Improving the stellar age determination through joint modeling of binarity and asteroseismology -- Grid modeling of the seismic red-giant binary KIC 9163796

A. Hanslmeier; B. Liagre; C. Johnston; D. Godoy-Rivera; D. H. Grossmann; D. Stello; J. C. Zinn; L. S. Schimak; L. Steinwender; N. Muntean

REVIEW 4 major objections 4 minor 2 cited by

Improving the stellar age determination through joint modeling of binarity and asteroseismology -- Grid modeling of the seismic red-giant binary KIC 9163796

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Combining binary, spectroscopic, and asteroseismic constraints dates the red-giant binary KIC 9163796 to 2.44 billion years with a 9 percent uncertainty.

desk verdict First joint grid model of KIC 9163796 shows binarity plus seismology can pin a giant's age to ~10-15%, but the headline 9% is built on an ad hoc error recipe that needs to be fixed before the precision claim holds. read the letter →

arxiv 2501.09018 v1 pith:W2MBJTAT submitted 2025-01-15 astro-ph.SR astro-ph.EP

D. H. Grossmann , P. G. Beck , S. Mathur , C. Johnston , D. Godoy-Rivera , J. C. Zinn , S. Cassisi , B. Liagre

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T. Masseron R. A. Garcia A. Hanslmeier N. Muntean L. S. Schimak L. Steinwender D. Stello

This is my paper · ORCID

classification astro-ph.SRastro-ph.EP

keywords asteroseismologystellaragedeterminationspectroscopicbinaryredgiantsubgiantgridmodelingKIC9163796

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 tries to show that constraints from binarity—two stars born at the same time from the same cloud—combined with asteroseismic oscillation measurements can pin down a red giant's age far more precisely than isochrone fitting alone. Applied to the double-lined spectroscopic binary KIC 9163796, whose components have nearly equal masses but very different locations in the Hertzsprung–Russell diagram, the joint modeling returns a common age of $2.44^{+0.25}_{-0.20}$ Gyr, a relative uncertainty near 9 percent. That is roughly an order of magnitude better than the 30–50 percent typical of single-giant isochrone ages, and the paper argues the same approach can turn well-observed binary systems into precision age anchors.

What carries the argument

The central machinery is a 12,096-model grid of single-star evolutionary tracks computed with MESA and processed with GYRE, searched pairwise with a reduced chi-square figure of merit. Each model pair must satisfy binary conditions: the primary mass is at least the secondary mass, the two stars have exactly the same age, the same initial helium, and, in the constrained cases, equal or spectroscopically fixed metallicity, with the observed mass ratio $q=1.015\pm0.005$ entering the fit. The fit compares effective temperatures, surface gravity, mass ratio, the primary's $\nu_{\max}$ from scaling relations, a local large-frequency separation $\Delta\nu$ derived from GYRE radial modes and corrected with the empirical factor $f_{\Delta\nu}$, and, in the final cases, the V-band magnitude difference between the components. This grid-plus-chi-square machinery is what lets the two stars' distinct positions in the Hertzsprung–Russell diagram act as two independent clocks reading out the same age.

What would settle it

Re-run the same grid and observables with a standard likelihood that includes all chi-square values and no outlier rejection: if the resulting 1-$\sigma$ credible interval is wider than roughly 30 percent relative, the claimed 9 percent precision is not supported. An independent measurement of the secondary's $\nu_{\max}$ that falls outside the best-fit model predictions would also rule out the adopted solution.

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Extended reading notes

Core claim

For KIC 9163796, modeling the red-giant primary and subgiant secondary simultaneously with the physical requirement that both components share one age and one initial composition yields a system age of $2.44^{+0.25}_{-0.20}$ Gyr (Case D2). The best-fitting models also require initial helium $Y\simeq0.27$–$0.30$, above the primordial helium abundance, initial metallicity at or below the spectroscopic value, and masses that agree with asteroseismic scaling relations. The authors conclude that adding binarity and asteroseismic constraints progressively breaks degeneracies—especially the mass–initial-helium degeneracy—and brings the reduced chi-square minima closer to unity, so the preferred solutions are both more precise and less overfitted.

Load-bearing premise

The quoted 9 percent age error rests on a non-standard error recipe: every model pair with reduced chi-square below one is treated as statistically equal, and outliers are then removed if judged inconsistent with the observed mass and metallicity; if that pruning is too aggressive, the true age uncertainty is larger than reported.

Editorial extensions

If this is right

Red-giant ages in double-lined spectroscopic binaries with both seismic and binary constraints can reach relative uncertainties near 9 percent, roughly an order of magnitude better than the 30–50 percent typical of single-star isochrone fitting.
Adding the binary conditions of co-evality, equal initial composition, and a fixed mass ratio moves best-fit reduced chi-square values closer to unity, indicating less overfitting and more realistic models.
The same fits recover parameters normally inaccessible to observations, such as initial helium abundance and the mixing-length parameter, and can test whether the mixing length changes as stars climb the subgiant and red-giant branches.
The approach is portable: the paper points to roughly 900 newly identified oscillating binary systems from Gaia DR3 cross-matches, plus PLATO target catalogs, as a future sample for this joint modeling.

Reading between the lines

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

If the 9 percent precision survives a full Bayesian re-analysis of the same grid, the method could be applied to many SB2 oscillating giants to map Galactic stellar ages far more sharply than single-star fits allow.
The gap between 9 percent (Case D2) and 13 percent (Case D3) shows that part of the quoted precision is borrowed from trusting the spectroscopic metallicity; higher-resolution spectroscopy would directly buy age precision.
The secondary's super-Nyquist $\nu_{\max}$ was deliberately left out of the fit, so future observations that resolve it offer a clean, independent check of the model's predicted luminosity difference.
Because the recovered helium values sit at the edge of the explored grid, and the paper itself cites a known grid-edge bias for helium, the absolute $Y$ estimates should be read as tentative until independent helium diagnostics are added.

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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 real contribution here is the first joint MESA/GYRE grid model of KIC 9163796, combining the SB2 mass ratio, both effective temperatures and gravities, νmax, and a newly derived local Δν with the magnitude difference as an extra luminosity constraint. That is new for this benchmark system, and the paper is transparent about the machinery: 12 096 models, inlists in the appendix, timestep resolution tests, αMLT and overshoot exploration. The qualitative result is solid: constraints from binarity shrink the age uncertainty from ~100% in Case A0 to roughly 10-15% in the physically motivated cases. I believe that conclusion will hold up.

What does not hold up is the quoted 9% uncertainty. The error recipe in Sect. 4.2 is the load-bearing weakness. The denominator n−m in Eq. (2) is never specified, and for Case C the observable count equals the free parameter count, so χ2_red is undefined without an arbitrary choice of m. The χ2_red < 1 threshold is therefore not a statistical statement. The scatter in age across the surviving grid points is not a confidence interval, and the outlier-removal step is completely unreported: no criterion, no count. On top of that, the headline Case D2 forces Z to the spectroscopic central value, which is less physical than D3, and D3 already gives 13%. The paper explicitly flags the Y grid-edge bias (Sect. 6.4) but does not propagate it. Systematics from αMLT, f_Δν, and overshoot are not folded into any quoted error. For these reasons, 2.44(+0.25,−0.20) Gyr is not a supported precision claim.

That said, the central argument is not circular. The age is fitted, not assumed, and the mass consistency in Sect. 6.2 is appropriately framed as a consistency check even if the grid was centered on BKP18's seismic mass. The paper is honest about several limitations, which is to its credit.

Bottom line: this deserves a serious referee, but not for the number in the abstract. The authors should be asked to specify the degrees of freedom, report the outlier removal in detail, replace the ad hoc recipe with a standard Δχ2 or Bayesian interval, and quote D3 or a properly marginalized uncertainty as the headline. Once that is done, the method demonstration and the benchmark age will be useful to anyone working on giant-star ages and Galactic archaeology.

Referee Report

4 major / 4 minor

Summary. This manuscript presents a grid-modeling study of the SB2 system KIC 9163796 with MESA and GYRE, combining constraints from binarity, spectroscopy, and asteroseismology. The authors construct a 12,096-model grid varying mass, initial metallicity, initial helium, and mixing length, and use a reduced chi-square figure of merit over effective temperatures, surface gravity, mass ratio, nu_max, Delta_nu, and magnitude difference, with common-age and common-composition constraints. They report a best age of 2.44(+0.25,-0.20) Gyr for Case D2 (9% relative uncertainty), masses near 1.3 solar masses, Y about 0.27-0.30, and Z around 0.004-0.006, and conclude that joint binary and asteroseismic modeling reduces giant-star age uncertainties by an order of magnitude.

Significance. If the quoted precision holds, this is a valuable demonstration for a rare benchmark system: an SB2 red-giant/subgiant pair with seismic detections, a well-determined mass ratio, and coevality constraints. The technical effort is substantial and should be credited: a large MESA grid, GYRE-based Delta_nu computation, a re-derived local Delta_nu, and explicit tests of alpha_MLT, overshooting, and T-tau choices. The mass-ratio constraint clearly shapes the solution, as seen in the diagonal M1-M2 structure of the residual maps. The main caveat is that the headline 9% uncertainty rests on a nonstandard and insufficiently documented error recipe; the more conservative Case D3 already gives 13%, and systematic terms from metallicity, alpha_MLT, and the helium grid-edge bias are not folded into the quoted uncertainty.

major comments (4)

[Section 4.2] The error-estimation recipe used for the headline age is not a confidence interval. The text states that all models with chi2_red < 1 have the same significance and that the scatter in age of these models defines the 1-sigma boundaries, but the accepted models are a discrete set of correlated evolutionary tracks rather than independent measurements, and the outlier-removal step ('test if those are consistent with stellar models for the observational mass/metallicity, and if not, remove them') is never quantified. Neither the number of accepted models nor the number and identity of removed outliers is reported, so the reader cannot check whether the 2.44(+0.25,-0.20) Gyr range is stable. This is load-bearing because Case D2's 9% uncertainty is the paper's central claim; the paper itself notes that standard error propagation does not work for age estimation, which makes validation of the replacement procedure mandatory.
[Eq. (2), Tables 3 and 4] The reduced chi-square used throughout depends on an unspecified number of fitted parameters m. For Case C the observables in the figure of merit are six (Teff1, Teff2, logg2, q, nu_max1, Delta_nu1) while the grid has six free parameters (M1, M2, Z, Y, alpha_MLT,1, alpha_MLT,2), so n-m can be zero and chi2_red is formally undefined; nevertheless Table 4 reports values between 0.05 and 0.9. Reporting m for each case is necessary because the chi2_red < 1 threshold used to define statistically equivalent models depends directly on this denominator. This issue affects the validity of the whole selection criterion, not just the size of the error bars.
[Table 4 and Section 7] The adopted best age comes from Case D2, which forces Z1 = Z2 = Zspec = 0.006, while the grid's best-fit metallicities in the less constrained cases are lower (Z about 0.004-0.005). Case D3, which allows Z within its 1-sigma spectroscopic range, yields 2.52(+0.31,-0.36) Gyr (about 13%), and D1 gives 2.58(+0.39,-0.42) Gyr. The 9% figure therefore reflects a single, deliberately chosen metallicity slice and does not include systematic uncertainty from Z, alpha_MLT, the f_Delta_nu correction, or the Y grid-edge bias acknowledged in Section 6.4. The paper should either adopt the more conservative D3 result as the headline or explicitly add these systematics to the quoted age uncertainty.
[Section 3 and Section 6.2] The grid's mass range is centered on BKP18's asteroseismic mass of 1.39 solar masses and extends three times its reported uncertainty, so the agreement between the modeled and scaling-relation masses in Section 6.2 is partly by construction. This should be stated explicitly; it does not invalidate the age analysis, but it weakens the claim that the mass agreement independently validates the models.

minor comments (4)

[Abstract and Table 4] The abstract states that the initial heavy-metal abundance is below the spectroscopic value, but this is not true for Case D2, where Z is forced to Zspec; clarify that this refers to the less constrained cases such as D3.
[Appendix B.2, Listing 2] The example inlist sets initial_z = 0.015, which is outside the grid range [0.004, 0.010] defined in Table 2; this is presumably a typo and should be corrected.
[Section 4.2, Eq. (3)] Equation (3) defines sigma_i,y but is never used in the paper; remove it or explain how it relates to the final uncertainty estimates.
[Throughout] There are numerous typographical artifacts such as 'di fferent' and 'ef fects' throughout the text; a careful copyedit is needed before publication.

Circularity Check

1 steps flagged · score 2.0 of 10

No equation-level circularity; the age is genuinely fitted, but the mass-agreement validation is partially circular because the grid's mass prior is centered on the same BKP18 asteroseismic mass.

other [Sect. 3 (grid construction) and Sect. 6.2 (mass agreement)]
"Sect. 3: "For the stellar mass range of the grid, we chose an interval centered on the mass of the primary reported by BKP18 from an asteroseismic analysis and extended three times the reported uncertainty towards higher and lower masses." Sect. 6.2: "All values from our modeling fall well within the 1-σ uncertainties of the scaling-based mass of both components (Fig. 12) and also agree with one another within uncertainties. This is an important indication of our model correctly reproducing the two stellar components of KIC 9163796.""

The grid's mass range (roughly 1.20-1.54 Msun) is constructed by centering on BKP18's asteroseismic mass for the primary (1.39 ± 0.06 Msun), which is the same quantity the modeling later claims to reproduce in Sect. 6.2. Because the output masses are selected from a grid whose prior is centered on that seismic mass, the 'agreement' with scaling-based masses is partly assured by construction and is not a fully independent confirmation. This circularity is partial and confined to the validation claim: the grid extends well beyond the 1-sigma band, and the central age result does not depend on the mass-agreement statement.

full rationale

The central age is produced by forward grid fitting: MESA/GYRE models with varied M, Z, Y, and alpha_MLT are compared via chi2 to spectroscopic (Teff, log g, q), seismic (nu_max, Delta_nu), and photometric (Delta m) observables under binary constraints Age1=Age2 and shared composition, with no age assumed as input. Metallicity is deliberately excluded from the figure of merit to avoid circularity ('we did not include it in the figure of merit, to avoid a circular argument'). The only concrete circular element is the validation of masses, since the grid's mass range is centered on BKP18's asteroseismic mass; this makes the Sect. 6.2 mass agreement a partially prior-driven consistency check rather than an independent prediction, but it does not feed back into the age derivation. The chi2_red<1 uncertainty recipe, unspecified degrees-of-freedom count, and unquantified outlier removal are statistical-validity concerns, not circularity. Self-citations (Beck et al. 2014, 2018, 2024) supply observational data and sample context that are externally falsifiable and are not used as an unverified theorem, so they do not raise the circularity score beyond this minor, non-load-bearing caveat.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

All four grid dimensions (M, Z, Y, alpha_MLT) are free parameters searched by chi-squared minimization; fov and f_Delta_nu are fixed constants chosen from tests or literature without propagated uncertainty. No new physical entities are introduced. The main axioms are standard binary coevality and the validity of 1D stellar models plus scaling relations for these stars.

free parameters (6)

Initial stellar mass M = 1.29 to 1.37 M_sun depending on case (Table 4)
Grid dimension over [1.20, 1.54] M_sun with step 0.01; the best value is set by chi-squared minimization against Teff, log g, q, nu_max, Delta_nu, and Delta m.
Initial heavy-element abundance Z = 0.004 to 0.007; D2 forced to 0.006
Grid dimension over [0.004, 0.010] with step 0.001; freely fitted cases prefer the lower boundary, while constrained cases use the spectroscopic value or its 1-sigma range.
Initial helium abundance Y = 0.27 to 0.30; some subcases at 0.32 to 0.33 when the grid is expanded
Grid dimension over [0.24, 0.30] with step 0.01; best values cluster at the high end, with a known grid-edge bias noted by the authors.
Mixing length alpha_MLT per component = 1.4, 1.5, or 1.6 (Table 4)
Only three discrete values are allowed, chosen independently for primary and secondary; equality is not enforced. This parameter strongly affects the HRD position and hence the derived age.
Overshooting parameter fov = 0.02 (fixed)
Chosen from a test of 0.020, 0.014, 0.002, and no overshooting because it best reproduces the observables; this is a fit-influenced constant with no propagated uncertainty.
Delta_nu correction factor f_Delta_nu = 0.974
Applied to GYRE large-frequency separations following Eq. 16 of Li et al. (2023), computed from the primary's observed centroids; its uncertainty is not propagated into the age or mass errors.

assumptions (6)

domain assumption The two stars formed together and share age, initial helium, and initial metallicity.
Used to impose Age1=Age2, Z1=Z2, and Y1=Y2; standard binary coevality assumption stated in Sect. 1 and applied in Cases A1 through D3.
domain assumption 1D MESA models with the chosen microphysics, Eddington T-tau relation, and exponential overshoot describe both stars.
The grid only varies M, Z, Y, and alpha_MLT; fov=0.02 and the Eddington boundary are fixed because they fit the observables best (Sect. 3, Appendix A).
domain assumption The asteroseismic scaling relations for nu_max and the f_Delta_nu correction of Li et al. (2023) are valid for both components.
Model nu_max is computed from scaling relations (Sect. 4.1) and GYRE Delta_nu is corrected with f_Delta_nu=0.974 (Sect. 3), with no systematic error budget.
domain assumption The BKP18 measurements of mass ratio, Teff, log g, nu_max, Delta_nu, Delta m_V, and [M/H] are accurate.
All key observables are taken from prior work by overlapping authors (Beck et al. 2018) and are not independently re-derived here.
domain assumption Initial Z equals current surface Z.
Adopted in Sect. 5.1 to map [M/H] to grid Z; the authors test this and find the evolutionary difference negligible.
ad hoc to paper Removing models younger than 0.5 Gyr and treating all chi2_red<1 models as equally significant, with ad hoc outlier deletion, yields valid confidence intervals.
Section 4.2; this paper-specific statistical convention drives the quoted age uncertainty and is not a standard chi-square confidence-interval construction.

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Pith. "Pith review of Improving the stellar age determination through joint modeling of binarity and asteroseismology -- Grid modeling of the seismic red-giant binary KIC 9163796." pith.science (2026). https://pith.science/paper/W2MBJTAT

@misc{pith2026250109018,
  author       = {Pith},
  title        = {Pith review of: Improving the stellar age determination through joint modeling of binarity and asteroseismology -- Grid modeling of the seismic red-giant binary KIC 9163796},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W2MBJTAT}},
  note         = {Machine review of arXiv:2501.09018}
}

abstract

Context. Typical uncertainties of ages determined for single star giants from isochrone fitting using single-epoch spectroscopy and photometry without any additional constraints are 30-50 %. Binary systems, particularly double-lined spectroscopic (SB2) binaries, provide an opportunity to study the intricacies of internal stellar physics and better determine stellar parameters, particularly the stellar age. Aims. By using the constraints from binarity and asteroseismology, we aim to obtain precise age and stellar parameters for the red giant-subgiant binary system KIC 9163796, a system with a mass ratio of 1.015 but distinctly different positions in the Hertzsprung-Russell diagram (HRD). Methods. We compute a multidimensional model grid of individual stellar models. From different combinations of figures of merit, we use the constraints drawn from binarity, spectroscopy, and asteroseismology to determine the stellar mass, chemical composition, and age of KIC 9163796. Results. Our combined-modeling approach leads to an age estimation of the binary system KIC 9163796 of 2.44$^{+0.25}_{-0.20}$ Gyr, which corresponds to a relative error in the age of 9 %. Furthermore, we found both components exhibiting equal initial helium abundance of 0.27 to 0.30, significantly higher than the primordial helium abundance, and an initial heavy metal abundance below the spectroscopic value. The masses of our models are in agreement with masses derived from the asteroseismic scaling relations. Conclusions. By exploiting the unique, distinct positions of KIC 9163796, we successfully demonstrated that combining asteroseismic and binary constraints leads to a significant improvement of precision in age estimation, that have a relative error below 10% for a giant star.

Figures

Figures reproduced from arXiv: 2501.09018 by the authors.

**Figure 1.** HRD depicting the positions of the primary (upward triangle) and secondary (downward triangle) component of KIC 9163796 according to the asteroseismic analysis from Beck et al. (2018). As references, the tracks of a 1 M⊙, 1.4 M⊙ and 2 M⊙ evolutionary track with the primary’s metallicity from MESA are provided as dashed lines. The background contour plot shows the density distribution of all targets from the input… view at source ↗

**Figure 2.** Comparison of the best fitting solutions for case A regarding the treatment of metallicity. The grey solutions have the metallicity varying freely in the modeled range (Case A0), the magenta solution only allows values where the metallicity of the primary equals the metallicity of the secondary (Case A1), while the royal blue solutions force both metallicities to be equal to the spectroscopic solution (Case A2). Th… view at source ↗

**Figure 3.** Secondary mass and χ 2 red-minima as a function of primary mass from the models with the condition of equal metallicity of both components Z1 = Z2 (Case A1). The color bar indicates the respective χ 2 redminima on a logarithmic scale. The residuals were calculated with enforcing M1 ≥ M2; the gray area represents the respective space where no χ 2 red is calculated due to this condition. The seismic solution, inclu… view at source ↗

Figures from the paper (6 more)

**Figure 5.** Figure 5: Comparison of the best fitting solutions regarding the treatment of metallicity (set equal for primary and secondary: magenta; set equal and to spectroscopic value: royal blue; set equal and within a 1-σ range of the spectroscopic metallicity: cyan). The figure of meri…

**Figure 6.** Figure 6: The residuals of the χ 2 red-Minimization as a function of the primary mass M1 and secondary mass M2 with the condition of equal metallicity within the uncertainty range of the spectroscopic value of both components Z1,2 = Zspec ±σZspec (Case C3); with the inclusion o…

**Figure 9.** Figure 9: Residuals of χ 2 red-Minimization in the mass-initial helium plane for both components (primary left, secondary right), for case D3. The best-fitting solution for each is marked as a magenta triangle [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

**Figure 10.** Figure 10: Residuals of the χ 2 red-minimization in the mass-metallicity plane for both components (primary left, secondary right), for identical metallicities for both components (Case D1). For this case, the magenta triangle marks the best-fitting solution. For the analogous …

**Figure 11.** Figure 11: Age estimations for the different cases of the figure of merit, including their uncertainties. The cases are calculated as described in Sect. 4, with the cases color coded as follows: magenta: Z1 = Z2; royal blue: Z1,2 = Zspec; cyan: Z1,2 = Zspec ±σZspec [PITH_FULL_…

**Figure 12.** Figure 12: Mass estimations for the primary for different cases of the figure of merit, including their uncertainties. The color coding is the same as in [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]

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

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, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

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write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

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