Diameters and Temperatures VII: High-angular resolution measurements of Solar-type stars with the CHARA Array

Ashley A. Elliott; Daniel Huber; Eliot Hiegel; Emelly D. Tiburcio; Gail Schaefer; Jeremy Jones; Kaspar von Braun; Michael Ireland; Tabetha S. Boyajian; Timothy R. White

REVIEW 2 major objections 5 minor 17 references

Diameters and Temperatures VII: High-angular resolution measurements of Solar-type stars with the CHARA Array

T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper reports interferometric angular diameters for 27 nearby solar-type stars and combines them with parallaxes and bolometric fluxes to obtain model-independent radii, effective temperatures, and luminosities, claiming typical…

desk verdict Solid, incremental interferometric survey of 27 solar-type stars with careful measurements, but the quoted ~1% radii omit calibrator diameter systematics that could push the true accuracy to ~2%. read the letter →

arxiv 2608.11440 v1 pith:N5A4PAND submitted 2026-08-11 astro-ph.SR astro-ph.EPastro-ph.IM

Tabetha S. Boyajian , Ashley A. Elliott , Emelly D. Tiburcio , Kaspar von Braun , Gail Schaefer , Timothy R. White , Daniel Huber , Michael Ireland

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Jeremy Jones Tyler Ellis Eliot Hiegel

This is my paper · ORCID

classification astro-ph.SRastro-ph.EPastro-ph.IM

keywords stellarangulardiametersopticalinterferometrysolar-typestarseffectivetemperatureradiievolutionmodelsexoplanethostlimbdarkening

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

This paper measures the angular sizes of 27 nearby solar-type stars with long-baseline optical interferometry and turns those diameters, together with parallaxes and bolometric fluxes, into radii, temperatures, and luminosities that do not depend on stellar models. The central claim is that these values reach about 1% accuracy in radius and about 1.5% in effective temperature, making the stars high-precision empirical benchmarks. The authors then compare the measured radii and temperatures with four independent stellar evolutionary grids and find that inferred masses agree to roughly 6% for most stars, while inferred ages scatter much more widely, with four metal-poor stars giving ages older than the Universe in every grid. If right, these results tighten the empirical anchors used to test stellar evolution theory and to characterize stars that host planets.

What carries the argument

The load-bearing mechanism is long-baseline interferometric measurement of stellar angular diameters: visibility data are fit to uniform-disk and limb-darkened disk models, with flux-conserving R-band limb-darkening coefficients, and uncertainties are propagated by Monte Carlo resampling at the calibration-bracket level. Temperatures then follow from the Stefan-Boltzmann relation expressed as $T_{\rm eff}(\mathrm{K}) = 2341 (F_{\rm bol}/\theta_{\rm LD}^2)^{0.25}$, where $F_{\rm bol}$ is the bolometric flux and $\theta_{\rm LD}$ the limb-darkened angular diameter, so the final radii and temperatures are anchored directly to observables rather than to stellar models.

What would settle it

Observe a subset of the same 27 stars with an independent calibration route that does not depend on the catalog calibrators, such as lunar occultation diameters or phase-referenced interferometry, and compare the resulting radii; a systematic offset between the two methods would reveal the calibrator zero-point error.

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Extended reading notes

Core claim

The paper's central discovery is a homogeneous set of model-independent fundamental properties for 27 solar-type dwarfs and mildly evolved subgiants spanning 4830 to 6390 K. For each star, limb-darkened angular diameters from interferometric visibility fits are combined with bolometric fluxes from spectral-energy-distribution fitting and zero-point-corrected Gaia parallaxes, giving radii with typical 1% uncertainties and effective temperatures with typical 1.5% uncertainties. Cross-comparison with four stellar evolutionary model grids shows that mass estimates agree within about 6% for most stars, while age estimates differ far more between grids, especially for metal-poor, alpha-enhanced stars whose model ages can exceed the age of the Universe, and for young and low-mass stars where grid tracks are closely spaced or insensitive to age.

Load-bearing premise

The adopted angular diameters of the calibrator stars are assumed to be accurate and unbiased, so any systematic error in those diameters shifts every measured stellar diameter, radius, and temperature together.

Editorial extensions

If this is right

The 27 stars become model-independent calibration points on the H-R diagram, giving stellar evolution codes fixed empirical targets near the main sequence and subgiant branch.
Exoplanet host stars in the sample get radii and temperatures that can shrink the fractional uncertainties in planet radius and density for their known planets.
The large grid-to-grid age scatter, including unphysical ages for four metal-poor stars, identifies where current evolutionary models need better treatment of abundances, alpha-enhancement, and boundary conditions.
Inferred masses agreeing within about 6% across the four grids supports moderate confidence in model-based mass estimates for solar-type stars, while ages should be treated as plausible ranges rather than precise values.
The two evolved subgiants show that model discrimination is strong on the subgiant branch but weak near the base of the giant branch, where tracks overlap and inferred masses and ages become unreliable.

Reading between the lines

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

If the calibrator zero-point is later revised, all 27 radii shift coherently; the relative ordering of stars is largely preserved, so population-level comparisons are safer than any single absolute radius.
Applying the same pipeline to a volume-limited sample of solar-type stars would turn these benchmarks into a statistical test of the mass-radius relation in the solar neighborhood, which the current target list cannot do by itself.
The authors' planned re-analysis with models that include alpha-enhanced compositions self-consistently is a natural test: if those models bring the four metal-poor stars below 14 Gyr, it would directly confirm that missing alpha-enhancement, not the data, drives the unphysical ages.
A direct comparison of the measured temperatures against asteroseismic temperatures for any stars in the sample that overlap with pulsation surveys would provide an independent check on the 1.5% temperature claim.

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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

Khaled, quick read on the new Boyajian et al. diameters paper. If you work in stellar interferometry or exoplanet host characterization, it's useful. It's the seventh in the series, so the method is established: CHARA/PAVO visibilities, limb-darkened diameters, Gaia parallaxes, PHOENIX SED fluxes, then Stefan-Boltzmann radii and Teff. The new content is the 27-star sample itself — several metal-poor stars, several exoplanet hosts — and a four-grid comparison of inferred masses and ages. The measurements look carefully reduced: Monte Carlo bootstrap with bracket resampling, a prior on limb-darkening, and a 2% systematic added to bolometric fluxes. They also give honest discussion of where models fail: the metal-poor stars get ages older than the Universe, and they say so.

The soft spot is the calibrator diameter zero-point. Table B1 uses JMMC estimated diameters for calibrators, and at the long PAVO baselines a 0.2 mas calibrator has V^2 ~ 0.75, not 1. A 3% error in θ_est changes the calibrator visibility by ~1-2%, which propagates almost one-to-one into the fitted science diameter. The bootstrap you describe resamples the measured visibilities within brackets, so it captures random noise and night-to-night transfer function scatter, but it never draws the calibrator diameter from its error distribution. If the JMMC catalog has a coherent zero-point bias, every one of the 27 radii shifts in the same direction. That means the quoted ~1% radii are optimistic; the true absolute accuracy is more like 1.5-2% unless the calibrator errors average out. This is a fixable caveat, not a reason to reject.

Other notes: the masses and ages from Kiauhoku are presented without propagating the input Teff/L uncertainties; the authors explicitly flag it, so it's fine for their grid-to-grid purpose. The 'model-independent' label is fair for R and Teff, since those do not invoke evolutionary models. The plots and table are clear. I'd accept this paper for peer review, but I would ask the authors to quantify the calibrator diameter systematic, even just a sensitivity test or an added quadrature term. It deserves a referee slot, and it will be a standard reference for these stars.

The calibration issue is a good excuse to bring it to reading group, if you want to see how the field handles transfer-function calibration.

Referee Report

2 major / 5 minor

Summary. The paper presents interferometric angular diameter measurements for 27 nearby solar-type stars obtained with the PAVO beam combiner at the CHARA Array. The authors determine uniform-disk and limb-darkened angular diameters, then combine these with Gaia parallaxes and bolometric fluxes from PHOENIX SED fits to derive stellar radii, effective temperatures, and luminosities, claiming typical uncertainties of ~1% in radius and ~1.5% in effective temperature. They compare the resulting empirical H-R diagram positions with four stellar evolutionary model grids (YREC, MIST, Dartmouth, Garstec) via the Kiauhoku interpolation tool to infer masses and ages and to assess grid-to-grid systematics, including discussions of metal-poor stars, young stars, and subgiants. The central derivation, Eq. (1), is a correct rearrangement of the Stefan-Boltzmann law, and the data analysis pipeline is described in considerable detail.

Significance. If the quoted precision holds, the paper provides a valuable homogeneous set of empirical anchors for solar-type stars, useful for testing stellar evolutionary models and for improving exoplanet host star characterization. The manuscript has notable strengths: a well-documented Monte Carlo uncertainty treatment (bracket bootstrapping, limb-darkening prior, and a 2% systematic on bolometric flux), openly available code (RADPy on GitHub), a sample spanning a range of metallicity and evolutionary states, and a transparent discussion of model grid limitations (e.g., the lack of alpha-enhancement in the grids and edge effects for low-mass stars). The main risk is the unpropagated calibrator angular diameter uncertainty, which is load-bearing for the headline precision claim. The model-comparison section is internally consistent but currently understates the role of measurement uncertainties in the mass and age estimates.

major comments (2)

[§2, Table B1, §3] The RADPy Monte Carlo described in §2 resamples visibilities within calibration brackets and draws the limb-darkening coefficient from a σ=0.02 prior, but it never samples the calibrator angular diameters θ_est listed in Table B1. This matters because at the PAVO long baselines (B≈278 m, λ≈800 nm) a calibrator with θ_est≈0.20 mas has x≈1.06 and V²≈0.75, so the calibrator is not a point source; a 3% error in θ_est changes the calibrator visibility by roughly 1–2% and maps to an ~1% shift in the fitted science θ_LD, comparable to the claimed radius uncertainties in Table 2. The text's statement that the bootstrap empirically includes bracket-to-bracket calibration variability does not capture a coherent scale error, and since all targets are calibrated through the same catalog scale, the quoted ~1% radius and ~1.5% Teff uncertainties are missing a systematic term. Please propagate the θ_est uncertainties through the calibration, or demonstrate explicitly why the adopted calibration is insensitive to them, and revise the uncertainty claims accordingly.
[§4, Table 3] The model-derived masses and ages in Table 3 are quoted to three decimal places, but the σ_Mass and σ_Age columns are purely grid-to-grid scatter; measurement uncertainties in Teff, L, and [Fe/H] are deliberately not propagated. The text states this, but the abstract and Section 4 nevertheless present 'mass and age estimates' and the 'agreement to within ~6%' without a total error budget. Because the input uncertainties are not negligible (e.g., 1.5% in Teff), the quoted fractional offsets should be explicitly labeled as model-systematic only, and the conclusion about mass agreement should be tempered or accompanied by a propagated measurement-error example. This does not invalidate the grid-comparison methodology, but the presentation is currently misleading.

minor comments (5)

[Introduction] The capitalization of 'Section' is inconsistent (e.g., 'In section 4' appears after 'In Section 2' and 'Section 3').
[Appendix C] The captions for Figures C1–C5 are identical; please indicate which stars appear in each figure or state that they are grouped by observing season.
[§2] The paper should briefly justify why linear limb-darkening coefficients in the R band (Claret and Bloemen 2011) are used for PAVO data dispersed over 630–950 nm, and how sensitive the diameters are to this choice.
[Table B2] The 'Bad Calibrators' table lists stars without stating the rejection criterion; a short note on why each star was excluded (e.g., binarity, rapid rotation, or poor visibility fit) would aid reproducibility.
[Table 3] For stars flagged as unreliable or non-convergent (such as HD 22879 and HD 42807), add an explicit symbol in the table itself rather than only in the table notes.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measured radii and effective temperatures are derived from external calibrator diameters, Gaia parallaxes, and photometric bolometric fluxes, while the evolutionary-model comparison is a separate interpretive step.

full rationale

The derivation chain is self-contained and externally anchored. Calibrated visibilities are fit to uniform-disk and limb-darkened angular diameter models using RADPy, with calibrator angular diameters adopted from the external JMMC/Bourgès et al. (2014) catalog (Table B1) and limb-darkening coefficients from Claret and Bloemen (2011). Bolometric fluxes come from PHOENIX SED fits to broadband photometry, with a 2% systematic added in quadrature; radii use zero-point-corrected Gaia parallaxes; effective temperatures are computed from the Stefan-Boltzmann law in Eq. (1). None of these inputs is the claimed output: the JMMC diameters, Gaia parallaxes, PHOENIX atmospheres, and Claret and Bloemen coefficients are all external to this paper, and the mass/age results are obtained by interpolating the measured Teff, L, and [Fe/H] onto the external Kiauhoku model grids (YREC, MIST, Dartmouth, Garstec). The paper does not fit the model grids to the measured quantities; it compares them and reports grid-to-grid scatter as model systematics. Self-citations, such as Boyajian et al. (2012) for the calibration strategy and Elliott (2025) for the RADPy software, are methodological references rather than load-bearing evidence, and the software is publicly available. The potential calibrator-diameter zero-point bias identified by the skeptic is a genuine systematic-error concern for accuracy, but it is not a circularity: the calibrator diameters are not defined in terms of the science-star diameters or temperatures, and a biased calibrator scale would be an external systematic, not a derivation of the result from its own inputs. The paper also explicitly flags known limitations, including unreliable model results for metal-poor stars and the lack of propagated measurement uncertainties in the Kiauhoku interpolation, which further supports the absence of a circular construction.

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

The derived quantities depend on no adjustable parameters fitted to the target data. Limb-darkening coefficients are fixed from external model grids, bolometric fluxes come from SED fits anchored to photometry, and extinction is fixed at zero. These are modeling assumptions, not free parameters tuned to make the result work.

assumptions (7)

standard math Stefan-Boltzmann law
Used in Equation (1) to convert bolometric flux and angular diameter into effective temperature; standard physics.
domain assumption Gaia parallax zero-point corrections are correctly applied
Parallaxes from Lindegren et al. (2021) with zero-point corrections are used in Section 3; if the correction is biased for these stars, radii and luminosities shift.
domain assumption JMMC calibrator angular diameters are accurate and unbiased
Section 2 and Appendix B: calibrator diameters from Bourges et al. (2014) are used to calibrate all visibilities; systematic errors propagate to every science diameter.
domain assumption PHOENIX model SEDs accurately represent stellar photospheres
Section 3: bolometric fluxes are derived from PHOENIX SED fits to broadband photometry; SED model bias would enter temperatures.
domain assumption Claret and Bloemen limb-darkening coefficients apply to this sample
Section 2: the R-band linear limb-darkening coefficient is taken from Claret and Bloemen (2011) with a 0.02 sigma prior; a wrong coefficient shifts limb-darkened diameters slightly.
domain assumption Stellar evolution grids and Kiauhoku interpolation are reliable
Section 4: YREC, MIST, Dartmouth, and Garstec grids are used for mass and age inference; grid errors are the object of study but are not independently certified.
domain assumption Interstellar extinction is negligible for all stars
Section 3 sets A_V = 0 for all targets due to proximity; reddening would bias bolometric flux and temperature estimates, though distances suggest the effect is small.

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Cite this review

Pith. "Pith review of Diameters and Temperatures VII: High-angular resolution measurements of Solar-type stars with the CHARA Array." pith.science (2026). https://pith.science/paper/N5A4PAND

@misc{pith2026260811440,
  author       = {Pith},
  title        = {Pith review of: Diameters and Temperatures VII: High-angular resolution measurements of Solar-type stars with the CHARA Array},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N5A4PAND}},
  note         = {Machine review of arXiv:2608.11440}
}

abstract

We present interferometric measurements of angular diameters for 27 nearby solar-type stars obtained with the Precision Astronomical Visible Observations (PAVO) beam combiner at the CHARA Array. The sample spans a broad range of metallicities, includes several known exoplanet hosts, and covers evolutionary stages from the zero-age main sequence to mildly evolved subgiants. Uniform-disk and limb-darkened angular diameters were measured for each target and combined with bolometric fluxes and Gaia parallaxes to determine precise, model-independent stellar radii, effective temperatures, and luminosities. We achieve typical uncertainties of $\sim1$\% in radius and $\sim1.5$\% in effective temperature. Comparisons with multiple stellar evolutionary model grids yield mass and age estimates and enable assessment of grid-to-grid systematics, highlighting sensitivities to abundances, evolutionary stage, and proximity to grid boundaries. Our results provide empirical benchmarks for testing stellar evolutionary theory, refining surface brightness-color relations, and improving the characterization of exoplanet host stars.

Figures

Figures reproduced from arXiv: 2608.11440 by the authors.

**Figure 1.** — Empirical H-R diagram showing our sample (blue crosses) along with all other stars with precise angular diameter measurements (gray circles; data source: https://www.chara.gsu.edu/science-highlights/stellar-diameters. Arrows point to the two post main-sequence subgiant stars, HD 190228 and HD 202568, discussed in §4. 4. STELLAR MODELS AND DISCUSSION Our sample comprises 27 solar-type dwarfs and mild subgiants with… view at source ↗

**Figure 2.** — Mass (blue circles, left axis) and age (red triangles, right axis) fractional offsets between stellar model grids as a function of mean model mass ( [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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A. A. Michelson and F. G. Pease, ApJ53, 249 (1921). R. H. Hanbury Brown, J. Davis, R. J. W. Lake, and R. J

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[2] [2]

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Stellar Diameters and Temperatures III. Main Sequence A, F, G, & K Stars: Additional high-precision measurements and empirical relations

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work page Pith review arXiv 2012