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arxiv: 2606.05762 · v1 · pith:IFBQWFPUnew · submitted 2026-06-04 · 🌌 astro-ph.GA · astro-ph.SR

Evolution of the stellar mass function in open clusters from a universal and unsegregated initial state

Lu Li , Zhaozhou Li , Zhengyi Shao , Zepeng Zheng , Long Wang This is my paper

Pith reviewed 2026-06-28 01:03 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.SR
keywords stellar mass functioninitial mass functionopen clustersmass segregationdynamical evolutionstar formation
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The pith

Young open clusters share a universal IMF slope of -2.29 with minimal early mass segregation.

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

The paper examines 163 open clusters with a Bayesian forward-modeling approach that accounts for binaries, contamination, and incompleteness. It establishes that clusters younger than about 300 million years begin with a mean initial mass function slope of -2.29 above half a solar mass, close to the Salpeter value but with an intrinsic scatter of 0.17, plus little mass segregation by the time gas is expelled around 10 million years. From this starting point, internal relaxation drives mass segregation on short timescales while tidal effects flatten the global mass function only after roughly 600 million years. This picture rules out formation models that require strong primordial segregation or large IMF differences across clusters.

Core claim

Young clusters (≲300 Myr) share a mean IMF slope of −2.29 in the mass range M≥0.5M⊙, consistent with the Salpeter slope but with an intrinsic scatter of 0.17, and exhibit minimal mass segregation at the onset of gas-free evolution (∼10 Myr). This universal zero-point for secular evolution is derived after correcting observational biases, and subsequent dynamical processing separates into rapid internal mass segregation and slower global MF flattening after ∼600 Myr.

What carries the argument

Bayesian forward-modeling framework that corrects for unresolved binaries, field contamination, and completeness bias to recover the initial mass function slope and spatial distribution.

If this is right

  • Mass segregation develops quickly through two-body relaxation after gas expulsion.
  • Global flattening of the mass function from tidal evaporation becomes dominant only after approximately 600 million years.
  • Star-forming scenarios that predict strong primordial mass segregation or large IMF variations across clusters are disfavored.
  • The measured initial state supplies an empirical baseline for simulations of cluster dynamical evolution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the zero-point holds, star formation must produce similar conditions even in different galactic environments.
  • Observations of clusters younger than 10 Myr could test whether any primordial inhomogeneities are erased even earlier.
  • The separation of timescales suggests that internal dynamics and external tides can be modeled independently in cluster evolution codes.

Load-bearing premise

The Bayesian corrections fully remove all systematic errors from binaries, contamination, and incompleteness so that the recovered IMF slopes and segregation signals reflect the true initial conditions.

What would settle it

A new sample of young clusters analyzed with independent bias corrections that yields a mean slope differing by more than the reported 0.17 scatter or shows strong primordial mass segregation.

Figures

Figures reproduced from arXiv: 2606.05762 by Long Wang, Lu Li, Zepeng Zheng, Zhaozhou Li, Zhengyi Shao.

Figure 1
Figure 1. Figure 1: Evolution of the stellar mass function of observed open clusters. (a): The global mass function slope (𝛼global) as a function of age for 163 open clusters (black points). Young clusters (< 300 Myr) show a tight distribution around the mean 𝛼 = −2.29 (black dashed line) with an intrinsic scatter of 0.17 (after correcting for measurement uncertainties), indicating a nearly universal initial condition consist… view at source ↗
Figure 2
Figure 2. Figure 2: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
read the original abstract

The stellar mass function (MF) and its spatial variation (mass segregation) within star clusters encode signatures of early formation physics and subsequent secular evolution. Yet, a coherent evolutionary picture remains elusive due to conflicting reports regarding the universality of the initial mass function (IMF) and the prevalence of primordial mass segregation. These discrepancies often arise from unresolved binaries, field contamination, and completeness bias. Here, we resolve these issues by analyzing 163 high-fidelity open clusters via a Bayesian forward-modeling framework. We reveal a remarkably simple initial state: young clusters ($\lesssim 300$ Myr) share a mean IMF slope of $-2.29$ in the mass range $M \geq 0.5 M_\odot$, consistent with the Salpeter slope but with an intrinsic scatter of 0.17, and exhibit minimal mass segregation at the onset of gas-free evolution ($\sim$10 Myr). This broadly universal "zero-point" for secular evolution disfavors star-forming scenarios that predict strong primordial segregation or significant IMF variations, and suggests that chaotic cluster assembly and gas expulsion efficiently erase any mild primordial inhomogeneities. By tracing the evolutionary sequence from $10^7$ to $10^{9.8}$ yr, we demonstrate that dynamical processing operates on distinct timescales: mass segregation proceeds rapidly via internal relaxation, whereas global MF flattening due to tidal evaporation becomes dominant only after $\sim$600 Myr. These findings impose robust observational constraints on the physics of star formation and early feedback and establish an empirical baseline for modeling secular stellar dynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript analyzes the stellar mass function (MF) and mass segregation in 163 open clusters using a Bayesian forward-modeling framework that corrects for unresolved binaries, field contamination, and completeness. It reports that young clusters (≲300 Myr) share a mean IMF slope of −2.29 (M ≥ 0.5 M⊙) consistent with Salpeter, with intrinsic scatter 0.17 and minimal mass segregation at the onset of gas-free evolution (~10 Myr). The work then traces secular evolution, finding rapid mass segregation via internal relaxation but global MF flattening from tidal evaporation only after ~600 Myr, implying a universal unsegregated initial state.

Significance. If the forward-modeling corrections are validated as unbiased, the large sample size and claimed universality would provide a valuable empirical zero-point for cluster evolution models, constraining star-formation scenarios that predict strong primordial segregation or IMF variations. The separation of dynamical timescales (segregation vs. evaporation) is a potentially useful observational benchmark.

major comments (1)
  1. [Methods (Bayesian forward-modeling framework)] The headline results (mean slope −2.29, scatter 0.17, minimal segregation at ~10 Myr) are obtained only after the Bayesian forward model subtracts binaries, contamination, and incompleteness. The manuscript must demonstrate that the posterior on IMF slope and segregation metric remains unbiased when nuisance parameters (binary fraction, mass-ratio distribution, field density) are marginalized; without explicit recovery tests on mock clusters that inject known slopes and radial distributions, residual covariance between these parameters and the recovered power-law index cannot be ruled out.
minor comments (2)
  1. [Abstract] Clarify whether the mass range M ≥ 0.5 M⊙ is uniformly applied or adjusted per cluster based on completeness limits.
  2. [Results (evolutionary sequence)] The evolutionary timeline references ~10 Myr, ~300 Myr, and ~600 Myr; a figure or table explicitly mapping these to the age bins used in the sample would improve traceability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review. We address the single major comment below and agree that additional validation is warranted.

read point-by-point responses

  1. Referee: The headline results (mean slope −2.29, scatter 0.17, minimal segregation at ~10 Myr) are obtained only after the Bayesian forward model subtracts binaries, contamination, and incompleteness. The manuscript must demonstrate that the posterior on IMF slope and segregation metric remains unbiased when nuisance parameters (binary fraction, mass-ratio distribution, field density) are marginalized; without explicit recovery tests on mock clusters that inject known slopes and radial distributions, residual covariance between these parameters and the recovered power-law index cannot be ruled out.

    Authors: We agree that explicit recovery tests on mock clusters are necessary to demonstrate that the posteriors on the IMF slope and segregation metric remain unbiased after marginalization over nuisance parameters. Although the forward-modeling framework is constructed to jointly sample all parameters, the original manuscript did not include such end-to-end recovery experiments. In the revised version we will add a dedicated subsection presenting recovery tests on synthetic clusters. These mocks will be generated with known input IMF slopes, segregation levels, binary fractions, mass-ratio distributions, and field densities, then analyzed with the identical pipeline; recovered posteriors and any residual biases or covariances will be reported. This addition will directly address the concern. revision: yes

Circularity Check

0 steps flagged

No circularity; results are direct empirical fits to cluster observations

full rationale

The paper reports an observational measurement of the IMF slope (-2.29 mean, 0.17 scatter) and minimal mass segregation in young clusters, obtained by applying a Bayesian forward-modeling framework to a sample of 163 open clusters. No load-bearing step reduces the quoted slope, scatter, or segregation metric to a quantity defined by the authors' own prior equations, self-citations, or fitted inputs renamed as predictions. The abstract and described method treat the framework as a correction tool whose outputs are the fitted parameters themselves; no self-definitional, uniqueness-imported, or ansatz-smuggled reductions appear. The derivation is therefore self-contained against external data.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The reported mean slope and scatter are fitted quantities; the analysis assumes a power-law form for the IMF above 0.5 solar masses and that the forward model removes all listed observational biases.

free parameters (2)
  • mean IMF slope = -2.29
    Fitted mean value of -2.29 from young cluster sample.
  • intrinsic scatter = 0.17
    Fitted dispersion of 0.17 around the mean slope.
axioms (2)
  • domain assumption The stellar mass function above 0.5 solar masses follows a single power-law form in young clusters.
    Invoked to extract the slope parameter from the data.
  • ad hoc to paper The Bayesian forward-modeling framework removes all effects of binaries, contamination, and incompleteness without introducing new biases.
    Central to the claim that the measured slope and segregation represent the true initial state.

pith-pipeline@v0.9.1-grok · 5822 in / 1452 out tokens · 39922 ms · 2026-06-28T01:03:19.695301+00:00 · methodology

discussion (0)

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Works this paper leans on

45 extracted references · 43 canonical work pages · 2 internal anchors

  1. [1]

    Exploring Galactic open clusters with Gaia. II Dynamical Evolution and Stellar Population Properties in Fifteen Nearby Open Clusters

    Alfonso, J., Vieira, K., & Garcia-Varela, A. 2024, arXiv e-prints, arXiv:2410.23527, doi: 10.48550/arXiv.2410.23527

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2410.23527 2024

  2. [2]

    , keywords =

    Allison, R. J., Goodwin, S. P., Parker, R. J., et al. 2009, MNRAS, 395, 1449, doi: 10.1111/j.1365-2966.2009.14508.x

    work page doi:10.1111/j.1365-2966.2009.14508.x 2009

  3. [3]

    S., Santos, Jr., J

    Angelo, M. S., Santos, Jr., J. F. C., Maia, F. F. S., & Corradi, W. J. B. 2023, MNRAS, 522, 956, doi: 10.1093/mnras/stad1038 Bastian,N.,Covey,K.R.,&Meyer,M.R.2010,ARA&A,48,339, doi: 10.1146/annurev-astro-082708-101642

    work page doi:10.1093/mnras/stad1038 2023

  4. [4]

    2008, ApJ, 685, 247, doi: 10.1086/590488

    Baumgardt, H., De Marchi, G., & Kroupa, P. 2008, ApJ, 685, 247, doi: 10.1086/590488

    work page doi:10.1086/590488 2008

  5. [5]

    , keywords =

    Baumgardt, H., & Kroupa, P. 2007, MNRAS, 380, 1589, doi: 10.1111/j.1365-2966.2007.12209.x

    work page doi:10.1111/j.1365-2966.2007.12209.x 2007

  6. [6]

    , keywords =

    Baumgardt, H., & Makino, J. 2003, MNRAS, 340, 227, doi: 10.1046/j.1365-8711.2003.06286.x

    work page doi:10.1046/j.1365-8711.2003.06286.x 2003

  7. [7]

    , keywords =

    Bonnell, I. A., & Davies, M. B. 1998, MNRAS, 295, 691, doi: 10.1046/j.1365-8711.1998.01372.x Bressan,A., Marigo,P., Girardi,L.,et al.2012, MNRAS,427,127, doi: 10.1111/j.1365-2966.2012.21948.x

    work page doi:10.1046/j.1365-8711.1998.01372.x 1998

  8. [8]

    2019, A&A, 632, A105, doi: 10.1051/0004-6361/201936612

    Chen, Y., Girardi, L., Fu, X., et al. 2019, A&A, 632, A105, doi: 10.1051/0004-6361/201936612

    work page doi:10.1051/0004-6361/201936612 2019

  9. [9]

    2014, MNRAS, 444, 1957, doi: 10.1093/mnras/stu1521 Domínguez, R., Fellhauer, M., Blaña, M., Farias, J

    Dib, S. 2014, MNRAS, 444, 1957, doi: 10.1093/mnras/stu1521 Domínguez, R., Fellhauer, M., Blaña, M., Farias, J. P., &

    work page doi:10.1093/mnras/stu1521 2014

  10. [10]

    2017, MNRAS, 472, 465, doi: 10.1093/mnras/stx1883

    Dabringhausen, J. 2017, MNRAS, 472, 465, doi: 10.1093/mnras/stx1883

    work page doi:10.1093/mnras/stx1883 2017

  11. [11]

    2022, MNRAS, 516, 5637, doi: 10.1093/mnras/stac2562

    Ebrahimi, H., Sollima, A., & Haghi, H. 2022, MNRAS, 516, 5637, doi: 10.1093/mnras/stac2562

    work page doi:10.1093/mnras/stac2562 2022

  12. [12]

    Giersz, M., & Heggie, D. C. 1996, MNRAS, 279, 1037, doi: 10.1093/mnras/279.3.1037

    work page doi:10.1093/mnras/279.3.1037 1996

  13. [13]

    Girichidis, P., Federrath, C., Allison, R., Banerjee, R., & Klessen, R. S. 2012, MNRAS, 420, 3264, doi: 10.1111/j.1365-2966.2011.20250.x Grudić, M. Y., Guszejnov, D., Hopkins, P. F., Offner, S. S. R., & Faucher-Giguère, C.-A. 2021, MNRAS, 506, 2199, doi: 10.1093/mnras/stab1347

    work page doi:10.1111/j.1365-2966.2011.20250.x 2012

  14. [14]

    Guszejnov, D., Markey, C., Offner, S. S. R., et al. 2022, MNRAS, 515, 167, doi: 10.1093/mnras/stac1737

    work page doi:10.1093/mnras/stac1737 2022

  15. [15]

    2008, ApJ, 675, 1319, doi: 10.1086/524650

    Harayama, Y., Eisenhauer, F., & Martins, F. 2008, ApJ, 675, 1319, doi: 10.1086/524650

    work page doi:10.1086/524650 2008

  16. [16]

    Hennebelle, P., & Grudić, M. Y. 2024, ARA&A, 62, 63, doi: 10.1146/annurev-astro-052622-031748

    work page doi:10.1146/annurev-astro-052622-031748 2024

  17. [17]

    W., Lu, J

    Hosek, Jr., M. W., Lu, J. R., Anderson, J., et al. 2019, ApJ, 870, 44, doi: 10.3847/1538-4357/aaef90 8

    work page doi:10.3847/1538-4357/aaef90 2019

  18. [18]

    L., Cantat-Gaudin, T., Anders, F., et al

    Hunt, E. L., Cantat-Gaudin, T., Anders, F., et al. 2026, A&A, 706, A341, doi: 10.1051/0004-6361/202557781

    work page doi:10.1051/0004-6361/202557781 2026

  19. [19]

    Krause, M. G. H., Charbonnel, C., Bastian, N., & Diehl, R. 2016, A&A, 587, A53, doi: 10.1051/0004-6361/201526685

    work page doi:10.1051/0004-6361/201526685 2016

  20. [20]

    Monthly Notices of the Royal Astronomical Society , author =

    Kroupa, P. 2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x

    work page doi:10.1046/j.1365-8711.2001.04022.x 2001

  21. [21]

    Disentangling the independently controllable factors of variation by interacting with the world

    Lada, C. J., & Lada, E. A. 2003, ARA&A, 41, 57, doi: 10.1146/annurev.astro.41.011802.094844

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1146/annurev.astro.41.011802.094844 2003

  22. [22]

    Lamers, H. J. G. L. M., Baumgardt, H., & Gieles, M. 2013, MNRAS, 433, 1378, doi: 10.1093/mnras/stt808

    work page doi:10.1093/mnras/stt808 2013

  23. [23]

    2023, Nature, 613, 460, doi: 10.1038/s41586-022-05488-1

    Li, J., Liu, C., Zhang, Z.-Y., et al. 2023, Nature, 613, 460, doi: 10.1038/s41586-022-05488-1

    work page doi:10.1038/s41586-022-05488-1 2023

  24. [24]

    2022, ApJ, 930, 44, doi: 10.3847/1538-4357/ac5f4f

    Li, L., & Shao, Z. 2022, ApJ, 930, 44, doi: 10.3847/1538-4357/ac5f4f

    work page doi:10.3847/1538-4357/ac5f4f 2022

  25. [25]

    2025, AJ, 170, 288, doi: 10.3847/1538-3881/ae0cb6

    Li, L., Shao, Z., Li, Z., & Fu, X. 2025, AJ, 170, 288, doi: 10.3847/1538-3881/ae0cb6

    work page doi:10.3847/1538-3881/ae0cb6 2025

  26. [26]

    2025, MiMO Open Cluster catalog, 1.0 National Astronomical Data Center of China, doi: 10.12149/101693

    Li, L., Shao, Z., Li, Z., & Fu, X. 2025, MiMO Open Cluster catalog, 1.0 National Astronomical Data Center of China, doi: 10.12149/101693

    work page doi:10.12149/101693 2025

  27. [27]

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

    Li, L., Shao, Z., Li, Z.-Z., et al. 2020, ApJ, 901, 49, doi: 10.3847/1538-4357/abaef3 Maíz Apellániz, J. 2008, ApJ, 677, 1278, doi: 10.1086/533525

    work page doi:10.3847/1538-4357/abaef3 2020

  28. [28]

    , keywords =

    Marks, M., Kroupa, P., & Baumgardt, H. 2008, MNRAS, 386, 2047, doi: 10.1111/j.1365-2966.2008.13165.x

    work page doi:10.1111/j.1365-2966.2008.13165.x 2008

  29. [29]

    McMillan, S. L. W., Vesperini, E., & Portegies Zwart, S. F. 2007, ApJL, 655, L45, doi: 10.1086/511763

    work page doi:10.1086/511763 2007

  30. [30]

    2002, ApJ, 576, 870, doi: 10.1086/341790

    Padoan, P., & Nordlund, Å. 2002, ApJ, 576, 870, doi: 10.1086/341790

    work page doi:10.1086/341790 2002

  31. [31]

    Parker, R. J. 2014, in Astrophysics and Space Science Proceedings, Vol. 36, The Labyrinth of Star Formation, ed. D. Stamatellos, S. Goodwin, & D. Ward-Thompson, 431, doi: 10.1007/978-3-319-03041-8_86

    work page doi:10.1007/978-3-319-03041-8_86 2014

  32. [32]

    J., Dale, J

    Parker, R. J., Dale, J. E., & Ercolano, B. 2015, MNRAS, 446, 4278, doi: 10.1093/mnras/stu2393 Pavlík, V., Kroupa, P., & Šubr, L. 2019a, A&A, 626, A79, doi: 10.1051/0004-6361/201834265 Pavlík, V., Kroupa, P., & Šubr, L. 2019b, A&A, 626, A79, doi: 10.1051/0004-6361/201834265

    work page doi:10.1093/mnras/stu2393 2015

  33. [33]

    S., et al

    Polak, B., Mac Low, M.-M., Klessen, R. S., et al. 2025, A&A, 695, A188, doi: 10.1051/0004-6361/202451785

    work page doi:10.1051/0004-6361/202451785 2025

  34. [34]

    Photometric content and validation

    Riello, M., De Angeli, F., Evans, D. W., et al. 2021, A&A, 649, A3, doi: 10.1051/0004-6361/202039587

    work page doi:10.1051/0004-6361/202039587 2021

  35. [35]

    Salpeter, E. E. 1955, ApJ, 121, 161, doi: 10.1086/145971

    work page doi:10.1086/145971 1955

  36. [36]

    2004, in American Institute of Physics Conference

    Skilling, J. 2004, in American Institute of Physics Conference

    2004

  37. [37]

    Series, Vol. 735, Bayesian Inference and Maximum Entropy Methods in Science and Engineering: 24th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. R. Fischer, R. Preuss, & U. V. Toussaint (AIP), 395–405, doi: 10.1063/1.1835238

    work page doi:10.1063/1.1835238

  38. [38]

    2017, MNRAS, 471, 3668, doi: 10.1093/mnras/stx1856

    Sollima, A., & Baumgardt, H. 2017, MNRAS, 471, 3668, doi: 10.1093/mnras/stx1856

    work page doi:10.1093/mnras/stx1856 2017

  39. [39]

    Speagle, J. S. 2020, MNRAS, 493, 3132, doi: 10.1093/mnras/staa278

    work page doi:10.1093/mnras/staa278 2020

  40. [40]

    1987, Dynamical Evolution of Globular Clusters

    Spitzer, L. 1987, Dynamical Evolution of Globular Clusters

    1987

  41. [41]

    1969, ApJL, 158, L139, doi: 10.1086/180451 Vázquez-Semadeni, E., Palau, A., Ballesteros-Paredes, J., Gómez, G

    Spitzer, Jr., L. 1969, ApJL, 158, L139, doi: 10.1086/180451 Vázquez-Semadeni, E., Palau, A., Ballesteros-Paredes, J., Gómez, G. C., & Zamora-Avilés, M. 2019, MNRAS, 490, 3061, doi: 10.1093/mnras/stz2736

    work page doi:10.1086/180451 1969

  42. [42]

    Vesperini, E., McMillan, S. L. W., & Portegies Zwart, S. 2009, ApJ, 698, 615, doi: 10.1088/0004-637X/698/1/615

    work page doi:10.1088/0004-637x/698/1/615 2009

  43. [43]

    2020, MNRAS, 497, 536, doi: 10.1093/mnras/staa1915

    Wang, L., Iwasawa, M., Nitadori, K., & Makino, J. 2020, MNRAS, 497, 536, doi: 10.1093/mnras/staa1915

    work page doi:10.1093/mnras/staa1915 2020

  44. [44]

    J., & Vesperini, E

    Webb, J. J., & Vesperini, E. 2016, MNRAS, 463, 2383, doi: 10.1093/mnras/stw2186

    work page doi:10.1093/mnras/stw2186 2016

  45. [45]

    2024, ApJS, 270, 9, doi: 10.3847/1538-4365/acfee5

    Xu, F., Wang, K., Liu, T., et al. 2024, ApJS, 270, 9, doi: 10.3847/1538-4365/acfee5

    work page doi:10.3847/1538-4365/acfee5 2024