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Testing the Breakdown of the Asteroseismic Scaling Relations in Luminous Red Giants

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Pith's one-line read The paper argues that the breakdown of asteroseismic scaling relations in luminous red giants is driven mainly by the large-frequency-separation mapping to mean density, not by the frequency of maximum power scaling.

desk verdict A careful, genuinely new decomposition of the luminous-giant scaling breakdown, but the central Δν-vs-νmax ranking rests on small samples and a selection procedure that could bias the trend; the modeling negative result is the strongest part. read the letter →

arxiv 2411.10520 v1 pith:K4H24EHW submitted 2024-11-15 astro-ph.SR

Amanda L. Ash , Marc H. Pinsonneault , Mathieu Vrard , Joel Zinn This is my paper · ORCID
classification astro-ph.SR
keywords asteroseismologyredgiantsscalingrelationsluminousgiantbranchlargefrequencyseparationofmaximumpowerstellarradiiopenclusters
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 asteroseismic scaling relations that turn measured oscillation frequencies into stellar masses and radii work well on the lower red giant branch and red clump, but they break down for luminous red giants, where seismic radii come out about 9% larger than parallactic radii. The paper isolates the two ingredients of the breakdown: the scaling that ties the large frequency separation $\Delta\nu$ to mean density and the scaling that ties the frequency of maximum power $\nu_{\max}$ to surface gravity. Using open cluster stars and the Milky Way's high-$\alpha$ sequence as independent mass benchmarks, it finds that the $\Delta\nu$ relation produces the more discrepant masses in the luminous giant regime, so the $\Delta\nu$ mapping is the larger contributor to the inflated radii. It then shows that two ways of computing the $\Delta\nu$ correction factor $F_{\Delta\nu}$ from stellar models, using all synthetic modes versus an observationally motivated subset with or without mixing-length calibration, shift the inferred radii by only 1 to 3 percent, too little to explain the breakdown.

What carries the argument

The argument runs through the single-parameter scaling relations, which let each observed asteroseismic quantity be tested separately against independent masses and radii. The $\nu_{\max}$-only relation is $$\frac{M_*}{M_\odot} = \frac{\nu_{\max}}{\nu_{\max,\odot}} \left(\frac{R_{\rm Gaia}}{R_\odot}\right)^2 \left(\frac{T_{\rm eff}}{T_{\rm eff,\odot}}\right)^{1/2},$$ and the $\Delta\nu$-only relation is $$\frac{M_*}{M_\odot} = \left(\frac{F_{\$\Delta$\nu}\,\$\Delta$\nu}{\$\Delta$\nu_\odot}\right)^2 \left(\frac{R_{\rm Gaia}}{R_\odot}\right)^3,$$ where $F_{\Delta\nu}$ is the correction factor mapping the observed large frequency separation to mean density through $(F_{\Delta\nu}\Delta\nu_{\rm obs})/\Delta\nu_\odot = ((M/M_\odot)/(R/R_\odot)^3)^{1/2}$. The benchmarks are the open clusters NGC 6819 and NGC 6791, with isochronal and eclipsing-binary masses, and the high-$\alpha$ sequence as a quasi-coeval population of median mass near $1.04\,M_\odot$. The paper also builds MESA stellar models and GYRE non-adiabatic synthetic frequency spectra to test how measuring $\Delta\nu$ from all modes versus an observationally accessible subset, with and without a metallicity-dependent mixing-length calibration, changes $F_{\Delta\nu}$ and therefore the inferred radius.

What would settle it

A luminosity-selected sample of luminous giants in additional open clusters, or with eclipsing-binary masses, comparing $\nu_{\max}$-only and $\Delta\nu$-only masses would settle the attribution: if the $\Delta\nu$-only masses no longer track the inflated seismic radii while the $\nu_{\max}$-only masses do, the breakdown would move to the $\nu_{\max}$ side.

Watch

Extended reading notes

Core claim

The central claim is that in luminous red giants, conventionally stars with seismic radii above about $30\,R_\odot$, the observed inflation of asteroseismic radii relative to Gaia parallactic radii originates primarily from the $\Delta\nu$-to-mean-density side of the joint scaling relations. The evidence comes from splitting the joint relations into a $\nu_{\max}$-only mass relation and a $\Delta\nu$-only mass relation, applied to open cluster stars and the high-$\alpha$ sequence used as a pseudo-cluster of known mean mass. The $\nu_{\max}$-only relation stays consistent with the high-$\alpha$ median mass across the giant branch, while the $\Delta\nu$-only relation runs over-massive in the 30 to 50 solar radius regime, mirroring the curvature of the joint scaling relations. The paper further claims that theoretical corrections to the $\Delta\nu$ mapping, through either mode selection or mixing-length calibration, alter inferred radii by only about 1 to 3 percent, which cannot account for the roughly 9 percent radius inflation, and that the $F_{\Delta\nu}$ correction is insensitive to the adopted mixing length calibrated to observed effective temperatures.

Load-bearing premise

The high-$\alpha$ sequence is treated as a pseudo-cluster with a single well-defined mass, median $1.04\,M_\odot$ for radii below $30\,R_\odot$, and a narrow age spread, and the 5-$\sigma$ mass cuts used to clean it are assumed not to bias the radius-dependent mass trend.

Editorial extensions

If this is right

  • The $\nu_{\max}$-only scaling relation is a reliable mass and radius estimator on the lower giant branch, so surveys that rely on $\nu_{\max}$ alone can proceed with caution there, but they should be calibrated separately before being extended to luminous giants.
  • The $\Delta\nu$-only relation is the part of the scaling relations that needs re-examination if the luminous-giant breakdown is to be fixed.
  • Changing the way $\Delta\nu$ is measured in theoretical spectra, or calibrating mixing length to observed effective temperatures, will not by itself remove the discrepancy in luminous giant radii.
  • Radius calibrations applied through a $F_{\nu_{\max}}$ term do not necessarily correct the mass scale, meaning that calibrated radii and calibrated masses are not interchangeable tests of the scaling relations.
  • Future population studies using only one asteroseismic parameter in the luminous giant regime should carry an extra systematic uncertainty until the physical source of the $\Delta\nu$ failure is identified.

Reading between the lines

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

  • If the $\Delta\nu$ attribution is correct, then surface-effect corrections applied to individual oscillation frequencies, which mainly act on the frequency pattern, would not be expected to cure the luminous-giant radius inflation either; the cause would more likely live in how luminous-giant structure maps onto the asymptotic relation.
  • A direct extension would be to measure $F_{\Delta\nu}$ empirically for luminous giants using asteroseismic radii anchored to eclipsing binaries at large radius, which would test whether the correction factor is radius dependent rather than merely method dependent.
  • The insensitivity of $F_{\Delta\nu}$ to mixing length suggests that the breakdown is not a convective-efficiency calibration problem, leaving non-adiabatic and atmospheric modeling, or missing physics such as magnetic fields or rotation, as the more promising explanations.
  • The small number of luminous cluster giants, four in NGC 6819 and one in NGC 6791, means that a larger cluster sample or a dedicated high-$\alpha$ sample with independent radii could sharpen the claim that $\Delta\nu$ dominates over $\nu_{\max}$.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper tests the asteroseismic scaling relations for luminous red giants by separating the contributions of νmax and Δν. It uses parallactic radii from Gaia and independent masses from the open clusters NGC 6791 and NGC 6819 and from the Milky Way's high-α sequence as benchmarks. The authors derive single-parameter scaling relations for νmax and Δν and compare the resulting masses with the benchmarks as a function of radius. They find that the Δν-only relation shows larger, radius-dependent deviations than the νmax-only relation, and they interpret this as evidence that the Δν scaling relation is the main contributor to the previously reported breakdown of the joint scaling relations in luminous giants. They then compute model-based FΔν corrections using MESA+GYRE grids and test the effects of mixing-length calibration and of measuring Δν from all modes versus an observationally motivated subset of modes. These model changes alter the inferred radii by only about 1–3%, which is too small to explain the ≈9% inflated seismic radii. The paper concludes that the theoretical FΔν corrections, at least within the tested model treatments, cannot resolve the luminous-giant discrepancy.

Significance. If the central attribution is correct, the paper identifies the Δν-to-mean-density mapping as the weak link in the asteroseismic scaling relations for luminous giants, which would directly affect Galactic archaeology and planned single-parameter asteroseismic programs such as the Roman Galactic Bulge Time Domain Survey. The modeling null result is also useful: it shows that two plausible model treatments (mixing-length calibration and mode selection) do not resolve the discrepancy, narrowing the search space. The paper is commendably transparent about its limitations: it states that the metallicity-binned Δν deviations are not at 3σ significance and that the cluster luminous-giant sample is only four stars in NGC 6819 and one in NGC 6791. The data and MESA/GYRE inlists are publicly available, which is a strength. The main empirical claim is therefore suggestive but not yet secure; the selection effects in the high-α sample and the small cluster sample need to be quantitatively addressed before the attribution can be regarded as established.

major comments (3)
  1. [Sec. 2.4.4 and Sec. 3.2.2, Eqs. (6)-(7), Figs. 5-6] The high-α sample is cleaned with a 5σ mass cut applied to the APOKASC3 catalog mass and to the single-parameter scaling-relation masses computed from Eqs. (6) and (7). Because the subsequent analysis is precisely the radius-dependent behavior of those same single-parameter masses, this constitutes a selection on the outcome variable. At fixed radius the single-parameter masses scatter widely, and in the luminous regime the 2–3% inter-pipeline scatter in Δν (Sec. 4.3.2) enlarges that scatter. A one-sided upper cut removes the most over-massive stars in each bin; in the small-N tail above ≈50 R⊙, where the errors are largest, this can depress the rolling median and create the downturn from over-massive to under-massive stars that is interpreted as the Δν curvature. The Δν-only mass scales as R^3 while the νmax-only mass scales as R^2 (Eqs. 6 and 7), so the same cut can affect the two trends differently and artificially produce the relative offset between them. The paper does not quantify this selection effect. Please add a quantitative test—for example, apply the same mass-cut and rolling-median procedure to synthetic data with no true breakdown and show that the observed Δν-versus-νmax difference is not reproduced; if it is reproduced, the central attribution is not secure.
  2. [Sec. 3.2.2 and Sec. 3.2.1, Tables 3-4] The paper's internal significance statements are weaker than the abstract's claim. Section 3.2.2 states that the metallicity-binned Δν deviations are 'not at a 3σ level of significance,' and Section 3.2.1 reports only four luminous giants in NGC 6819 and one in NGC 6791. Despite this, the abstract asserts that 'the Δν-scaling relation contributes to the observed breakdown in luminous giants more than the νmax relation.' The cluster luminous-giant masses for the single-parameter relations are statistically consistent with the isochrone mass in both clusters (Tables 3 and 4, 'Luminous RGB' rows). Please either soften the abstract to match the stated significance (e.g., 'tentatively indicates' or 'we find suggestive evidence'), or add a combined statistical test across the high-α bins and the cluster stars that accounts for the selection effect raised in the first major comment. The current wording overstates the evidential weight of the analysis.
  3. [Sec. 2.4.4 and Sec. 3.2.2] The high-α 'pseudo-cluster' benchmark mass (median 1.04 M⊙ for R < 30 R⊙) is used as the seismic-independent reference, but its provenance is not explicitly stated. If this median mass is derived from APOKASC3 catalog masses, then it is not independent of the scaling relations being tested; a global zero-point error in the APOKASC3 calibration would be hidden, and only the radius-dependent trend would be meaningful. Please clarify how the benchmark mass is computed (isochrones, APOKASC3, or other) and test the sensitivity of the Figs. 5 and 6 trends to the assumed benchmark mass and to its possible variation with radius. This is important because the central attribution depends on the benchmark being a valid single-mass reference across the entire giant branch.
minor comments (6)
  1. [Sec. 2.4.2] The text says NGC 6791 has a turnoff age of '≈ 8 Myr'; this should read '≈ 8 Gyr' to be consistent with the adopted isochrone age of 8.3 ± 0.3 Gyr in Sec. 2.4.3.
  2. [Eq. (6) and Sec. 3, Fig. 4] Equation (6) shows the νmax-only mass without any Fνmax term, while the surrounding text and the middle panel of Fig. 4 indicate that a constant Fνmax is applied. Please clarify whether Eq. (6) should include Fνmax and, if so, where it enters; this affects the absolute mass scale, though not the radius-dependent curvature.
  3. [Figs. 5 and 6] The y-axis labels are rendered as 'max' instead of 'νmax'; the symbols are missing in several axis labels and captions throughout the paper (e.g., 'Rseis', 'Mhigh'). Please ensure the math mode renders correctly.
  4. [Table 1 caption] The caption contains the typo 'Asteroseiemic'; should be 'Asteroseismic'.
  5. [Sec. 5, bullet list] The bullet 'astreroseismic scaling relationships' contains a typo; should be 'asteroseismic'.
  6. [Sec. 3.2.2, KS test sentence] The sentence 'Using a Kolmogorov-Smirnov (KS) tests we confirm...' has a subject-verb agreement error; should be 'Using Kolmogorov-Smirnov (KS) tests, we confirm...'.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: the central claim is anchored to external Gaia and cluster benchmarks, with only minor self-referential inputs.

full rationale

The paper's central claim—that Δν contributes more than νmax to the luminous-giant breakdown—is tested against external benchmarks: Gaia parallactic radii (Sec. 2.3), cluster isochronal masses (Sec. 2.4.3), and the high-α sequence's independently motivated median mass (Sec. 2.4.4). The single-parameter masses in Eqs. 6 and 7 are therefore not defined in terms of the quantities they are used to predict; the comparison is not forced by construction. The FΔν modeling result is a null result: the paper demonstrates insensitivity to mixing length by computing sound-speed profiles and frequency spacings across αmlt = 1.4–2.3 (Figs. 13–14), so the conclusion does not depend on the αmlt calibration being correct. The main self-referential elements are the use of the APOKASC3 catalog (Pinsonneault et al. 2024, with overlapping authorship) and the calibration of the αmlt–[Fe/H] relation using APOKASC3 corrected seismic masses (Sec. 4.3.1). These are inputs, not load-bearing conclusions: APOKASC3 is tied to the fundamental scale, and the FΔν insensitivity result would survive a different calibration. The paper itself limits the strength of its attribution, noting the small number of luminous cluster stars (Sec. 3.2.1), that the Δν discrepancy 'is not at a 3σ level of significance' (Sec. 3.2.2), and that 'the robustness of this conclusion is limited by small sample size and large uncertainties' (Sec. 4). The 5σ mass cut applied to the single-parameter masses when selecting the high-α sample (Sec. 2.4.4) is a selection-on-outcome robustness concern that is not quantified, but it is not a stated identity or a fitted parameter renamed as a prediction; the observed rolling-median curvature is not logically forced by the cut. Overall, no load-bearing circular step was identified.

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

The central claims rest on three classes of inputs: the empirical scaling relations and their calibration constants, the assumption that Gaia/cluster/high-alpha benchmarks are seismic-independent and unbiased, and the MESA/GYRE model setup (non-adiabatic modes, grey Eddington atmosphere, mixing length calibration, overshoot parameters). The model setup contains two fitted calibrations (Fnu_max constants and the mixing length relation) and several adopted parameters.

free parameters (4)
  • Constant Fnu_max values for RGB and RC = 0.9959 (RGB), 0.9937 (RC)
    Adopted from prior calibration instead of the radius-dependent APOKASC3 values (Sec. 3). Chosen to isolate trends in scaling-relation deviations; affects absolute masses but not the reported qualitative trends.
  • Mixing length calibration relation = alpha_mlt = 0.247 [Fe/H] + 1.869
    Linear fit to APOKASC3 RGB stars with R less than 20 R_sun (Sec. 4.3.1) and used to assign alpha_mlt to models that produce FΔν. The paper demonstrates FΔν is insensitive to alpha_mlt, but the relation is still a fitted input.
  • Convective overshoot parameters = f = 0.0014 (text) or 0.014 (inlist); f0 = 0.004
    Adopted ad hoc values for exponential overshoot in Eq. 11; the text and Appendix A disagree by a factor of 10, which is an internal inconsistency that could affect model structure.
  • Gaussian envelope parameters for measuring Delta nu = alpha = 0.66, beta = 0.88
    Adopted from Mosser et al. (2012) to weight mode separations (Eq. 13). The choice affects the synthetic Delta nu values, and the paper tests two mode-selection variants but not these envelope parameters.
assumptions (5)
  • domain assumption The asteroseismic scaling relations Eqs. (1)-(5) hold with empirical correction factors Fnu_max and FDelta_nu.
    Basis of the entire analysis; the breakdown itself is defined as a deviation from these relations (Sec. 1.1).
  • domain assumption The high-alpha sequence is an approximately coeval, single-mass pseudo-cluster with a well-defined median mass.
    Used as the seismic-independent mass benchmark in Sec. 3.2.2, following Miglio et al. (2021) and Roberts et al. (2024). If the sequence has significant mass dispersion or contamination, the inferred Delta nu versus nu_max deviations change.
  • domain assumption Gaia parallaxes, APOGEE temperatures, and 2MASS photometry yield unbiased seismic-independent radii when propagated through the Stefan-Boltzmann law.
    The parallactic radii are the fundamental comparison for both the single-parameter mass tests and the FDelta_nu radius comparisons (Secs. 2.3 and 4.4).
  • domain assumption Non-adiabatic GYRE frequencies computed from MESA models with a grey Eddington T-tau atmosphere adequately represent the radial mode spectrum of luminous red giants.
    The FDelta_nu values in Sec. 4 assume this model physics; the paper notes luminous giants have tenuous atmospheres and lacks a quantitative alternative (Sec. 4).
  • domain assumption Surface effects on frequencies are absorbed into the empirical Fnu_max term rather than modelled separately.
    The paper explicitly assumes this based on Li et al. (2023) and Pinsonneault et al. (2024) in Sec. 1.1, which affects the mapping from observed to theoretical frequencies.

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Cite this review

Pith. "Pith review of Testing the Breakdown of the Asteroseismic Scaling Relations in Luminous Red Giants." pith.science (2026). https://pith.science/paper/K4H24EHW

@misc{pith2026241110520,
  author       = {Pith},
  title        = {Pith review of: Testing the Breakdown of the Asteroseismic Scaling Relations in Luminous Red Giants},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K4H24EHW}},
  note         = {Machine review of arXiv:2411.10520}
}
abstract

Nearly all cool, evolved stars are solar-like oscillators, and fundamental stellar properties can be inferred from these oscillations with asteroseismology. Scaling relations are commonly used to relate global asteroseismic properties, the frequency of maximum power $\nu_{max}$ and the large frequency separation $\Delta \nu$, to stellar properties. Mass, radius, and age can then be inferred with the addition of stellar spectroscopy. There is excellent agreement between seismic radii and fundamental data on the lower red giant branch and red clump. However, the scaling relations appear to breakdown in luminous red giant stars. We attempt to constrain the contributions of the asteroseismic parameters to the observed breakdown. We test the $\nu_{max}$ and $\Delta \nu$ scaling relations separately, by using stars of known mass and radius in star clusters and the Milky Way's high-$\alpha$ sequence. We find evidence that the $\Delta \nu$-scaling relation contributes to the observed breakdown in luminous giants more than the $\nu_{max}$ relation. We test different methods of mapping the observed $\Delta \nu$ to the mean density via a correction factor, $F_{\Delta \nu}$ and find a $\approx 1 - 3\%$ difference in the radii in the luminous giant regime depending on the technique used to measure $F_{\Delta \nu}$. The differences between the radii inferred by these two techniques are too small on the luminous giant branch to account for the inflated seismic radii observed in evolved giant stars. Finally, we find that the $F_{\Delta \nu}$ correction is insensitive to the adopted mixing length, chosen by calibrating the models to observations of $T_{eff}$.

Figures

Figures reproduced from arXiv: 2411.10520 by the authors.

Figure 1
Figure 1. Radius - Teff diagram for NGC 6791 and NGC 6819. Lines indicate best fit isochrone and shaded regions indicate errors on best fit isochrone. The triangular points are the parallactic radius before correcting random errors using the cluster parallaxes. The circular points are the parallactic radii after correcting for random errors using the cluster parallax. See Sec. 2.4.3 for the parameters of the isochrones Cluste… view at source ↗
Figure 2
Figure 2. High-α sequence selection. High-α stars are green points above the dotted line. The dotted line is given by the prescription in Roberts et al. (2024) for the νmax only scaling relation, and M∗ M⊙ =  F∆ν∆ν ∆ν⊙ 2 RGaia R⊙ 3 (7) for the ∆ν only scaling relation. The APOKASC3 catalog contains an additional correction term, Fνmax , that is used to correct νmax in the scaling relations. However, as we are in￾terested … view at source ↗
Figure 3
Figure 3. Cluster weighted average mass results. Left panel: NGC 6819 mass results compared to an isochrone mass and the mass of NGC 6819 given in Handberg et al. (2017). Right: NGC 6791 mass results compared to an isochrone mass. The parameters of the isochrone can be found in section 2.4.3. This plot shows results for the lower RGB gold sample, the lower RGB silver sample and the RC. The luminous giants are omitted due to s… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Component analysis of the scaling relations using clusters in M∗ v. R∗ plane. Different colors indicate different samples within the cluster. The colored dotted lines are the weighted mean masses of a particular sample within a cluster. Left: Masses computed using the …
Figure 5
Figure 5. Figure 5: Component analysis of the scaling relations using high-α sequence stars. The x-axis is the fractional mass difference between mass computed using the scaling relations and the median mass of the high-α sequence. The purple vertical dashed line is the zero-offset point …
Figure 6
Figure 6. Figure 6: Component analysis of the scaling relations using high￾α sequence stars binned by metallicity. The lines and axes of this figure follow the same convention as [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: Calibrated mixing length relationships. Left Panel: Calibrated mixing lengths as a function of [Fe/H]. The points in grey are the individual calibrations for RGB stars in APOKASC3. The plotted [Fe/H] values are the Salaris corrected values. The blue line is the final m…
Figure 8
Figure 8. Figure 8: Calibrated mixing length as a function of [Fe/H] for different methods. The different color lines show the Salaris￾corrected [Fe/H] - calibrated αmlt relationship (dark blue), the orig￾inal [Fe/H] - calibrated αmlt relationship (light blue), and the cal￾ibrated αmlt re…
Figure 10
Figure 10. Figure 10: Fractional difference between Rseis and Rgaia v. Rseis for different models. The solid colored line uses F∆ν correction factors for uncalibrated models and the dashed lines use the αmlt - [Fe/H] calibration. Green lines use all of the available modes computed by GYRE …
Figure 11
Figure 11. Figure 11: Comparison between calibration scales used in this pa￾per and the APOKASC3 catalog. The axes are the seismic radius computed with different correction terms over the Gaia radius ver￾sus νmax . Results from this study are given by the dark blue, light blue, dark green,…
Figure 12
Figure 12. Figure 12: Fractional difference between Rseis and Rgaia v. Rseis for different models. The plot follows the same conventions as 10. However, this plot has been broken into sub-panels for different metallicity bins. 2 0 2 4 6 10 6 10 7 10 8 c s mlt = 1.4 mlt = 1.7 mlt = 2.0 mlt …
Figure 13
Figure 13. Figure 13: Sound speed vs. acoustic radius for models with dif￾ferent radii and mixing lengths. The solid and dashed lines refer to stars with 50R⊙ and 10R⊙, respectively. The different color lines indicate different mixing lengths in the model. The bottom panel shows the fracti…
Figure 14
Figure 14. Figure 14: Frequency spectra for models of different stellar ra￾dius and mixing length. Top panel: The y-axis of this figure is the frequency of a given mode on the x-axis. The triangle points are measurements for a model with a radius of 10R⊙. The circle points have a radius of…
Figure 15
Figure 15. Figure 15: Echelle diagram for synthetic frequency spectra. Top panel: Synthetic frequency spectrum for a 1M⊙, 15R⊙ star. Bottom panel: Synthetic frequency spectrum for a 1M⊙, 50R⊙ star. The green shaded region is the width of the Gaussian envelope used to select modes to comput…

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Pith tools

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