate to the stated levels of about 1 km/s and 0.02 dex.
    The HDBSCAN inputs and all cluster mean parameters inherit the APOGEE pipeline calibrations described in Section 2.2.
  • domain assumption Gaia EDR3 astrometry and Bailer-Jones distances are reliable for these clusters.
    Positions, parallaxes, and proper motions from Gaia and distances from Bailer-Jones et al. (2021) feed both the clustering and the orbit integrations.
  • domain assumption The GravPot16 Besancon-based potential with the adopted bar parameters represents the Milky Way sufficiently well.
    Orbital elements and the Lagrange point resonance claims in Section 4.1 depend on this model, including the bar pattern speed, orientation, and solar position.
  • domain assumption Cantat-Gaudin and Anders (2020) ages are accurate enough for the 1 Gyr and 2 Gyr age bins.
    The age split used for the metallicity gradient comparison is taken entirely from that catalog, and the paper does not independently verify cluster ages.
  • domain assumption HDBSCAN clusters found in the chosen windows correspond to physical open clusters rather than density artifacts.
    The method identifies groups in the combined feature space, but the paper does not validate each cluster with isochrone fitting or independent membership codes beyond cross-matching a few cases.

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Pith. "Pith review of Open cluster members in APOGEE DR17 I. Dynamics and star members." pith.science (2026). https://pith.science/paper/6K4P6MM3

@misc{pith2026250619936,
  author       = {Pith},
  title        = {Pith review of: Open cluster members in APOGEE DR17 I. Dynamics and star members},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6K4P6MM3}},
  note         = {Machine review of arXiv:2506.19936}
}
read the original abstract

Context. Open clusters (OCs) are groups of stars formed from the same cloud of gas and cosmic dust. They play an important role in studies of star formation and evolution and our understanding of galaxy structure and dynamics. Aims. The main objective of this work is to identify stars that belong to OCs using astrometric data from Gaia EDR3 and spectroscopic data from APOGEE DR17. Furthermore, we investigate the metallicity gradients and orbital properties of the OCs in our sample. Methods. By applying the HDBSCAN clustering algorithm to these data, we identified observed stars in our galaxy with similar dynamics, chemical compositions, and ages. The orbits of the OCs were also calculated using the GravPot16 code. Results. We find 1,987 stars that tentatively belong to 49 OCs; 941 of these stars have probabilities above 80 \% of belonging to OCs. Our metallicity gradient presents a two-slope shape for two measures of different Galactic center distances -- the projected Galactocentric distance and the guiding center radius to the Galactic center -- as already reported in previous work. However, when we separate the OCs by age, we observe no significant difference in the metallicity gradient slope beyond a certain distance from the Galactic center. Our results show a shallower gradient for clusters younger than 2 Gyr than those older than 2 Gyr. All our OCs dynamically assemble the disk-like population very well, and they are in prograde orbits, which is typical for disk-like populations. Some OCs resonate with the Galactic bar at the Lagrange points L4 and L5.

Figures

Figures reproduced from arXiv: 2506.19936 by the authors.

Figure 1
Figure 1. Cluster tree, or dendrogram, produced by HDBSCAN [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. mclS ize vs. σ([Fe/H]) of M 67. The blue squares represent all stars, the red circles stars with probabilities greater than 50 %, and the green triangles stars with probabilities greater than 80 %. standard deviation of the mean metallicity of stars with mem￾bership probabilities greater than 80%. This assumes, of course, that OCs have homogeneous chemical abundances. We note that in cases where the standard deviati… view at source ↗
Figure 4
Figure 4. Probabilities from this work vs. probabilities from [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: Kinematics and orbital elements of selected OCs. Panel (a): Galactocentric RV (V [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Ensemble of half a million orbits in the frame corotating with the bar for two selected OCs, projected on the equatorial (top) [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Distributions in Galactocentric coordinations X and [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Metallicity gradient, where RGC is the projected Galactocentric distance and the RGuide is obtained from the average between apocenter and pericenter. Blue circles represent the 49 OCs of this work. In panels (a) and (b), the red lines represent the median of [Fe/H] fo…

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Open Cluster Chemical Abundances and Mapping Survey XI. First Gradients from SDSS/MWM BOSS Determined Clusters

    astro-ph.GA 2026-07 conditional novelty 5.0 of 10

    Using 95 new young open clusters from SDSS-V/BOSS, the OCCAM survey finds the Galactic radial metallicity gradient is about -0.08 dex/kpc and does not evolve significantly with cluster age.

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