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REVIEW 3 major objections 5 minor 225 references

The initial mass functions of three nearby open clusters are top-light and show real cluster-to-cluster variation, challenging the universality of the stellar IMF.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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For Alpha Persei, the Pleiades, and Praesepe, the initial mass function is top-light (α_high ≈ 2.98 ± 0.22) and shows possible cluster-to-cluster scatter, based on Gaia DR3 plus N-body emulator inference.

T0 review reviewed 2026-08-01 challenge →

load-bearing objection Careful, honest forward-modeling of three open clusters' initial IMFs that is only as strong as its gas-free evolution assumption—worth a serious referee, but the top-light headline should be read as conditional. the 3 major comments →

arxiv 2607.17300 v1 pith:ZFCLPOT4 submitted 2026-07-19 astro-ph.GA astro-ph.SR

The initial conditions and initial mass functions of Alpha Persei, Pleiades and Praesepe

L. Hobart , H. Baumgardt , S. Sweet This is my paper
classification astro-ph.GA astro-ph.SR
keywords initial mass functionopen clustersbinary starsN-body simulationsmachine learning emulatorbroken power lawstellar populationsdynamical evolution
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper asks what the stellar initial mass function (IMF) was at birth for three nearby open clusters, after correcting for unresolved binaries and the dynamical loss of low-mass stars. By matching N-body simulations through a machine-learning emulator to high-precision astrometric and photometric survey data, the authors infer an average IMF that is a three-stage broken power law with slopes near 1.2, 1.7, and 3.0 in the low, intermediate, and high mass ranges, with break masses near 0.25 and 0.96 solar masses. The high-mass slope is steeper than the canonical value of 2.35, so the IMF is top-light, and the measured scatter between clusters (σh≈0.29) indicates that the high-mass IMF is not universal. A sympathetic reader cares because this directly constrains whether star formation depends on environment and affects predictions for massive star counts, supernovae, and black hole yields.

Core claim

On its own terms, the paper establishes that the present-day mass functions of the three clusters, once binaries are accounted for and the clusters are evolved backward in time, are best reproduced by a three-segment broken power law with average slopes αl=1.24±0.29, αm=1.72±0.09, αh=2.98±0.22 and break masses at 0.25±0.02 and 0.96±0.14 solar masses. This represents a top-light IMF compared with the canonical field IMF, and the dispersion σh=0.29±0.16 in the high-mass slope between clusters is evidence for cluster-to-cluster variation, while the intermediate slope shows none. The authors also derive the most probable initial number of systems, binary fraction, and half-mass radius for each c

What carries the argument

The central object is the three-stage broken power-law mass function, defined by slopes αl, αm, αh and two break masses. The load-bearing machinery is a forward-modelling pipeline: clean membership selection from astrometric and photometric data down to roughly 0.1 solar masses, a Bayesian Monte Carlo procedure that corrects the present-day mass function for unresolved binaries, and a grid of N-body simulations whose outputs are approximated by a Gaussian-process emulator, allowing Hamiltonian Monte Carlo to sample the initial cluster parameters (system number, binary fraction, half-mass radius, IMF slopes) that best match the observations.

Load-bearing premise

The whole inference assumes that early gas removal does not significantly influence the subsequent evolution of the clusters, so they can be modelled as if born gas-free; if gas expulsion removes most of the initial mass, the inferred IMF changes drastically.

What would settle it

Run the same forward-model with primordial gas expulsion (e.g., instantaneous removal of 50-75% of the mass) for at least one cluster, such as Praesepe, and compare its predicted present-day mass function, binary fraction, and half-mass radius to the same astrometric and photometric observations; if the gas-expelled models fit equally well or better, the top-light, gas-free IMF is not uniquely identified.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • A top-light IMF in open clusters implies fewer high-mass stars per unit cluster mass than the canonical IMF, lowering predicted supernova and compact-remnant rates for such systems.
  • Cluster-to-cluster scatter in the high-mass slope suggests the IMF is not universal; environment (density, metallicity) must shape the relative numbers of massive stars, with consequences for interpreting integrated-light observations of unresolved galaxies.
  • The recovered initial conditions provide a self-consistent starting point for simulations of cluster evolution, tidal tails, and mass segregation, matching observed radial distributions and tidal tail counts.
  • The consistent intermediate-mass slope near 1.7 indicates that the substellar-to-solar-mass regime may be more universal than the high-mass end, corroborating recent field-star measurements.
  • The demonstrated combination of N-body simulations with machine-learning emulators makes full forward-modelling of cluster IMFs computationally feasible for the large samples of clusters in new astrometric catalogues.

Where Pith is reading between the lines

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

  • The gas-free assumption is the critical hinge: if gas expulsion at birth removes a large fraction of the cluster mass, the inferred IMF slopes change considerably, so the top-light conclusion is conditional on this assumption being valid.
  • Because the low-mass slope depends on the adopted mass-luminosity conversion, direct mass measurements of binary stars from future astrometry could tighten the low-mass IMF and the position of the first break.
  • The emulator-plus-N-body approach can be applied to any cluster with precise astrometry, making it possible to measure IMF variation across a large, homogeneous sample and test environmental dependencies directly.
  • A larger sample might reveal whether the observed high-mass scatter is stochastic sampling noise or a true environmental trend, and whether a survivor bias skews the observed average.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper determines the initial mass functions (IMFs) and initial dynamical conditions of the open clusters Alpha Persei, Pleiades, and Praesepe. Using Gaia DR3 astrometry/photometry supplemented by UKIDSS and Hipparcos, the authors construct membership samples to 0.10–0.17 M_sun, measure unresolved binary fractions via Monte Carlo/Bayesian fits, and then infer initial cluster properties by forward-modelling with N-body simulations whose outputs are emulated with Gaussian processes and sampled with Hamiltonian Monte Carlo. They report a three-stage broken-power-law IMF with average slopes alpha_l = 1.24 ± 0.29, alpha_m = 1.72 ± 0.09, alpha_h = 2.98 ± 0.22, break masses near 0.25 and 0.96 M_sun, and intrinsic scatter in the high-mass slope (sigma_h = 0.29 ± 0.16). They conclude that the IMF in these open clusters is top-light compared with Salpeter/Kroupa and may vary between clusters.

Significance. If the main result holds, it would strengthen the evidence that the IMF is not universal and depends on environmental conditions, and it would provide a novel methodological template for inferring initial cluster conditions by combining N-body simulations, machine-learning emulators, and Bayesian sampling. The paper is transparent about many of its assumptions and makes member catalogues and mass estimates publicly available. It also compares explicitly with the competing gas-expulsion analysis of Weis et al. (2025). The main value of the paper is the demonstration that a fully forward-modelled dynamical-evolution correction is feasible for open clusters; the reliability of the headline IMF slopes, however, depends critically on the gas-free initial-condition assumption and on the treatment of break masses, as detailed below.

major comments (3)
  1. [Section 5.4, Table 5] The inference is conditional on the assumption that early gas removal does not significantly affect subsequent cluster evolution (abstract; Section 5). The paper itself notes that Weis et al. (2025) find, with instantaneous gas expulsion, a very different Praesepe IMF (alpha_h = 4.1, alpha_l = 0.4) compared with the present alpha_h = 2.86, alpha_l = 1.93. The authors argue that unresolved binaries explain much of the difference, but this is not quantitatively supported: Section 4 and Figure 10 show that binary corrections change the slopes by roughly 0.1–0.5 and have 'little effect at the high mass end.' A ~1.2 dex difference in alpha_h cannot plausibly be absorbed by the binary correction. Because the emulator and HMC posterior are restricted to gas-free initial conditions, the quoted uncertainties in Table 5 cover only statistical and emulator uncertainty under that assumption; they do
  2. [Sections 5.1–5.2, Table 5] The break masses are not fitted; they are adopted from the observed PDMF. Section 5.1 states: 'We used the same break points m_x1 and m_x2 as the observed clusters rather than leaving them as free parameters.' Consequently, the break masses quoted in the abstract and Section 5.4 (0.24–0.50 M_sun and 0.91–1.20 M_sun) are not independently inferred from the N-body/HMC analysis; they come from the PDMF fits of Table 2. The reported slope values are therefore conditional on these breaks. If dynamical evolution shifts the breaks, the inferred initial slopes could be biased. The paper's assertion that the break points remain stable during evolution is plausible but is not demonstrated. I request a sensitivity test in which the break masses are treated as free parameters (or at least varied over the PDMF uncertainties) and the resulting IMF slope posteriors are shown to be unaffected.
  3. [Section 3.3, Section 2.1] The PDMF fitting truncates the sample at a magnitude limit chosen for Gaia completeness but does not model the completeness function of the combined Gaia+UKIDSS dataset. Section 3.3 applies a manual lower bound 'due to the completeness of Gaia at fainter magnitudes', but no completeness correction is applied to the inferred mass function. If the UKIDSS-only faint stars (Section 2.1) are not complete, or if the Gaia limit is not actually complete at the cluster distances, the low-mass slope alpha_l and the first break mass m_x1 will be biased. Since alpha_l = 1.24 ± 0.29 is part of the reported average IMF, the paper should either demonstrate that the adopted lower bound lies above any incompleteness or incorporate an explicit completeness model into the fits. This is particularly important because the low-mass slope is already sensitive to the mass–luminosity relation, and an incompleten
minor comments (5)
  1. [Section 2.2] For Alpha Persei, the initial proper motions and parallax are listed as mu_alpha = 19.997 mas/yr, mu_delta = -45.548 mas/yr, omega = 5.718 mas — identical to the Pleiades starting values. This is inconsistent with Table 1 and with the cluster's actual motion. Please correct this typo and verify that the iterative filtering converged to the values in Table 1.
  2. [Section 5.4, Figure 15] The reported average slopes and dispersions do not follow trivially from Table 5. For example, alpha_m = 1.72 ± 0.09 equals the inverse-variance weighted mean of the alpha_m,star values in Table 5 (1.64, 1.67, 2.23), but the quoted alpha_h = 2.98 ± 0.22 does not match the weighted mean of the Table 5 alpha_h values (which would be ~3.15 or 3.18). Please state explicitly whether the averages and dispersions are computed from full posterior samples, from the median values, or by a hierarchical model, and give the corresponding formula.
  3. [Section 5.2] The concentration parameter c is omitted from the emulator because it 'had little significant correlation' with the test statistics. Please report the range of c values sampled and show that setting the initial tidal radius equal to the Jacobi radius does not bias the inferred half-mass radii or the IMF slopes.
  4. [General] The text switches between alpha_med (abstract) and alpha_m (body and tables) for the intermediate-mass slope. Use one notation throughout for consistency.
  5. [Figures] In the review copy, several figures contain garbled axis labels (e.g., Figures 1, 2, 4, 5, 11, 12, 16). This may be a rendering artifact, but please ensure the published version has legible labels and legends.

Circularity Check

1 steps flagged

Forward-modeling chain is self-contained; minor issue: initial IMF break masses are adopted from the observed PDMF and then presented as part of the inferred IMF.

specific steps
  1. fitted input called prediction [Section 5.1 (emulator training), Section 5.4 (average IMF), Abstract]
    "We used the same break points m x1 and m x2 as the observed clusters rather than leaving them as free parameters to reduce the complexity of the model. ... we find the average IMF to be given by ... break masses of m x1 = 0.25 ± 0.02 M⊙ and m x2 = 0.96 ± 0.14 M⊙."

    The quoted initial break masses are not inferred by the N-body/emulator stage; Section 5.1 fixes them to the present-day PDMF break masses, so the values reported in Section 5.4 and the Abstract are a restatement of the observed PDMF input by construction. However, the central IMF-slope results are genuinely fitted to independent present-day observables (PDMF slopes, half-mass radius, binary fraction, surface density), so this does not force the headline top-light or scatter conclusions.

full rationale

The paper's central derivation is a self-contained forward-modeling analysis: initial system number, binary fraction, half-mass radius, and IMF slopes are fit with an emulator/HMC pipeline to reproduce present-day PDMF slopes, binary fraction, half-mass radius, and surface density profiles. These observables are independent of the fitted initial slopes, and the high-mass slope is additionally constrained by the present-day half-mass radius rather than only by the high-mass PDMF. No equation in the paper reduces an inferred quantity to a fitted input by construction, aside from the break masses, which are explicitly fixed to the observed PDMF break masses and then reported as part of the 'best-fitting initial mass function.' This is a minor conflation of input and output but does not affect the main IMF-slope claims. Self-citations (e.g., Baumgardt et al. 2023, Khalaj & Baumgardt 2013) are used for comparison and methodology, not as unverified load-bearing premises, and the results are checked against external determinations. The gas-free early-evolution assumption and the disagreement with Weis et al. (2025) are explicitly acknowledged systematic limitations, not circularity. Overall, the derivation chain is largely independent and externally falsifiable; the only circularity-adjacent element is the presentational treatment of the adopted break masses.

Axiom & Free-Parameter Ledger

30 free parameters · 9 axioms · 0 invented entities

The central inference is built on many fitted parameters (mass-function slopes, break masses, binary fractions, initial conditions) and on several physical assumptions. The most consequential assumption—gas-free evolution—is flagged by the authors and directly contested by a cited study (Weis et al. 2025). No new entities are introduced.

free parameters (30)
  • IMF low-mass slope αl (Alpha Persei) = 0.98 ± 0.23
    Fitted to PARSEC masses + N-body inference (Table 5).
  • IMF low-mass slope αl (Pleiades) = 0.80 ± 0.27
    Fitted to PARSEC masses + N-body inference (Table 5).
  • IMF low-mass slope αl (Praesepe) = 1.93 ± 0.24
    Fitted to PARSEC masses + N-body inference (Table 5).
  • IMF intermediate-mass slope αm (Alpha Persei) = 1.64 ± 0.25
    Fitted to PARSEC masses + N-body inference (Table 5).
  • IMF intermediate-mass slope αm (Pleiades) = 1.67 ± 0.09
    Fitted to PARSEC masses + N-body inference (Table 5).
  • IMF intermediate-mass slope αm (Praesepe) = 2.23 ± 0.26
    Fitted to PARSEC masses + N-body inference (Table 5).
  • IMF high-mass slope αh (Alpha Persei) = 2.60 ± 0.19
    Fitted to PARSEC masses + N-body inference (Table 5).
  • IMF high-mass slope αh (Pleiades) = 3.33 ± 0.10
    Fitted to PARSEC masses + N-body inference (Table 5).
  • IMF high-mass slope αh (Praesepe) = 2.86 ± 0.36
    Fitted to PARSEC masses + N-body inference (Table 5).
  • Break mass mx1 (Alpha Persei) = 0.30 ± 0.06 M_sun
    Fitted in PDMF (Table 2), then fixed for IMF inference.
  • Break mass mx1 (Pleiades) = 0.24 ± 0.02 M_sun
    Fitted in PDMF (Table 2), then fixed for IMF inference.
  • Break mass mx1 (Praesepe) = 0.50 ± 0.11 M_sun
    Fitted in PDMF (Table 2), then fixed for IMF inference.
  • Break mass mx2 (Alpha Persei) = 0.95 ± 0.34 M_sun
    Fitted in PDMF (Table 2), then fixed for IMF inference.
  • Break mass mx2 (Pleiades) = 0.91 ± 0.12 M_sun
    Fitted in PDMF (Table 2), then fixed for IMF inference.
  • Break mass mx2 (Praesepe) = 1.20 ± 0.33 M_sun
    Fitted in PDMF (Table 2), then fixed for IMF inference.
  • Present-day binary fraction fbin (Alpha Persei) = 0.238 ± 0.012
    Fitted via Bayesian Monte Carlo CMD simulations (Table 4).
  • Present-day binary fraction fbin (Pleiades) = 0.200 ± 0.008
    Fitted via Bayesian Monte Carlo CMD simulations (Table 4).
  • Present-day binary fraction fbin (Praesepe) = 0.221 ± 0.010
    Fitted via Bayesian Monte Carlo CMD simulations (Table 4).
  • Initial binary fraction fbin_ini (Alpha Persei) = 0.346 ± 0.019
    Inferred from N-body emulator fit (Table 5).
  • Initial binary fraction fbin_ini (Pleiades) = 0.303 ± 0.012
    Inferred from N-body emulator fit (Table 5).
  • Initial binary fraction fbin_ini (Praesepe) = 0.242 ± 0.015
    Inferred from N-body emulator fit (Table 5).
  • Initial number of systems Nsys_ini (Alpha Persei) = 1127
    Inferred from N-body emulator fit (Table 5).
  • Initial number of systems Nsys_ini (Pleiades) = 1670
    Inferred from N-body emulator fit (Table 5).
  • Initial number of systems Nsys_ini (Praesepe) = 2105
    Inferred from N-body emulator fit (Table 5).
  • Initial 3D half-mass radius rh_ini (Alpha Persei) = 5.63 pc
    Inferred from N-body emulator fit (Table 5).
  • Initial 3D half-mass radius rh_ini (Pleiades) = 4.45 pc
    Inferred from N-body emulator fit (Table 5).
  • Initial 3D half-mass radius rh_ini (Praesepe) = 4.34 pc
    Inferred from N-body emulator fit (Table 5).
  • Empirical M-L spline coefficients = Not tabulated
    B-spline fitted to eclipsing-binary data; parameters not provided in the paper.
  • Main-sequence polynomial coefficients (each cluster) = Not given
    Used to identify stick-out binaries; fitted to observed main sequence but coefficients not reported.
  • Membership filtering thresholds = σα=σδ=1 mas/yr, σω=0.25 mas, χ²=11.345, P>0.75, radius=15°
    Chosen by hand; affect the member sample and therefore all subsequent measurements.
axioms (9)
  • domain assumption Early gas removal does not significantly influence subsequent cluster evolution.
    Stated in abstract and §5; if false, inferred IMF changes (see §5.4, Weis et al. 2025).
  • domain assumption Newtonian N-body dynamics with NBODY7 accurately models cluster evolution.
    Used throughout Section 5; no relativistic or hydrodynamical effects considered.
  • domain assumption IMF break masses mx1 and mx2 are invariant under dynamical evolution.
    Section 5, 'we find the break points remain relatively stable over the cluster's evolution'—stated without demonstration.
  • domain assumption Gaia DR3, UKIDSS, and HIPPARCOS samples are complete down to applied magnitude limits and member selection is clean.
    Manual removal of outliers in §2; no completeness function applied.
  • ad hoc to paper Flat mass-ratio distribution for binary secondaries; semi-major axes log-uniform between 50 stellar radii and 1000 AU.
    §4.2 and §5.1; not empirically derived; alternative pairing schemes are acknowledged.
  • domain assumption All stellar remnants (NS/BH) are ejected immediately.
    §5.1, with reference to Pavlík et al. (2018).
  • domain assumption Adopted PARSEC/MIST isochrones and empirical M-L relation give unbiased stellar masses.
    §3; low-mass slope sensitive to this choice (acknowledged).
  • domain assumption King (1962) density profile with concentration tied to Jacobi radius describes initial cluster structure.
    §5.1; concentration parameter omitted in emulator.
  • domain assumption The Gaussian-process emulator trained on a Latin hypercube is sufficiently accurate for inference.
    §5.1; R² reported for test subset but emulator accuracy vs. true N-body outputs not fully quantified.

reviewed 2026-08-01 · how reviews work

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Cite this review

Pith. "Pith review of The initial conditions and initial mass functions of Alpha Persei, Pleiades and Praesepe." pith.science (2026). https://pith.science/paper/ZFCLPOT4

@misc{pith2026260717300,
  author       = {Pith},
  title        = {Pith review of: The initial conditions and initial mass functions of Alpha Persei, Pleiades and Praesepe},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZFCLPOT4}},
  note         = {Machine review of arXiv:2607.17300}
}
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abstract

We have determined the initial mass function (IMF) and structural properties of the open clusters Alpha Persei, Pleiades and Praesepe using Gaia DR3 astrometry and photometry. Cluster members were identified using primarily Gaia astrometry, supplemented with near-infrared UKIDSS and optical HIPPARCOS survey data with stellar masses down to $0.10-0.17$ MSun. We measure and correct for unresolved binaries in each cluster using photometry and Monte Carlo simulations in a Bayesian framework, finding present-day fractions between ($20.0\pm0.8$)% and ($23.8\pm1.2$)%. Through a novel approach that combines N-body simulations with machine learning emulators and MCMC algorithms, we have also determined the most probable initial number of stars, binary fraction, half-mass radius and mass function under the assumption that early gas removal does not significantly influence the subsequent cluster evolution. We find a best-fitting initial mass function described by a three-stage broken power-law distribution with break masses in the ranges $0.24-0.50$ MSun and $0.91-1.20$ MSun and average slopes of $\alpha_{\rm med}=1.72\pm0.09$ and $\alpha_{\rm high}=2.98\pm0.22$. While the low-mass slope remains sensitive to the adopted mass-luminosity relation, this IMF reproduces the present-day clusters well once their dynamical evolution is taken into account. We find evidence of scatter in the high mass IMF between the individual clusters, as described by the measured dispersions in mass function slopes of ${\sigma}_{\rm high}=0.29\pm0.16$, whereas the intermediate mass slope shows no significant variation with ${\sigma}_{\rm med}=0.00\pm0.14$. Our findings provide additional evidence for a (compared to a Salpeter MF) top-light IMF and a cluster-to-cluster variation of the IMF. They therefore provide constraints on the universality of the IMF and its dependence on environmental conditions.

Figures

Figures reproduced from arXiv: 2607.17300 by H. Baumgardt, L. Hobart, S. Sweet.

Figure 1
Figure 1. Figure 1: Proper motion distribution of stars in Praesepe in right ascension and declination. Black points show background stars whereas red points indicate cluster members identified through PM and parallax filtering. Cluster members are clearly separated from the background population, forming a compact over-density. if they were unresolved multiple star systems. There were also a number of stars that appeared sli… view at source ↗
Figure 2
Figure 2. Figure 2: Colour magnitude diagrams of filtered Praesepe member stars based on the combined photometric information of Gaia DR3, HIPPARCOS and UKIDSS. Left: Colour magnitude diagram using Gaia G magnitudes and G-GRP colours. Right: Colour magnitude diagram using UKIDSS J magnitudes and Y-J colours. The colour coding of each star indicates which catalogue it is observed in: either Ga (Gaia), U (UKIDSS), H (HIPPARCOS)… view at source ↗
Figure 3
Figure 3. Figure 3: Colour-magnitude diagrams (CMDs) for Alpha Persei, Pleiades and Praesepe (left to right). The top row shows the absolute magnitude MG against (G-GRP), while the bottom row shows MG against (GBP-GRP). In each panel, the PARSEC v2.0 isochrone using values from prior work is shown in orange and the corresponding MIST isochrone in blue. Grey dashed lines indicate masses along the isochrone for PARSEC models. S… view at source ↗
Figure 4
Figure 4. Figure 4: Empirical mass–luminosity relation for low-mass stars. The black points show the sample of eclipsing binaries used to calibrate the relation given in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Posterior distributions for the parameters of the three-segment broken power-law IMF model for the Pleiades. The fitted parameters include the three power-law slopes (α1, α2, α3), the two break masses (mbreak,1 and mbreak,2), and the minimum and maximum stellar masses (mmin and mmax) with 1σ credible intervals. Most parameters, excluding mmax, are well constrained with approximately uni-modal posterior dis… view at source ↗
Figure 6
Figure 6. Figure 6: Present-day mass functions (PDMFs) for Alpha Persei, the Pleiades, and Praesepe (left to right). In each panel, the favoured broken power-law model (either two- or three-segment, depending on the cluster) is shown for masses estimated using three different methods: PARSEC isochrones (solid blue), MIST isochrones (dashed orange), and the empirical mass–luminosity relation (dot–dashed green). The resulting P… view at source ↗
Figure 7
Figure 7. Figure 7: Cluster observed present day mass functions using PARSEC v2.0 isochrone masses, uncorrected for binaries or dynamical evolution. Black points show the fraction of stars in each log mass bin with 1σ error bars, assuming Poisson statistics. The solid red line indicates the best-fitting three-segment broken power-law model [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Identified ’stick-out’ stars in Praesepe. (left) CMD of Praesepe with observable ‘stick-out’ stars that lie above the main sequence highlighted with red triangles and the main sequence polynomial fit in blue. The CMD uses Gaia photometry in the G and GRP passbands. (centre) Praesepe stellar spatial distribution with stick-out stars highlighted in red. (right) Cumulative fraction of stick-out stars (red das… view at source ↗
Figure 9
Figure 9. Figure 9: shows the posterior distribution of each cluster. We see that there is good convergence for the estimates of the system MF and binary fraction. The best fitting parameters given by these distributions are listed in [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Binary corrections of the PDMF of Pleiades. Binary correction leads to a relatively larger fraction of low and intermediate mass stars compared to high mass stars due to additional, unseen low mass stars that are binary companions. that correspond to these properties and compare the final state of different initial parameter combinations to observables of the cluster such as the current binary fraction an… view at source ↗
Figure 11
Figure 11. Figure 11: The derived highest likelihood stellar IMF (red) for each cluster compared to its PDMF (black). The mass function ξ(log m) is scaled such that the curves reflect simulated stellar losses of ≈ 15%, 9% and 49% for Alpha Persei, Pleiades and Praesepe respectively. We see that Praesepe is more evolved and thus has a larger number of low mass stars that have been stripped over time, whereas Alpha Persei and Pl… view at source ↗
Figure 12
Figure 12. Figure 12: The observed surface density profile of Praesepe (black) and the surface density profile of a simulation using the best fitting parameters (red dashed). There is good agreement between the two curves, showing the validity of the derived parameters. We also show the best fitting Plummer model for the observed surface density (blue dot-dashed) with Plummer radius a = 4.26 ± 0.11 and Nstar = 1367 ± 40 [PITH… view at source ↗
Figure 13
Figure 13. Figure 13: Cumulative distribution of stars in each cluster with respect to radius (black). Cluster members are split into two groups, showing the different radial distribution of high mass stars > 1M⊙ and low mass stars < 1M⊙ which indicates the presence of mass segregation. We also show the radial distribution of simulations using the best fitting parameters (red) which are in good agreement, despite mass segregat… view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of IMF measurements of Alpha Persei, Pleiades, Prae￾sepe and other stellar bodies. The mass range in M⊙ which the value was calculated over is noted underneath each data point. The red vertical line and shaded region depict the mean IMF slope values for our three measured clusters with uncertainty. The grey vertical line corresponds to the slope values from the canonical Kroupa (2001) IMF. dete… view at source ↗
Figure 15
Figure 15. Figure 15: Average open cluster initial mass function (IMF) (black solid line) compared to the canonical IMF from Kroupa (2001) (red dashed) and the average globular cluster IMF from Baumgardt et al. (2023) (blue dot-dashed). All three curves are normalised such that the area under the curve is unity. The open cluster IMF closely follows the canonical shape but exhibits a flat￾tening at intermediate masses and a ste… view at source ↗
Figure 16
Figure 16. Figure 16: Corner plot of input parameter posterior distribution samples for Alpha Persei, Pleiades and Praesepe. These samples are distributed around the highest likelihood initial parameters for each cluster. We fit for the best combination of initial number of stellar systems (Nsys,ini), initial binary fraction (fbin,ini), initial 3D half-mass radius (rh,ini), and the system IMF slopes for the low, intermediate, … view at source ↗
Figure 17
Figure 17. Figure 17: Stellar luminosity functions of Alpha Persei, Pleiades and Praesepe, uncorrected for unresolved binary companions or dynamical evolution. Error bars correspond to 1σ = √ N assuming Poisson statistics [PITH_FULL_IMAGE:figures/full_fig_p027_17.png] view at source ↗

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