Stellar Dynamics in Open Clusters Increases the Binary Fraction and Mass Ratios: Evidence from Photometric Binaries in 35 Open Clusters

Aaron M. Geller; Anna C. Childs

REVIEW 4 major objections 4 minor 1 cited by

Stellar Dynamics in Open Clusters Increases the Binary Fraction and Mass Ratios: Evidence from Photometric Binaries in 35 Open Clusters

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Binary fractions and mass ratios in open clusters rise with dynamical age.

desk verdict A careful, data-rich extension to 35 clusters whose binary-fraction trend looks robust, but whose q-shape correlation with dynamical age is exposed to a distance-dependent completeness confound that needs a real test before the dynamical interpretation is accepted. read the letter →

arxiv 2506.20889 v1 pith:HFEFAH3T submitted 2025-06-25 astro-ph.SR astro-ph.GA

Anna C. Childs , Aaron M. Geller This is my paper · ORCID

classification astro-ph.SRastro-ph.GA

keywords openclustersbinarystarsmassratiodynamicalagerelaxationtimephotometricbinariesBayesianinferencestellardynamics

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 aims to show that stellar dynamics, not just conditions at birth, reshape the binary populations of open clusters. Using the BASE-9 Bayesian fitting code on Gaia DR3, Pan-STARRS, and 2MASS photometry of 35 clusters, the authors identify unresolved binary stars and measure their mass ratios. They report that the binary fraction rises with cluster dynamical age—the number of half-mass relaxation times a cluster has lived—and that the trend is stronger in cluster cores. The mass-ratio distribution also changes: dynamically young clusters show multi-modal distributions, while dynamically old clusters show uniform distributions with a peak near equal masses, resembling field binaries. The authors interpret this as dynamical encounters and exchanges that destroy low-mass-ratio binaries and build up high-mass-ratio ones, with the caveat that the sample is small.

What carries the argument

The load-bearing tool is BASE-9, a Bayesian code that fits PARSEC isochrones through all 11 photometric bands simultaneously and returns posterior probabilities for each star's membership, primary mass, secondary mass, and binarity. The comparison sample is then defined carefully: main-sequence stars with primary mass 0.7–1.1 solar masses (slightly lowered for the two oldest clusters), binaries with $q > 0.5$, and members within three King-model core radii, with at least 100 such stars per cluster (31 of 35 clusters). Dynamical age is the cluster age in units of the half-mass relaxation time, $t_{\rm rh} = 0.346 N r_{c,3D}^{3/2}/\sqrt{G M_{\rm tot} \ln \Lambda}$, which quantifies how many relaxation timescales the cluster has experienced. The $q$-distribution shapes are diagnosed with the Hartigan Dip test for unimodality and compared with Kolmogorov–Smirnov and Anderson–Darling tests.

What would settle it

Inject synthetic binary populations with a fixed input binary fraction and mass-ratio distribution into the observed color-magnitude diagrams of these clusters across the full distance and age range, then run the same BASE-9 recovery; if the recovered binary fraction and mass-ratio distribution still rise with dynamical age, the trends are real, while if the trends vanish or shrink to the injected population, they are selection effects. A complementary check is a radial-velocity survey of the same clusters, which detects binaries independently of photometric mass ratio.

Watch

Extended reading notes

Core claim

On the authors' own terms, the central discovery is a statistical connection between how dynamically evolved an open cluster is and what its binary population looks like. Across 35 clusters, both the global binary fraction and the core binary fraction correlate with dynamical age (Pearson r = 0.5 and 0.6, respectively), and the median mass ratio of main-sequence binaries also rises with dynamical age (r = 0.5, or 0.6 in the core). The mass-ratio distributions of dynamically young clusters (less than about 2 half-mass relaxation times) and old clusters (greater than about 15) are statistically distinct: young clusters show multi-modal $q$ distributions rising toward $q = 1$ and toward the survey limit $q = 0.5$, while old clusters show a uniform distribution with a peak near $q = 1$ that matches field solar-type binaries. The paper interprets these patterns as evidence that dynamical encounters preferentially disrupt or evaporate low-$q$ binaries and that exchange encounters favor similar-mass companions, pushing binary populations toward higher mass ratios as clusters age.

Load-bearing premise

The analysis assumes that the mass-limited main-sequence sample (primary masses 0.7–1.1 solar masses, mass ratios above 0.5, within three core radii) is equally complete in all 35 clusters; if older or more distant clusters systematically miss faint, low-mass-ratio binaries, the correlations with dynamical age could be selection artifacts rather than dynamical processing.

Editorial extensions

If this is right

If the trend is real, the binary fraction of an open cluster is not set at birth; it grows over relaxation timescales, most rapidly in the core.
The mass-ratio distribution of dynamically old clusters matching the field suggests many solar-type field binaries were dynamically processed inside clusters before dispersal.
Cluster mass matters: lower-mass clusters retain multi-modal $q$ distributions, while higher-mass clusters show unimodal distributions, meaning total mass acts as a proxy for how much dynamical processing has occurred.
The $q \approx 1$ 'twin' peak seen in old clusters and in the field may be partly built by stellar exchanges rather than being purely primordial.

Reading between the lines

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

A sharper test of the dynamical-processing interpretation would compare clusters of similar dynamical age but very different central density: if encounters drive the effect, denser clusters should show more extreme shifts in the mass-ratio distribution.
The photometric method cannot distinguish a true $q \approx 1$ binary from a triple whose combined light mimics one; if hidden tertiaries are common, part of the twin peak in old clusters could be unidentified triples, a possibility the paper itself notes.
The same approach applied to globular clusters or to clusters closer than 500 pc could reveal whether the shift toward high $q$ saturates once clusters are dynamically old or continues to strengthen.
One could test whether the binary-fraction trend with dynamical age is driven by evaporation of low-mass single stars rather than by binary creation; measuring the mass functions of the same clusters should show that low-mass single stars are depleted in dynamically old systems.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The genuinely new thing here is the scale and the q-distribution claim: 35 open clusters analyzed uniformly with BASE-9, showing binary fraction rising with dynamical age (r=0.5, t=3.4) and an even stronger core trend (r=0.6, t=3.8), plus a statistical distinction between q distributions of young and old clusters, with old clusters looking like the field. The binary-fraction trend was already in Donada et al. and Cordoni et al., but the q-shape transition is new and, if real, is the kind of anchor that links cluster dynamics to the field's twin excess. The paper is careful, the methods are mostly clear, and the authors are honest that the dynamical interpretation is an interpretation. They also ship the data on Zenodo and an interactive explorer, which should count for something.

Now the soft spots, in proportion. The binary-fraction correlation itself is not easily killed by photometric incompleteness: missing faint low-q binaries in distant clusters would pull the measured fraction down, opposite to the observed rise. That part looks solid. But the q-shape and median-q correlations are much more exposed. The dynamically old clusters in Table 1 skew to 1.5-4 kpc; the young ones are mostly within 1.2 kpc. The paper itself shows that adding 2MASS boosts recovery most for low-q binaries, and 2MASS is shallow. At 3-4 kpc, a q≈0.5 secondary near the bottom of the 0.7-1.1 Msun primary range is right around the 2MASS limit, so the very data that helps you see low-q binaries is differentially missing in the old, distant clusters. That can produce exactly the shift toward q=1 and the rising median q they report. No injection-recovery test or completeness map is presented. That's the load-bearing gap.

The statistics also have unpolished edges: the reported r and t values do not propagate uncertainties on binary fraction or dynamical age; the sample cuts are data-driven with no stability check; the K-S test compares post-hoc extreme age groups; and the Dip statistic is sensitive to sample size, which is larger for the old, massive clusters. None of these are fatal on their own, but they weaken the quantitative claim.

Bottom line: this is a solid, useful paper that deserves a serious referee, but the referee should send it back for a completeness test (simulated binaries injected into the actual photometry, as a function of distance and q) and for uncertainty propagation on the correlations. I would bring it to reading group and would probably cite the binary-fraction sample, but I would not hang the field-twin link on the q-shape until the completeness question is answered.

Referee Report

4 major / 4 minor

Summary. This manuscript uses the BASE-9 Bayesian code on Gaia DR3, Pan-STARRS, and 2MASS photometry for 35 open clusters to identify photometric binaries, derive cluster parameters, and constrain binary mass ratios. After restricting the sample to main-sequence primaries of 0.7-1.1 solar masses, q > 0.5, and r < 3 core radii, the authors report that the binary fraction increases with cluster dynamical age (r = 0.5, and r = 0.6 for the core), that the mass-ratio distributions of dynamically young and old clusters are statistically distinct, and that the median mass ratio increases with dynamical age (r = 0.5, and r = 0.6 for the core). They interpret these trends as evidence that dynamical encounters, mass segregation, and exchange interactions increase both the binary fraction and the mass ratios of binaries in open clusters, and they connect the old-cluster and field q distributions.

Significance. If the reported trends are real, this would be an important observational result for our understanding of binary evolution in open clusters, providing one of the largest photometric samples to constrain how the mass-ratio distribution changes with dynamical age. The authors should be credited for combining 11 photometric bands, validating their BASE-9 parameters against APOGEE metallicities and literature values, comparing their binary fractions with previous work, and making their data publicly available on Zenodo. However, the central q-shape claim is vulnerable to a distance-dependent completeness artifact: Table 1 shows that dynamically old clusters tend to be more distant, while Section 3.2 shows that 2MASS photometry, which is the shallowest band set used, is especially important for recovering low-q binaries. No injection-recovery test or completeness map is presented. The binary-fraction correlation is less susceptible to this particular artifact, but its significance is also not fully established because uncertainties on the binary fractions and dynamical ages are not propagated into the correlation statistics.

major comments (4)

[Section 3.4, Figures 6 and 8] The Pearson correlations in Figure 6 (r = 0.5, t = 3.4; core r = 0.6, t = 3.8) and Figure 8 (median q versus Age/trh, r = 0.5; core r = 0.6) are computed from point estimates without propagating the asymmetric uncertainties listed in Table 1. Binary fractions carry errors as large as about ±0.08 in some clusters, and the dynamical ages often have uncertainties of tens of percent (for example, NGC 2627 has Age/trh = 18.2 with +16.2/-16.2). Consequently, the reported t-statistics do not measure the statistical significance of these correlations; the authors should provide confidence intervals or p-values obtained by bootstrap or Monte Carlo propagation that incorporates the measurement uncertainties.
[Section 3.2, Table 1, Figures 7-8] The central mass-ratio result may be a distance-dependent selection artifact. Section 3.2 demonstrates that adding 2MASS photometry improves binary recovery and that the improvement is largest for low-q binaries, yet 2MASS is the shallowest of the three surveys. Table 1 shows a strong confound: clusters with Age/trh > 15 are mostly at 1.5-4 kpc (e.g., NGC 2506 at 3058 pc, Berkeley 32 at 3333 pc, Berkeley 39 at 4042 pc), while clusters with Age/trh < 2 are mostly at 0.6-1.2 kpc. At 3-4 kpc, a 0.7-1.1 solar mass primary with q near 0.5 has a secondary near or below the 2MASS limit, removing exactly the photometric information that most helps BASE-9 identify low-q binaries. The observed shift toward q near 1 in dynamically old clusters is precisely the signature this selection would produce. The manuscript does not include an injection-recovery test or completeness map, so this alternative explanation remains open and must be addressed before the dynamical interpretation can be accepted.
[Section 3.5, Figure 7] The K-S and Anderson-Darling tests compare seven clusters with Age/trh < 2 to nine clusters with Age/trh > 15, groups that were selected after inspecting the q distributions shown in Figure 12. Because the grouping is post-hoc and uses the same data used to define the hypothesis, the reported p-values (about 9e-12 and 0.001) are not valid significance levels. In addition, individual stars within a cluster are not independent draws, so tests that pool stars across clusters inflate the apparent significance. A cluster-level permutation test, or a pre-specified split with bootstrap resampling over clusters, is needed to support the claim that the q distributions differ with dynamical age.
[Section 3.3] Several sample-definition choices are data-driven: the lower primary-mass cut of 0.7 solar masses is chosen where the observed fb,q(M1)/fb,q ratio is lowest, the upper cut of 1.1 solar masses is set by the turnoff of most clusters, the q > 0.5 cut follows from the claimed completeness limit, and the N >= 100 and r < 3rc cuts are motivated by the same dataset used for the trend analysis. This does not invalidate the trends by itself, but it means the reported Pearson coefficients should be tested for robustness to reasonable alternative cuts (for example, q > 0.6, M1 = 0.8-1.0 solar masses, or r < 2.5rc). Without such robustness checks, part of the observed correlation could reflect the optimization of the sample cuts rather than the underlying physical relation.

minor comments (4)

[Section 2.1] The phrase 'low-redenning' should be 'low-reddening'.
[Section 3.4, Eq. (2)] The text refers to 'Coulombs constant' where the Coulomb logarithm is meant; also, the quantities N, M_Tot, and the three-dimensional core radius r_{c,3D} used in Eq. (2) are not fully defined in the text.
[Table 1 caption] The caption begins with 'T able' and should read 'Table'.
[Abstract and Section 4] The phrase 'strong correlation' is used without reporting confidence intervals; adding the intervals from the propagated uncertainties would make the strength of the evidence easier to assess.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: binary fractions and mass-ratio trends are compared against independently derived dynamical ages and external literature benchmarks.

full rationale

The central correlations (binary fraction and median q versus dynamical age) are not constructed from the fitted values they are meant to predict. Dynamical age is computed from independently fitted King-model core radii, cluster mass, and the standard half-mass relaxation time formula (Eq. 2), none of which is defined in terms of the binary fraction or mass-ratio distribution. The binary fractions and q distributions come from BASE-9 fits to the photometry, but the paper validates the cluster parameters against external data: APOGEE metallicities, Hunt & Reffert (2023) and Dias et al. (2021) distances/ages/reddenings, and literature binary fractions (Figures 2-4). The q distributions of old clusters are compared to the field q distribution from Raghavan et al. (2010), an external benchmark. The reliance on Paper I (Childs et al. 2024) and Cohen et al. (2020) for the BASE-9 methodology is a normal methodological self-citation, not a load-bearing circular step: the present paper's conclusions are not derived from those papers' conclusions, and the method is independently testable against external catalogs. No fitted parameter is renamed as a prediction, and no uniqueness theorem or ansatz is imported from the authors' prior work to force the interpretation. The main caveats (distance-dependent 2MASS completeness, q>0.5 detection limit, small sample size) are selection-effect concerns that could weaken the physical interpretation, but they are not circularity: they do not make the measured correlation equal to an input by construction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The analysis rests on the fidelity of BASE-9 and PARSEC models, the membership and contamination treatment, and the completeness of the mass-limited sample. The main fitted choices are sample-definition thresholds rather than physical constants.

free parameters (4)

Per-cluster minimum membership p-value = 0.002 to 0.448 (Table 1)
Tuned per cluster to achieve about 1% estimated field contamination; enters every member and binary list.
Primary mass window for ML-MS sample = 0.7 to 1.1 solar masses; upper limits 1.0 and 0.98 for Berkeley 39 and NGC 188
Chosen from the data in Figure 5 and turnoff locations; defines the sample used for all binary fraction and q comparisons.
Mass-ratio completeness cut = q > 0.5
Adopted because BASE-9 cannot reliably recover lower-q binaries; the young cluster distribution rises toward this cut, so part of the measured valley shape is set by the cut itself.
Radial cut = r < 3 core radii
Applied to limit field contamination in the outer cluster; affects both binary fraction and q distributions.

assumptions (5)

domain assumption BASE-9 with PARSEC isochrones and 11-filter photometry correctly classifies single stars and binaries and estimates component masses.
All binary identifications and mass ratios come from this model; Section 3.1 and Section 3.3.
domain assumption HDBSCAN groups correspond to true cluster members and field contamination is isotropic.
Membership and the contamination correction in Eq. (1) both depend on this.
domain assumption The mass-limited main-sequence sample is completeness-matched across clusters of different distance, reddening, and density.
Assumed in Section 3.3; if false, age trends in binary fraction and q can be selection artifacts.
domain assumption The half-mass relaxation time formula with Lambda = 0.1N is valid for all 35 clusters.
Eq. (2) with a standard Coulomb logarithm choice sets the dynamical age used in every correlation.
domain assumption King (1962) model with chi-square-selected effective radius gives unbiased core and tidal radii.
Core radius defines the core binary fraction and enters the relaxation time.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Stellar Dynamics in Open Clusters Increases the Binary Fraction and Mass Ratios: Evidence from Photometric Binaries in 35 Open Clusters." pith.science (2026). https://pith.science/paper/HFEFAH3T

@misc{pith2026250620889,
  author       = {Pith},
  title        = {Pith review of: Stellar Dynamics in Open Clusters Increases the Binary Fraction and Mass Ratios: Evidence from Photometric Binaries in 35 Open Clusters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HFEFAH3T}},
  note         = {Machine review of arXiv:2506.20889}
}

read the original abstract

Using the Bayesian Analysis of Stellar Evolution-9 (BASE-9) code and Gaia DR3, Pan-STARRS, and 2MASS data, we identify photometric binaries in 35 open clusters (OCs) and constrain their masses. We find a strong correlation between the binary fraction and cluster dynamical age and an even stronger correlation between core binary fraction and cluster dynamical age. We find the binary mass-ratio (q) distribution of dynamically young OCs is statistically distinct from that of the old OCs. On average, dynamically young OCs display multi-modal q distributions rising toward unity and toward our detection limit of q=0.5 while more dynamically evolved clusters display more uniform q distributions often with a peak near q=1. Interestingly, the uniform q distribution with a peak near q=1 is consistent with binaries in the field. We also observe a similar transition from multi-modal to unimodal q distributions when comparing low mass to high mass OCs in our sample. Lastly, we find a correlation between the median q of the binary population in a cluster and the cluster dynamical age. We interpret these results as an indication that dynamical encounters tend to increase the fraction of high-mass-ratio binaries within a given cluster -- particularly within the cluster's core where stellar dynamics are likely more important. This may be the result of stellar exchanges that tend to produce binaries with larger q and/or the preferential disruption or evaporation of lower q binaries.

Figures

Figures reproduced from arXiv: 2506.20889 by the authors.

**Figure 2.** Average values of the cluster member metallicity from APOGEE, where available, versus the BASE-9 derived cluster metallicity. For the black points, the APOGEE error bars show the standard deviation of the multiple measurements taken in the given cluster, and the gray point identifies the single OC where only one measurement was available and so instead, we use the APOGEE uncertainty on the measurement for the erro… view at source ↗

**Figure 3.** A comparison of our derived cluster distances, reddening, ages and core radii to Dias et al. (2021) and (Hunt & Reffert 2021), where available. The 1:1 line is shown with a black diagonal. 3.3. Defining a consistent binary sample Similar to Paper I, we aim to compare MS binary fractions over the same primary-mass range between clusters to look for correlations between binary fractions and cluster parameters. Again… view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: Top: Our binary fraction (BASE-9 fb(q > 0.6)) with all 11 filters compared to the binary fractions from Jadhav et al. (2021); Cordoni et al. (2023); Donada et al. (2023) (Literature fb(q > 0.6)). Middle: The same plot but our binary fractions are found using only Gai…

**Figure 5.** Figure 5: Left: Box and whisker plot of the binary fraction in bins of primary mass (fb,q(M1)) normalized by the cluster’s fb. Right: Box and whisker plot of fb,q,M normalized by this binary fraction in the core fb,q,M,rc, in bins of distance from the cluster center (in units of…

**Figure 6.** Figure 6: Left: fb,q,M versus OC dynamical age for our primary sample. Right: fb,q,M,rc versus OC dynamical age for our primary sample. The line of best fit is shown in red. constant, MTot is the total mass of the cluster and Λ is Coulombs constant which we assume to be 0.1N (Gi…

**Figure 7.** Figure 7: We find statistically distinct distributions of q > 0.5 between dynamically young (blue) and dynamically old (yellow) OCs. Left panel: q distribution for ML-MS high mass ratio binaries in seven dynamically young clusters with ages less than 2 trh. Middle panel: q distr…

**Figure 8.** Figure 8: Left: Total OC mass versus the Dip statistic for the q distribution in our primary sample. Right: OC dynamical age versus median q value in our primary sample. in a higher q binary.) All of these processes may contribute to explaining our finding, as a combination of …

**Figure 9.** Figure 9: CMDs of all the cluster members in our full sample of 35 OCs, as well as the isochrone of best fit in red. The stars are colored black if they are single stars and the binary stars are colored by their mass ratio. Members from Hunt & Reffert (2023) that lie within the …

**Figure 10.** Figure 10: King model fits to the data (blue points) in our full sample (35 OCs). The gray shaded region shows the 1 − σ bounds for the fit [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]

**Figure 11.** Figure 11: Correlation matrix for various cluster parameters in our primary sample of 31 OCs. Li, L., Shao, Z., Li, Z.-Z., et al. 2020, ApJ, 901, 49, doi: 10.3847/1538-4357/abaef3 Lindegren, L., Bastian, U., Biermann, M., et al. 2021, A&A, 649, A4, doi: 10.1051/0004-6361/2020396…

**Figure 12.** Figure 12: Mass-ratio (q) distributions for q > 0.5 for all ML-MS binaries within three core radii for all 35 OCs. Pang, X., Wang, Y., Tang, S.-Y., et al. 2023, AJ, 166, 110, doi: 10.3847/1538-3881/ace76c Qin, S., Zhong, J., Tang, T., & Chen, L. 2023, ApJS, 265, 12, doi: 10.3847…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

The Bimodal Mass Ratio Distribution of the Hyades
astro-ph.SR 2026-08 conditional novelty 6.0 of 10

Mass ratios of Hyades binaries derived from color-magnitude positions are inconsistent with random orbital orientations, and a deconvolved re-analysis yields a bimodal distribution that depends on primary mass.

Reference graph

Works this paper leans on

67 extracted references · 11 canonical work pages · cited by 1 Pith paper

[1]

Albrow, M. D. 2024, MNRAS, 528, 6211, doi: 10.1093/mnras/stae425

doi:10.1093/mnras/stae425 2024
[2]

S., & Albrow, M

Alexander, J. S., & Albrow, M. D. 2025, MNRAS, 536, 471, doi: 10.1093/mnras/stae2636

doi:10.1093/mnras/stae2636 2025
[3]

2024, A&A, 689, A18, doi: 10.1051/0004-6361/202450901 Astropy Collaboration, Robitaille, T

Alfonso, J., Garc ´ ıa-Varela, A., & Vieira, K. 2024, A&A, 689, A18, doi: 10.1051/0004-6361/202450901 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A. M., Sip˝ ocz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f Astropy Collabora...

doi:10.1051/0004-6361/202450901 2024
[4]

Bate, M. R. 2000, Monthly Notices of the Royal Astronomical Society, 314, 33

work page 2000
[5]

Bate, M. R. 2009, MNRAS, 392, 590, doi: 10.1111/j.1365-2966.2008.14106.x

arXiv 2009
[6]

2012, MNRAS, 427, 127, doi: 10.1111/j.1365-2966.2012.21948.x

Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127, doi: 10.1111/j.1365-2966.2012.21948.x

arXiv 2012
[7]

2010, Monthly Notices of the Royal Astronomical Society, 409, L54, doi: 10.1111/j.1745-3933.2010.00946.x

Bressert, E., Bastian, N., Gutermuth, R., et al. 2010, Monthly Notices of the Royal Astronomical Society, 409, L54, doi: 10.1111/j.1745-3933.2010.00946.x

arXiv 2010
[8]

M., Nelan, E

Caballero-Nieves, S. M., Nelan, E. P., Gies, D. R., et al. 2014, The Astronomical Journal, 147, 40, doi: 10.1088/0004-6256/147/2/40

work page doi:10.1088/0004-6256/147/2/40 2014

Show all 67 references

[9]

2003, PASP, 115, 763, doi: 10.1086/376392

Chabrier, G. 2003, PASP, 115, 763, doi: 10.1086/376392

2003 doi
[10]

C., & Geller, A

Childs, A. C., & Geller, A. M. 2025, doi: 10.5281/zenodo.15733690

2025 doi
[11]

C., Geller, A

Childs, A. C., Geller, A. M., von Hippel, T., Motherway, E., & Zwicker, C. 2024, ApJ, 962, 41, doi: 10.3847/1538-4357/ad18c0

2024 doi
[12]

E., Geller, A

Cohen, R. E., Geller, A. M., & von Hippel, T. 2020, AJ, 159, 11, doi: 10.3847/1538-3881/ab59d7

2020 doi
[13]

P., Marino, A

Cordoni, G., Milone, A. P., Marino, A. F., et al. 2023, A&A, 672, A29, doi: 10.1051/0004-6361/202245457

2023 doi
[14]

B., & Fahlman, G

Cote, P., Richer, H. B., & Fahlman, G. G. 1991, AJ, 102, 1358, doi: 10.1086/115961 de La Fuente Marcos, R. 1998, PASP, 110, 1117, doi: 10.1086/316220

1991 doi
[15]

S., Monteiro, H., Moitinho, A., et al

Dias, W. S., Monteiro, H., Moitinho, A., et al. 2021, MNRAS, 504, 356, doi: 10.1093/mnras/stab770

2021 doi
[16]

2023, A&A, 675, A89, doi: 10.1051/0004-6361/202245219 Duchˆ ene, G., & Kraus, A

Donada, J., Anders, F., Jordi, C., et al. 2023, A&A, 675, A89, doi: 10.1051/0004-6361/202245219 Duchˆ ene, G., & Kraus, A. 2013, ARA&A, 51, 269, doi: 10.1146/annurev-astro-081710-102602

2023 doi
[17]

M., Jørgensen, J

Evans, Neal J., I., Dunham, M. M., Jørgensen, J. K., et al. 2009, The Astrophysical Journal Supplement Series, 181, 321, doi: 10.1088/0067-0049/181/2/321

2009 doi
[18]

M., Ivanova, N., & Rasio, F

Fregeau, J. M., Ivanova, N., & Rasio, F. A. 2009, ApJ, 707, 1533, doi: 10.1088/0004-637X/707/2/1533

2009 doi
[19]

M., Joshi, K

Fregeau, J. M., Joshi, K. J., Zwart, S. F. P., & Rasio, F. A. 2002, The Astrophysical Journal, 570, 171

2002
[20]

Friel, E. D. 1995, ARA&A, 33, 381, doi: 10.1146/annurev.aa.33.090195.002121

1995
[21]

2015, arXiv e-prints, arXiv:1511.04789

Frinchaboy, P., & Thompson, B. 2015, arXiv e-prints, arXiv:1511.04789. https://arxiv.org/abs/1511.04789

2015 arXiv
[22]

M., Hurley, J

Geller, A. M., Hurley, J. R., & Mathieu, R. D. 2012, The Astronomical Journal, 145, 8

2012
[23]

Giersz, M., & Heggie, D. C. 1994, MNRAS, 268, 257, doi: 10.1093/mnras/268.1.257

1994 doi
[24]

B., & Perets, H

Ginat, Y. B., & Perets, H. B. 2024, MNRAS, 531, 739, doi: 10.1093/mnras/stae1241

2024 doi
[25]

Goodwin, S. P. 2013, MNRAS, 430, L6, doi: 10.1093/mnrasl/sls037

2013 doi
[26]

A., & Hartigan, P

Hartigan, J. A., & Hartigan, P. M. 1985, The Annals of Statistics, 13, 70

1985
[27]

Heggie, D. C. 1975, Monthly Notices of the Royal Astronomical Society, 173, 729, doi: 10.1093/mnras/173.3.729

1975 doi
[28]

Heggie, D. C. 2003, in Astrophysical Supercomputing using Particle Simulations, ed. J. Makino & P. Hut, Vol. 208, 81, doi: 10.48550/arXiv.astro-ph/0111045

2003 doi arXiv
[29]

2014, A&A, 561, A93, doi: 10.1051/0004-6361/201322559

Heiter, U., Soubiran, C., Netopil, M., & Paunzen, E. 2014, A&A, 561, A93, doi: 10.1051/0004-6361/201322559

2014 doi
[30]

L., & Reffert, S

Hunt, E. L., & Reffert, S. 2021, A&A, 646, A104, doi: 10.1051/0004-6361/202039341 —. 2023, A&A, 673, A114, doi: 10.1051/0004-6361/202346285

2021 doi
[31]

Hurley, J., & Tout, C. A. 1998, MNRAS, 300, 977, doi: 10.1046/j.1365-8711.1998.01981.x

1998
[32]

V., Roy, K., Joshi, N., & Subramaniam, A

Jadhav, V. V., Roy, K., Joshi, N., & Subramaniam, A. 2021, AJ, 162, 264, doi: 10.3847/1538-3881/ac2571

2021 doi
[33]

A., & Phelps, R

Janes, K. A., & Phelps, R. L. 1994, AJ, 108, 1773, doi: 10.1086/117192

1994 doi
[34]

Ji, J., & Bregman, J. N. 2015, ApJ, 807, 32, doi: 10.1088/0004-637X/807/1/32

2015 doi
[35]

2024, ApJ, 971, 71, doi: 10.3847/1538-4357/ad5344

Jiang, Y., Zhong, J., Qin, S., et al. 2024, ApJ, 971, 71, doi: 10.3847/1538-4357/ad5344

2024 doi
[36]

1962, AJ, 67, 471, doi: 10.1086/108756

King, I. 1962, AJ, 67, 471, doi: 10.1086/108756

1962 doi
[37]

J., & Lada, E

Lada, C. J., & Lada, E. A. 2003, Annual Review of Astronomy and Astrophysics, 41, 57, doi: 10.1146/annurev.astro.41.011802.094844

2003 arXiv
[38]

C., Ritter, L

Layden, A. C., Ritter, L. A., Welch, D. L., & Webb, T. M. A. 1999, The Astronomical Journal, 117, 1313

1999
[39]

D., Vanderburg, A., Gosnell, N

Leiner, E., Mathieu, R. D., Vanderburg, A., Gosnell, N. M., & Smith, J. C. 2019, ApJ, 881, 47, doi: 10.3847/1538-4357/ab2bf8 17 0 2 GBP GRP 6 8 10 12 14 16 18 20 G Trumpler 3 0 2 GBP GRP Collinder 394 0 2 GBP GRP NGC 2301 0 2 GBP GRP NGC 2323 0 2 GBP GRP NGC 2287 0 2 GBP GRP N...

2023 doi
[40]

2020, ApJ, 901, 49, doi: 10.3847/1538-4357/abaef3

Li, L., Shao, Z., Li, Z.-Z., et al. 2020, ApJ, 901, 49, doi: 10.3847/1538-4357/abaef3

2020 doi
[41]

2021, A&A, 649, A4, doi: 10.1051/0004-6361/202039653

Lindegren, L., Bastian, U., Biermann, M., et al. 2021, A&A, 649, A4, doi: 10.1051/0004-6361/202039653

2021 doi
[42]

2025a, AJ, 169, 116, doi: 10.3847/1538-3881/ada380 —

Liu, R., Shao, Z., & Li, L. 2025a, AJ, 169, 116, doi: 10.3847/1538-3881/ada380 —. 2025b, AJ, 169, 116, doi: 10.3847/1538-3881/ada380

doi
[43]

R., Schiavon, R

Majewski, S. R., Schiavon, R. P., Frinchaboy, P. M., et al. 2017, AJ, 154, 94, doi: 10.3847/1538-3881/aa784d

2017 doi
[44]

Seleznev, A. F. 2023, AJ, 165, 45, doi: 10.3847/1538-3881/aca666

2023 doi
[45]

A., Seleznev, A

Malofeeva, A. A., Seleznev, A. F., & Carraro, G. 2022, AJ, 163, 113, doi: 10.3847/1538-3881/ac47a3

2022 doi
[46]

1970, ApJ, 160, 135, doi: 10.1086/150412

Mansbach, P. 1970, ApJ, 160, 135, doi: 10.1086/150412

1970 doi
[47]

2011, Monthly Notices of the Royal Astronomical Society, 417, 1684, doi: 10.1111/j.1365-2966.2011.19257.x

Marks, M., Kroupa, P., & Oh, S. 2011, Monthly Notices of the Royal Astronomical Society, 417, 1684, doi: 10.1111/j.1365-2966.2011.19257.x

2011
[48]

2013, A&A, 560, A16, doi: 10.1051/0004-6361/201322480

Martins, F., & Palacios, A. 2013, A&A, 560, A16, doi: 10.1051/0004-6361/201322480

2013 doi
[49]

D., & Geller, A

Mathieu, R. D., & Geller, A. M. 2009, Nature, 462, 1032

2009
[50]

2017, Journal of Open Source Software, 2, 205, doi: 10.21105/joss.00205

McInnes, L., Healy, J., & Astels, S. 2017, Journal of Open Source Software, 2, 205, doi: 10.21105/joss.00205

2017 doi
[51]

O., & Seleznev, A

Mikhnevich, V. O., & Seleznev, A. F. 2024, Astronomy Reports, 68, 121, doi: 10.1134/S1063772924700161

2024 doi
[52]

P., Piotto, G., Bedin, L

Milone, A. P., Piotto, G., Bedin, L. R., et al. 2012, A&A, 540, A16, doi: 10.1051/0004-6361/201016384

2012 doi
[53]

P., Cordoni, G., et al

Mohandasan, A., Milone, A. P., Cordoni, G., et al. 2024, A&A, 681, A42, doi: 10.1051/0004-6361/202347424

2024 doi
[54]

M., Childs, A

Motherway, E., Geller, A. M., Childs, A. C., Zwicker, C., & von Hippel, T. 2024, ApJL, 962, L9, doi: 10.3847/2041-8213/ad18bf

2024 doi
[55]

Offner, S. S. R., Moe, M., Kratter, K. M., et al. 2023, in Astronomical Society of the Pacific Conference Series, Vol. 534, Protostars and Planets VII, ed. S. Inutsuka, Y. Aikawa, T. Muto, K. Tomida, & M. Tamura, 275, doi: 10.48550/arXiv.2203.10066 20 0.6 0.8 1.00 5 N Trumpler...

2023 doi arXiv
[56]

2023, AJ, 166, 110, doi: 10.3847/1538-3881/ace76c

Pang, X., Wang, Y., Tang, S.-Y., et al. 2023, AJ, 166, 110, doi: 10.3847/1538-3881/ace76c

2023 doi
[57]

2023, ApJS, 265, 12, doi: 10.3847/1538-4365/acadd6

Qin, S., Zhong, J., Tang, T., & Chen, L. 2023, ApJS, 265, 12, doi: 10.3847/1538-4365/acadd6

2023 doi
[58]

A., Henry, T

Raghavan, D., McAlister, H. A., Henry, T. J., et al. 2010, ApJS, 190, 1, doi: 10.1088/0067-0049/190/1/1

2010 doi
[59]

2016, BASE-9: Bayesian Analysis for Stellar Evolution with nine variables, Astrophysics Source Code Library, record ascl:1608.007

Robinson, E., von Hippel, T., Stein, N., et al. 2016, BASE-9: Bayesian Analysis for Stellar Evolution with nine variables, Astrophysics Source Code Library, record ascl:1608.007. http://ascl.net/1608.007

2016
[60]

E., de Koter, A., et al

Sana, H., de Mink, S. E., de Koter, A., et al. 2012, Science, 337, 444, doi: 10.1126/science.1223344

2012 doi
[61]

F., Cutri, R

Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163, doi: 10.1086/498708

2006 doi
[62]

2007, MNRAS, 380, 781, doi: 10.1111/j.1365-2966.2007.12116.x

Sarajedini, A. 2007, MNRAS, 380, 781, doi: 10.1111/j.1365-2966.2007.12116.x

2007
[63]

Spangler, S. R. 2025, Research Notes of the American Astronomical Society, 9, 34, doi: 10.3847/2515-5172/adb48a

2025 doi
[64]

2022, A&A, 659, A59, doi: 10.1051/0004-6361/202142186

Tarricq, Y., Soubiran, C., Casamiquela, L., et al. 2022, A&A, 659, A59, doi: 10.1051/0004-6361/202142186

2022 doi
[65]

2014, AJ, 147, 87, doi: 10.1088/0004-6256/147/4/87 van Dyk, D

Tokovinin, A. 2014, AJ, 147, 87, doi: 10.1088/0004-6256/147/4/87 van Dyk, D. A., Degennaro, S., Stein, N., Jefferys, W. H., & von Hippel, T. 2009, Annals of Applied Statistics, 3, 117, doi: 10.1214/08-AOAS219SUPP von Hippel, T., Jefferys, W. H., Scott, J., et al. 2006, ApJ, 64...

2014 doi
[66]

G., Henry, T

Winters, J. G., Henry, T. J., Jao, W.-C., et al. 2019, AJ, 157, 216, doi: 10.3847/1538-3881/ab05dc

2019 doi
[67]

M., Childs, A

Zwicker, C., Geller, A. M., Childs, A. C., Motherway, E., & von Hippel, T. 2024, ApJ, 967, 44, doi: 10.3847/1538-4357/ad39c6

2024 doi

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Albrow, M. D. 2024, MNRAS, 528, 6211, doi: 10.1093/mnras/stae425

doi:10.1093/mnras/stae425 2024

[2] [2]

S., & Albrow, M

Alexander, J. S., & Albrow, M. D. 2025, MNRAS, 536, 471, doi: 10.1093/mnras/stae2636

doi:10.1093/mnras/stae2636 2025

[3] [3]

2024, A&A, 689, A18, doi: 10.1051/0004-6361/202450901 Astropy Collaboration, Robitaille, T

Alfonso, J., Garc ´ ıa-Varela, A., & Vieira, K. 2024, A&A, 689, A18, doi: 10.1051/0004-6361/202450901 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A. M., Sip˝ ocz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f Astropy Collabora...

doi:10.1051/0004-6361/202450901 2024

[4] [4]

Bate, M. R. 2000, Monthly Notices of the Royal Astronomical Society, 314, 33

work page 2000

[5] [5]

Bate, M. R. 2009, MNRAS, 392, 590, doi: 10.1111/j.1365-2966.2008.14106.x

arXiv 2009

[6] [6]

2012, MNRAS, 427, 127, doi: 10.1111/j.1365-2966.2012.21948.x

Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127, doi: 10.1111/j.1365-2966.2012.21948.x

arXiv 2012

[7] [7]

2010, Monthly Notices of the Royal Astronomical Society, 409, L54, doi: 10.1111/j.1745-3933.2010.00946.x

Bressert, E., Bastian, N., Gutermuth, R., et al. 2010, Monthly Notices of the Royal Astronomical Society, 409, L54, doi: 10.1111/j.1745-3933.2010.00946.x

arXiv 2010

[8] [8]

M., Nelan, E

Caballero-Nieves, S. M., Nelan, E. P., Gies, D. R., et al. 2014, The Astronomical Journal, 147, 40, doi: 10.1088/0004-6256/147/2/40

work page doi:10.1088/0004-6256/147/2/40 2014