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REVIEW 3 major objections 6 minor 50 references

Deep Photometric and Astrometric Investigation of the Non-relaxed Star Cluster Stock 3 using Gaia DR3

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Gaia DR3 proper motions yield 73 members of Stock 3, a 16 Myr cluster at 2.9 kpc with mass 135 solar masses.

desk verdict A workmanlike Gaia DR3 re-analysis of Stock 3 whose astrometry and distance are credible, but whose total mass and IMF slope rest on an acknowledged photometric incompleteness that the paper never corrects. read the letter →

arxiv 2501.11997 v1 pith:S3RA2J6U submitted 2025-01-21 astro-ph.SR astro-ph.GA

A. Ahmed , Amira R. Youssef , M.S. El-Nawawy , W. H. Elsanhoury This is my paper · ORCID
classification astro-ph.SRastro-ph.GA
keywords openclustersStock3GaiaDR3proper-motionmembershipinitialmassfunctionstellaragesegregationparallaxzero-point
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 re-derives the disputed basic parameters of the open cluster Stock 3 from Gaia DR3. A proper-motion membership selection identifies 73 stars with membership probability at least 80 percent, and these members yield a mean parallax-based distance of $3.20 \pm 0.36$ kpc and an isochrone-based distance of $2.945 \pm 0.700$ kpc, with an age of $16.00 \pm 4.00$ Myr. Summing the member masses from a 16 Myr isochrone mass-luminosity relation gives a total mass of $135.54 \pm 15.13$ $M_\odot$ and an IMF slope $\alpha = 2.24 \pm 0.69$, in agreement with the Salpeter value. The paper additionally finds that Stock 3 is not dynamically relaxed ($\tau \approx 3$) yet shows mass segregation, so the segregation's origin cannot be settled from these data. A fair reader would care because this places a previously inconsistent set of cluster parameters onto one homogeneous Gaia DR3 basis.

What carries the argument

The argument is carried by the proper-motion membership formalism of Balaguer-Núñez et al. (1998) as implemented by Yadav et al. (2013): cluster and field stars are each represented by Gaussian frequency functions in the vector point diagram, and the membership probability of each star is the ratio of the cluster contribution to the total. That machinery selects the 73 likely members that all later parameter estimates use. A second load-bearing piece is the fourth-degree polynomial mass-luminosity relation built from the 16 Myr Marigo et al. (2017) isochrones, which converts each member's absolute $G$ magnitude into a mass; summing these masses gives $135.54 \pm 15.13$ $M_\odot$, and the binned mass histogram gives the slope $\Gamma = 1.24$, i.e. $\alpha = 1 + \Gamma = 2.24$.

What would settle it

A deeper, completeness-corrected census of the cluster field, for example Gaia DR4 or ground-based photometry reaching below the current $G \approx 20.2$ mag membership limit, would settle the mass and IMF claims: if the added faint members raise the cluster mass well above $135.54$ $M_\odot$ or shift the fitted slope away from $\alpha \approx 2.24$, the paper's main conclusions break down.

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Extended reading notes

Core claim

The central claim is that Stock 3 is a young, moderately distant open cluster whose bulk properties can be read from Gaia DR3 after a proper-motion membership cut. The 73 high-probability members share a mean proper motion ($\mu_\alpha \cos\delta = -2.0673 \pm 0.0173$ mas yr$^{-1}$, $\mu_\delta = -0.4657 \pm 0.0192$ mas yr$^{-1}$) and a zero-point-corrected parallax of $0.3122 \pm 0.0351$ mas. Fitting 16 Myr Marigo isochrones to the colour-magnitude diagram gives $E(B-V)=0.97$ mag, extinction $A_G=2.66$ mag, and a distance of $2.945 \pm 0.700$ kpc. The cluster's total mass is $135.54 \pm 15.13$ $M_\odot$ and its mass-function slope is $\alpha = 2.24 \pm 0.69$, close to Salpeter's 2.35 over the sampled mass range of about 1 to 9.5 $M_\odot$. Dynamically, the cluster has a relaxation time of $5.28 \pm 0.94$ Myr against an age of about 16 Myr, so it is not fully relaxed; the paper finds statistically significant mass segregation but concludes that, because the age already exceeds the relaxation time, the observed segregation cannot be unambiguously attributed to initial conditions or to dynamics.

Load-bearing premise

The load-bearing premise is that the 73 proper-motion-selected members form a complete enough census for the total mass and IMF slope; the paper's own luminosity function shows photometric incompleteness around $M_G=1$ to 3 mag and fainter than about 4 mag, and no completeness correction is applied before summing masses or fitting the mass function.

Editorial extensions

If this is right

  • Stock 3 becomes a well-characterized young open cluster at about 2.9 kpc with 73 probable members on a homogeneous Gaia DR3 basis, replacing the widely scattered literature values.
  • The measured mass-function slope $\alpha=2.24\pm0.69$ is consistent with the Salpeter value, so the cluster's present-day mass function does not require a non-standard IMF.
  • With $\tau \approx 3$, Stock 3 is not dynamically relaxed, so any mass segregation seen in it cannot be produced by two-body relaxation alone within its current age.
  • The cluster's mean proper motion and parallax give a kinematic anchor for follow-up radial-velocity work and for checking future astrometric catalogues.

Reading between the lines

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

  • Because the paper's own luminosity function shows incompleteness around $M_G = 1$ to 3 mag and fainter than about 4 mag, the quoted total mass and IMF slope likely undercount low-mass members; a completeness-corrected luminosity function would test how much the mass and $\alpha$ change.
  • The membership cut uses an assumed intrinsic proper-motion dispersion of 0.075 mas yr$^{-1}$; re-fitting the two-dimensional proper-motion distribution rather than adopting a fixed dispersion would show how sensitive the 73-member census and the derived cluster mass are.
  • If Stock 3 is truly 16 Myr old with a relaxation time near 5 Myr, it is a promising target for studying mass segregation in a very young cluster; radial-velocity dispersion and binary fraction measurements would sharpen that test.
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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 / 6 minor

Summary. The manuscript presents a Gaia DR3-based study of the open cluster Stock 3. Using proper-motion membership selection (73 members with P ≥ 80%), the authors derive a cluster center and radius, mean proper motion and parallax, and an isochrone fit that gives age 16 Myr, reddening E(B−V) = 0.97 mag, and distance 2.945 kpc, which is consistent with the parallax-based distance of 3.203 kpc. They further compute a total mass of 135.54 M☉ and an IMF slope α = 2.24, and analyze the dynamical state, velocity ellipsoid, and 3D morphology.

Significance. If the results hold, the paper provides an updated parameter set for Stock 3 in agreement with recent DR2 work and with an internally consistent parallax check. The use of Gaia DR3 astrometry with zero-point correction and the explicit comparison to earlier studies are strengths. However, the headline mass and IMF slope are not yet established because the member sample is incomplete and no completeness correction is applied; the dynamical-state claim is also internally inconsistent. The paper's main value is therefore as a DR3 update for a relatively young, distant cluster, pending the revisions outlined below.

major comments (3)
  1. [§7, Figs. 8–9] The total cluster mass and IMF slope are computed from the 73 proper-motion members without any completeness correction, despite the paper's own statement in Section 7 that the luminosity function 'reflects the incompleteness in the photometry' at M_G ≈ 1–3 and > ≈ 4 mag (Fig. 8). With a detection limit near G ≈ 20.2 and the adopted distance modulus, the sample is incomplete at the faint end, and the non-uniform dip at M_G ≈ 1–3 means even the bright end is not demonstrably complete. Summing the masses of the detected members to obtain M_cl = 135.54 ± 15.13 M☉ therefore yields a lower limit on the detected-member mass, not the cluster total mass, and the least-squares fit over the entire mass range in Fig. 9 is biased by the incompleteness. The authors should either apply a completeness correction or explicitly report the mass as a lower limit and restrict the IMF fit to the magnitude/mass interval that is photometrically complete.
  2. [§8, Eq. (12), Table 3] There is an internal contradiction in the dynamical-state analysis. The text states T_R = 5.28 ± 0.94 Myr and 'the cluster is not dynamically relaxed yet,' while immediately afterward it notes that the cluster's age (16 Myr) is larger than the relaxation time and therefore 'such result can not resolve the debate.' The computed τ = Age/T_R = 3.03 (Table 3) exceeds unity, which by the paper's own criterion (τ ≫ 1 for relaxation) implies the cluster is at least partially relaxed. The conclusion (Section 10) repeats the claim that the cluster is not dynamically relaxed. This contradiction must be corrected, and the mass-segregation interpretation should be adjusted accordingly.
  3. [§6, Fig. 7] The age and distance modulus are obtained by visual inspection of isochrone fits, with no quantitative fitting statistic; the quoted uncertainties (16.00 ± 4.00 Myr, 15.00 ± 0.30 mag) appear to be adopted rather than derived. Because the same Marigo isochrone is then used to convert luminosities to masses in Section 7, the uncertainties on M_cl and α do not include isochrone model systematics. A more transparent fitting procedure (e.g., a χ² or maximum-likelihood grid) and propagation of isochrone systematics would strengthen the central results.
minor comments (6)
  1. [§4, Eq. (5)] Equation (5) is malformed as printed; the expression for the effectiveness E cannot be evaluated from the current typesetting. Please rewrite it with explicit parentheses and summation limits.
  2. [Figures 4, 11, 13] Several figure axis labels contain LaTeX artifacts such as '/uni00000003/uni0000000b/...' in the compiled version. Please replace these with proper symbols and unit labels.
  3. [§10] The conclusion lists 'µδ = 0.4657 ± 0.0192' with a positive sign, whereas Section 5 and Table 4 give −0.4657 ± 0.0192. This appears to be a typographical sign error.
  4. [Table 3] The cluster-center coordinates x_c, y_c, z_c are reported as 2056.30, 669.13, and 4111.43 pc, respectively; the z_c value is implausibly large for a cluster at ~3 kpc. Please specify the coordinate origin and check the transformation for a unit or sign error.
  5. [§7, after Eq. (9)] The paper says 'The complete list of the cluster is available online,' but no URL or machine-readable table is included in the arXiv submission. Please provide the full member table as supplementary material.
  6. [Throughout] The manuscript contains numerous language and typographical errors (e.g., 'calculatiions', 'red-filed circles', 'Our results are in a quite fair agreement'). A careful language edit would improve readability.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity found: the central distance/age/mass/IMF results are obtained by standard fitting to external Gaia and Marigo isochrone data, checked against independent parallax and Salpeter benchmarks, and the self-citations are confined to ancillary kinematic calculations.

full rationale

The derivation chain is not circular by construction. The distance modulus, age, and reddening are obtained by fitting the observed CMD to external Marigo et al. (2017) isochrones (Section 6), and the resulting isochrone distance (2.945 kpc) is explicitly compared with—not substituted for—the independently measured Gaia parallax distance (3.203 kpc). The stellar masses are read off this isochrone through the MLR polynomial (Eq. 9), but the IMF slope (alpha = 2.24) is not an input to that fit: it is determined by the observed distribution of stars in mass bins (Figure 9) and compared with the external Salpeter value. No equation in the paper reduces a predicted quantity to a fitted parameter by definition. The only author-overlapping citations (Bisht et al. 2020, 2021, 2022; Elsanhoury et al. 2018, 2021, 2022) are used in Section 9 for velocity-ellipsoid and apex computations, which are ancillary to the paper's central distance/age/mass/IMF claims; they do not carry the load of those claims. The admitted photometric incompleteness in the luminosity function (Section 7) is a data-quality limitation affecting the mass sum and slope, but it is not a circularity: it does not make the output equal to the input. Hence a low circularity score is appropriate.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The central parameters rest on standard Gaia DR3 data and conventional isochrone and membership methods. The most fragile input is the treatment of the 73 members as a complete sample for the total mass and IMF, which the authors themselves note is incomplete. The relaxation-time interpretation also contains an internal inconsistency.

free parameters (8)
  • Intrinsic proper-motion dispersion for cluster members (σ_c) = 0.075 mas/yr
    Set from the Girard et al. (1989) assumption of a 1 km/s radial velocity dispersion; used in the Balaguer-Núñez membership probability calculation in Section 4.
  • VPD cluster zone center and radius = center (-2.10, -0.50) mas/yr, radius 0.5 mas/yr
    Chosen by eye from the vector-point diagram in three magnitude bins (Section 4, Figure 2).
  • Photometric reddening E(GBP-GRP) = 1.25 mag
    Adopted as the average of the visually estimated range 1.15-1.35 mag from the isochrone fit (Section 6).
  • Observed distance modulus (m-M)_obs = 15.00 ± 0.30 mag
    Taken from visual isochrone fitting in Section 6 and used to compute the photometric distance.
  • Cluster age = 16.00 ± 4.00 Myr
    Best-fitting Marigo et al. (2017) isochrone chosen by visual inspection (Section 6).
  • IMF slope (Γ or α) = Γ = 1.24, α = 2.24 ± 0.69
    Least-squares fit to the binned mass function over the incomplete member sample (Section 7, Figure 9).
  • King profile background density and core radius = fbg = 19.93 ± 0.35 stars/arcmin², rc = 0.79 ± 0.13 arcmin
    Fitted to the radial density profile in Section 3; not central to the age and distance claims.
  • Isochrone metallicity Z = 0.0152
    Fixed to a Marigo et al. (2017) grid value; not varied in the fit (Section 6).
assumptions (7)
  • domain assumption Cluster and field proper-motion distributions are bivariate Gaussians (Balaguer-Núñez et al. 1998).
    Underlies the membership probability calculation in Section 4.
  • domain assumption Open clusters have radial velocity dispersion near 1 km/s (Girard et al. 1989).
    Sets the intrinsic proper-motion dispersion of 0.075 mas/yr for cluster members in Section 4.
  • domain assumption Lindegren et al. (2021) parallax zero-point corrections are valid for the selected stars.
    Applied to all 73 members when computing corrected parallaxes in Section 5.
  • domain assumption Marigo et al. (2017) isochrones with Z=0.0152 represent Stock 3's stellar population.
    Used to determine age, distance, and the mass-luminosity relation in Sections 6 and 7.
  • domain assumption Extinction ratios E(B-V)=0.775×E(GBP-GRP) and AG=2.74×E(B-V) apply on this line of sight.
    Used to convert colour excess to extinction and distance in Section 6.
  • ad hoc to paper The 73 selected members form a representative sample for deriving the total mass and IMF.
    This assumption is contradicted by the paper's own statement of photometric incompleteness in Section 7; the total mass and IMF are likely lower limits.
  • domain assumption The standard relaxation-time formula (Equation 12) with the half-mass radius from Equation 13 is applicable to Stock 3.
    Used in Section 8 to classify the cluster's dynamical state, with an interpretation that conflicts with the computed τ=3.03.

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Cite this review

Pith. "Pith review of Deep Photometric and Astrometric Investigation of the Non-relaxed Star Cluster Stock 3 using Gaia DR3." pith.science (2026). https://pith.science/paper/S3RA2J6U

@misc{pith2026250111997,
  author       = {Pith},
  title        = {Pith review of: Deep Photometric and Astrometric Investigation of the Non-relaxed Star Cluster Stock 3 using Gaia DR3},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/S3RA2J6U}},
  note         = {Machine review of arXiv:2501.11997}
}
abstract

The study presents both photometric and kinematic analyses of the non-relaxed open cluster Stock 3 with Gaia DR3 which found to be positioned at 2.945 $\pm$ 0.700 kpc and having an age of 16.00 $\pm$ 4.00 Myr. We analyse the data to infer the membership and thus determine the total mass, IMF and the dynamical and kinematical status.

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Reviewed August 10, 2026 · model on record in the stance chip above.