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Advancing accuracy in age determinations of old-disk stars using an oscillating red giant in an eclipsing binary

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Pith's one-line read This paper shows that the mass of a 10-billion-year-old red giant, measured dynamically from its eclipsing binary orbit, agrees within 1.4% with the mass inferred from its pulsation frequencies, validating asteroseismic ages for the Milky…

desk verdict A solid, carefully quantified benchmark for asteroseismic masses in old low-mass giants, with an honest but unresolved RV residual that argues for a slightly more conservative dynamical mass uncertainty. read the letter →

arxiv 2504.17853 v1 pith:KS43PJWF submitted 2025-04-24 astro-ph.SR astro-ph.GA

J. S. Thomsen , A. Miglio , K. Brogaard , J. Montalbán , M. Tailo , W. E. van Rossem , G. Casali , D. Jones
show 21 more authors
T. Arentoft L. Casagrande D. Sebastian G. Buldgen A. Triaud M. Matteuzzi A. Stokholm M. N. Lund B. Mosser P. F. L. Maxted J. Southworth J. T. Gadeberg N. Koivisto Z. Gray V. Pinter K. Matilainen A. A. Djupvik J. Jessen-Hansen F. Grundahl D. Slumstrup S. Frandsen
This is my paper · ORCID
classification astro-ph.SRastro-ph.GA
keywords asteroseismologyeclipsingbinaryredgiantbranchstellarmassdeterminationagesMilkyWaythickdiskKIC10001167solar-likeoscillations
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 sets out to test whether asteroseismology can weigh the oldest stars accurately, not just precisely. It does this with KIC 10001167, an eclipsing binary in the Milky Way's thick disk whose red giant shows solar-like oscillations; it is the only known thick-disk system with data good enough for a 2%-level test. From the binary orbit the authors obtain a model-independent red-giant mass of $0.9337\pm0.0077\,M_\odot$, and from the pulsation frequencies a seismic mass of $0.947\pm0.015\pm0.009\,M_\odot$. The two agree within 1.4%, so the asteroseismic mass scale, and the roughly 10 Gyr age built on it, appears accurate at the percent level. If that holds, asteroseismology can be used to date the Milky Way's early assembly and to train age estimates for millions of other stars.

What carries the argument

The load-bearing object is the detached eclipsing binary KIC 10001167: a red giant and a faint main-sequence companion on a 120-day eccentric orbit, observed for four years by space photometry and followed up with 45 high-resolution spectra. The machinery is two-sided. On the dynamical side, combined analysis of the eclipses and the two radial-velocity curves (semi-amplitudes $K_{\rm RG}=24.983$ km/s, $K_{\rm MS}=27.81$ km/s) pins the masses through Kepler's laws; the red-giant mass scales roughly as $K_{\rm MS}(K_{\rm RG}+K_{\rm MS})^2/\sin^3 i$. On the asteroseismic side, individual radial-mode frequencies are fitted with Bayesian stellar-modelling codes, applying a two-term surface correction, to yield mass, radius, and age. The argument is carried by the agreement between a model-independent dynamical mass and a model-dependent seismic mass; because age depends on mass as roughly $M^{-3}$, a 1.4% mass agreement translates into a several-percent age check.

What would settle it

Measure the companion's orbital semi-amplitude with a method that does not depend on deblending the two spectra, for example astrometric photocenter motion or high-signal-to-noise infrared spectroscopy of the companion alone. If a clean measurement moved $K_{\rm MS}$ outside $27.81\pm0.11$ km/s by more than about 0.14 km/s, the dynamical mass would shift by roughly 1% and the 1.4% agreement with the seismic mass would break; conversely, confirming the paper's independent cross-correlation value of $28.00\pm0.12$ km/s would tighten the agreement still further.

Watch

Extended reading notes

Core claim

Working from 45 new high-resolution spectra and four years of space-based photometry, the paper measures the double-lined orbit of KIC 10001167 and derives a dynamical mass for the red giant of $0.9337\pm0.0077\,M_\odot$ (0.8%), independent of stellar models. It then infers the mass from the star's individual radial oscillation modes using forward modelling with stellar grids, obtaining $0.947\pm0.015\pm0.009\,M_\odot$ (1.6%). The two determinations agree within 1.4% (0.8$\sigma$), and the corresponding ages, $10.33\pm0.48\pm0.38$ Gyr from the dynamical mass and $9.68\pm0.64\pm0.56$ Gyr from seismology, agree within 1$\sigma$. The authors conclude that detailed modelling of individual oscillation frequencies delivers masses, and therefore ages, for old low-mass red giants that are not only precise but accurate, and that KIC 10001167 is the first thick-disk benchmark capable of demonstrating this at the 2% level.

Load-bearing premise

The comparison rests on the measured Doppler semi-amplitude of the faint companion, whose light is only about 1.8% of the system's total; a small systematic error in that measurement would shift the dynamical mass by roughly twice the relative error, and the claimed 1.4% agreement would not survive a bias of about 0.7%.

Editorial extensions

If this is right

  • If the 1.4% mass agreement holds, asteroseismic masses from individual mode frequencies are accurate to about 1–2% for old, low-mass red giants, not just precise to that level.
  • The seismic age of $9.68\pm0.64\pm0.56$ Gyr and the dynamical age of $10.33\pm0.48\pm0.38$ Gyr agree within 1$\sigma$, so percent-level mass accuracy propagates into the age scale for roughly 10 Gyr-old thick-disk stars.
  • KIC 10001167 becomes the first thick-disk benchmark where a model-independent 1% mass and a seismic mass better than 2% coexist, anchoring the age scale used to reconstruct the Milky Way's early assembly.
  • Asteroseismically calibrated masses can serve as a training set for data-driven age inference applied to millions of stars, extending precise ages far beyond the seismic sample.
  • Future eclipsing binaries identified by space-based photometric surveys and by astrometric binary orbits can enlarge this calibration sample to other metallicities and Galactic populations.

Reading between the lines

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

  • If the mass agreement generalizes to other old low-mass giants, the dominant remaining uncertainty in asteroseismic ages will shift from mass to the stellar-model input physics (helium, mixing, mass loss), so the next calibration targets should be binaries spanning different metallicities and masses.
  • The radius difference that remains after the mass agreement, with the photometric radius falling between the seismic and dynamical values, makes KIC 10001167 a testbed for limb-darkening and surface-correction systematics; a future astrometric radius at the 0.5% level could separate those explanations.
  • A longer radial-velocity baseline could reveal whether the residual signal in the red giant's velocities is a circumbinary companion; if so, the system would become a rare combined test of asteroseismology and three-body dynamics.
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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 / 4 minor

Summary. The paper presents a combined eclipsing-binary and asteroseismic analysis of KIC 10001167, an old, high-[alpha/Fe] thick-disk system hosting an oscillating red giant. Using Kepler photometry, 45 FIES radial-velocity measurements, two independent binary-modeling codes (JKTEBOP and PHOEBE 2), infrared flux method photometry, Gaia astrometry, and Bayesian stellar modeling with CLÉS and MESA grids, the authors derive a dynamical red-giant mass of 0.9337 ± 0.0077 Msun (0.8%) and an asteroseismic mass of 0.947 ± 0.015 (stat) ± 0.009 (syst) Msun, claiming agreement within 1.4%. They also obtain a dynamical radius of 13.03 ± 0.12 R_sun and an asteroseismic radius of 12.748 ± 0.068 ± 0.055 R_sun, a 2.1-sigma difference they acknowledge and partially attribute to unquantified systematics. The inferred ages are 10.33 ± 0.48 ± 0.38 Gyr from dynamical constraints and 9.68 ± 0.64 ± 0.56 Gyr from asteroseismic constraints. The central claim is that this agreement validates asteroseismic mass and age determinations for old low-mass red giants at the roughly 1-2% accuracy level, with implications for Galactic archaeology.

Significance. If the claimed agreement is robust, this is a valuable benchmark: KIC 10001167 is currently the only old thick-disk eclipsing binary with a red giant whose mass can be measured both dynamically and asteroseismically at percent-level precision. The analysis is unusually thorough: two independent binary codes agree to 0.4 sigma, uncertainties are estimated with bootstrap or Monte Carlo methods, and many potential systematics (limb darkening, third light, light travel time, tidal effects, mass loss, choice of stellar grids, frequency extraction pipelines) are explicitly investigated. The comparison is genuinely non-circular: the dynamical mass is derived from eclipse timing and radial velocities, while the asteroseismic mass comes from fitting individual-mode frequencies plus photospheric constraints. These strengths are substantial. However, the headline accuracy claim is sensitive to the reliability of the faint main-sequence semi-amplitude K_MS and to an unmodeled residual signal in the red-giant radial velocities, as detailed below.

major comments (3)
  1. [Section 3.2, Table D.1, Appendix B] The dynamical mass anchor is set by K_MS, and the two independent determinations of this quantity differ by 0.19 km/s: 27.81 ± 0.11 km/s from the broadening-function analysis and 28.00 ± 0.12 km/s from the CCF analysis in Table B.1. Since M_RG scales approximately as K_MS (K_RG + K_MS)^2 / sin^3 i, this 0.7% difference changes the dynamical mass by roughly 1.4%, which is exactly the size of the claimed mass agreement. The argument that the difference is statistical (1.6 sigma) is not by itself sufficient for an accuracy claim at the percent level. Please either propagate the CCF value through a full binary fit and quote the resulting mass, or add a systematic uncertainty on K_MS of at least this magnitude to the quoted dynamical mass. The manuscript already contains the information needed for this test, and it would directly settle whether the 1.4% agreement is robust or partly a consequence of the adopted K_MS value.
  2. [Appendix B] The radial velocities of the red giant show a clear residual signal after subtracting the two-body Keplerian solution, with short-term variation and a possible trend, and the paper states that a longer baseline is necessary to identify its origin. An unrecognized circumbinary companion, activity, or line-profile variation could bias the recovered K_RG and the shared orbital elements (period, eccentricity, argument of periastron), and hence the derived masses. Adding a 91 m/s jitter term absorbs the excess scatter but does not demonstrate that the orbital parameters are unbiased. Please quantify the sensitivity of the derived masses to this residual signal, for example by adding a linear trend or a sinusoid to the RV model and reporting the shift in K_RG, K_MS, and the resulting mass. Without such a test, the quoted 0.8% dynamical mass uncertainty may underestimate the true systematic error, and the 1.4% agreement with the asteroseismic mass is not yet demonstrated at the claimed accuracy level.
  3. [Section 3.3, Table 1] The asteroseismic radius (12.748 ± 0.068 ± 0.055 R_sun) is 2.1 sigma smaller than the dynamical radius (13.03 ± 0.12 ± 0.09 R_sun). The paper acknowledges this discrepancy but does not fold it into the systematic budget of the mass comparison. Since the radius mismatch indicates that at least one of the two analyses carries a systematic error larger than its quoted uncertainty, the conclusion that asteroseismic masses of old low-mass RGB stars are accurate to 1-2% needs either an expanded systematic budget that incorporates this tension or a quantitative argument that the radius discrepancy cannot affect the inferred mass. As written, the radius tension leaves the headline accuracy claim less secure than the 1.4% mass agreement alone suggests.
minor comments (4)
  1. [Section 2.6] The text refers to "KIC1000167" in one place; this appears to be a typo for KIC 10001167.
  2. [Section 2.7, Eq. (1)] The phrase "a cubica3" should read "a cubic term a_3" for clarity.
  3. [Table D.1] The PHOEBE 2 effective temperature of the red giant is listed as "~4804+40-29" while the text explains that Teff,RG is poorly constrained because the boosting coefficient is uncoupled; the table entry should be flagged accordingly so that readers do not mistake it for a measured constraint.
  4. [Appendix B] The sentence in Appendix B stating that the CCF-based K_MS of 28.00 km/s is "1.6 sigma higher" would be more useful if accompanied by the correlation between K_MS and the other orbital parameters, since a single-parameter comparison does not capture the full covariance.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: dynamical and asteroseismic masses are inferred from independent data sets, and the model grids used are external inputs with stated physics.

full rationale

The paper's central comparison is between a dynamical mass from eclipse photometry and radial velocities (Sect. 2.3, Table D.1: M_RG = 0.9337 +/- 0.0078 M_sun) and an asteroseismic mass from fitting individual mode frequencies with AIMS (Sect. 3.3: M_sis = 0.947 +/- 0.015 M_sun). The reference asteroseismic fit (Sect. 2.7) uses six radial-mode frequencies, nu_max, and APOGEE DR17 Teff and metallicity as constraints; it does not use the dynamical mass or radius. The stellar model grids (CLES from Montalban et al. 2021 and the MESA grid of Tailo et al., in prep) are precomputed model sets with specified input physics, not quantities fitted to the target comparison. The surface correction of Ball & Gizon (2014) has two free parameters derived in the fit, but these are not defined in terms of the target mass and do not encode the dynamical result. The age inference that adopts the dynamical mass and radius as constraints is presented separately and is not used to produce the asteroseismic mass that is being tested. The residual RV signal discussed in Appendix B and the 1.6-sigma difference between BF and CCF determinations of K_MS are accuracy/systematic concerns for the dynamical anchor, but they are not cases where a prediction reduces by construction to a fitted input or to a self-citation. No circular step can be exhibited from the paper's own equations or fitting setup.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The mass comparison is an independent check, so the ledger contains no circular drivers. The free parameters listed are the ordinary fitted parameters of the binary and asteroseismic analyses; no ad hoc entities or unexplained normalization constants are introduced. More than half the axioms are standard practices of the field, each tested in appendices where feasible.

free parameters (8)
  • Surface correction coefficients a_-1 and a_3 (Ball & Gizon 2014, Eq. 1) = Not quoted; fitted by AIMS in each run.
    Two free parameters in the two-term surface correction applied to theoretical mode frequencies; they absorb near-surface modeling uncertainties and are central to the asteroseismic mass inference.
  • Stellar mass, initial metal fraction Z, and age = M = 0.947 ± 0.015 (stat) ± 0.009 (syst) M_sun; Z and age quoted only via posteriors.
    Sampled parameters in AIMS; these are the inference targets but are fitted to the observed frequencies, nu_max, Teff, and [Fe/H].
  • Initial helium fraction Y = Not quoted; tied to an enrichment law in the reference CLÉS fit, free in one MESA test.
    In the reference fit Y follows an assumed enrichment relation; one systematic run samples Y freely with a lower bound at the primordial value.
  • Radial-velocity jitter for the red giant = 91 m/s
    Fixed from the best-fit JKTEBOP RG residuals and added in quadrature to RV uncertainties to account for correlated noise (Appendix A).
  • Limb darkening coefficient h1 (power-2 law) for the red giant = 0.669 +0.029 -0.030
    Fitted in JKTEBOP; h2 fixed from Claret & Southworth (2022). Appendix D.2 shows the RG radius changes by at most 0.3% across prescriptions.
  • Adopted reddening E(B-V) = 0.0350 ± 0.0105
    Chosen as a conservative compromise among three dust maps; used in the IRFM effective temperature and radius, but does not directly affect the mass comparison.
  • Main-sequence RV semi-amplitude K_MS = 27.81 ± 0.11 km/s
    Fitted to 45 FIES RVs; dominates the dynamical mass error budget. A CCF-based method gives 28.00 ± 0.12 km/s (Appendix B), a 1.6 sigma difference.
  • Scaling-relation correction factor f_Delta_nu = 0.95863
    Interpolated from Rodrigues et al. (2017) for the Appendix G.5 scaling-relation masses; not used in the central individual-frequency inference.
assumptions (7)
  • domain assumption Stellar structure and evolution models (CLÉS and MESA) with standard input physics are reliable for RGB stars of this mass, metallicity, and age.
    The asteroseismic inference compares observed frequencies to these models; errors in opacities, equation of state, or convection would bias the inferred mass. Input physics follows Miglio et al. (2021a) and solar-calibrated mixing length.
  • domain assumption The red giant is on the first ascent red giant branch, not in the core-helium-burning clump.
    Supported by the absence of detectable mixed dipole modes, synthetic power spectra comparisons, the unphysical post-RGB fit, and the binary survival argument (Appendix H).
  • domain assumption Mass loss on the RGB up to the current luminosity is negligible.
    The models include no mass loss; Reimers-prescription estimates give 0.6-1.8% mass loss for eta=0.2-0.6, quoted as a systematic comparable to the adopted age uncertainty (Appendix J).
  • domain assumption Tidal interaction with the companion has not significantly perturbed the red giant's internal structure or seismic properties.
    The tidal circularization parameter is below the critical value of Verbunt & Phinney (1995), and no significant apsidal motion is detected (Appendix I).
  • domain assumption The two-term Ball & Gizon surface correction adequately represents the systematic frequency offset between observed and model modes.
    The correction includes a cubic and inverse term; the mean-density inversion in Appendix G.4 shows no specific disagreement, but the form itself is assumed.
  • domain assumption There is no significant third light or background contamination in the photometry.
    Target pixel files show no nearby sources below G=17, and an injected third star is undetectable below a 0.5% luminosity ratio (Appendices D.1 and E).
  • domain assumption The Gaia parallax zero-point correction, the adopted reddening, and the astrometric treatment of the binary are correct within the quoted uncertainties.
    Used for the IRFM radius and luminosity, and for the kinematic membership classification, not for the mass comparison.

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Pith. "Pith review of Advancing accuracy in age determinations of old-disk stars using an oscillating red giant in an eclipsing binary." pith.science (2026). https://pith.science/paper/KS43PJWF

@misc{pith2026250417853,
  author       = {Pith},
  title        = {Pith review of: Advancing accuracy in age determinations of old-disk stars using an oscillating red giant in an eclipsing binary},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KS43PJWF}},
  note         = {Machine review of arXiv:2504.17853}
}
abstract

The study of resonant oscillation modes in low-mass red giant branch stars enables their ages to be inferred with exceptional ($\sim$10%) precision, unlocking the possibility to reconstruct the temporal evolution of the Milky Way at early cosmic times. Ensuring the accuracy of such a precise age scale is a fundamental yet difficult challenge. Since the age of red giant branch stars primarily hinges on their mass, an independent mass determination for an oscillating red giant star provides the means for such assessment. We analyze the old eclipsing binary KIC10001167, which hosts an oscillating red giant branch star and is a member of the thick disk of the Milky Way. Of the known red giants in eclipsing binaries, this is the only member of the thick disk that has asteroseismic signal of high enough quality to test the seismic mass inference at the 2% level. We measure the binary orbit and obtain fundamental stellar parameters through combined analysis of light curve eclipses and radial velocities, and perform a detailed asteroseismic, photospheric, and Galactic kinematic characterization of the red giant and binary system. We show that the dynamically determined mass $0.9337\pm0.0077 \rm\ M_{\odot}$ (0.8%) of this 10 Gyr-old star agrees within 1.4% with the mass inferred from detailed modelling of individual pulsation mode frequencies (1.6%). This is now the only thick disk stellar system, hosting a red giant, where the mass has been determined both asteroseismically with better than 2% precision, and through a model-independent method at 1% precision, and we hereby affirm the potential of asteroseismology to define an accurate age scale for ancient stars to trace the Milky Way assembly history.

Figures

Figures reproduced from arXiv: 2504.17853 by the authors.

Figure 1
Figure 1. α-enhancement level vs. iron-abundance from APOGEE DR17, for stars with 1.5 < log g < 3, with KIC 10001167 highlighted. 3. Results In this section we summarize the analysis results for KIC 10001167. 3.1. Spectroscopic, photometric, and kinematic analysis Based on the photospheric chemical composition and Milky Way kinematics of KIC 10001167, Montalbán et al. (2021) classified it as a member of the Milky Way’s in-sit… view at source ↗
Figure 3
Figure 3. Top: Frequency-power spectrum divided by the granulation background, both in original (light) and uniformly smoothed (dark, window=0.15µHz). Vertical lines highlight the observed radial (ℓ=0), dipole (ℓ=1) and quadrupole (ℓ=2) modes. Middle: Échelle diagram, with the axes flipped for illustration, showing observed radial ℓ = 0 and quadrupole ℓ = 2 frequencies, and best-fit frequencies from our reference radial mode … view at source ↗
Figure 4
Figure 4. Top: Hertzsprung-Russell diagram with luminosity of RG and MS from eclipsing binary radius and IRFM temperature (this work). Included is two isochrones calculated from the MESA grid of stellar models used in this paper. Also shown are eclipsing binary measure￾ments from Gaulme et al. (2016), and asteroseismic inference of the RG from Montalbán et al. (2021). Bottom: The mass and radius of the same sources, along wit… view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: illustrates the comparison between mass, radius and age for our measurements and the literature. We find that our as￾teroseismic mass measurements based on detailed seismic mod￾elling agree with the dynamical mass to a level of 1.4%, which corresponds to 0.8σ, or 0.3σ …

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Pith tools

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