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Asteroseismology of HD 23734, HD 68703, and HD 73345 using K2-TESS Space-based Photometry and High-resolution Spectroscopy

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Three stars once reported as non-pulsating are δ Scuti pulsators, and their radial overtone orders are identified from TESS photometry.

desk verdict Solid photometry and abundance work undercut by a radial-mode identification that contradicts the paper's own adopted Δν. read the letter →

arxiv 2508.20680 v1 pith:IIGR2KOK submitted 2025-08-28 astro-ph.SR

Santosh Joshi , Athul Dileep , Eugene Semenko , Mrinmoy Sarkar , Otto Trust , Peter De Cat , Patricia Lampens , Marc-Antoine Dupret
show 9 more authors
Surath C. Ghosh David Mkrtichian Mathijs Vanrespaille Sugyan Parida Abhay Pratap Yadav Pramod Kumar S. P. P. Goswami Muhammed Riyas Drisya Karinkuzhi
This is my paper · ORCID
classification astro-ph.SR
keywords asteroseismologyδScutistarschemicallypeculiarstars:oscillationsradialmodeidentificationTESSphotometryK2echellediagram
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 re-examines three A/F-type stars — HD 23734, HD 68703, and HD 73345 — that a ground-based survey had flagged as chemically peculiar candidates and reported as photometrically quiet. Combining K2 and TESS space photometry with new high-resolution spectra, the authors argue that all three are instead chemically normal δ Scuti pulsators, with both rotational modulation and multiple pulsation frequencies present in the same light curves. The central result is a radial mode identification for each star: overtone orders n=3 and 4 for HD 23734, n=1, 3, and 4 for HD 68703, and n=3, 4, and 5 for HD 73345, from which masses, ages, radii, and large frequency separations are derived. A steady radial-velocity drift in HD 73345 is read as evidence of a long-period binary companion. If the identifications hold, three 'quiet' stars become calibrated asteroseismic targets whose seismic ages can be weighed against cluster and evolutionary-track ages.

What carries the argument

The device that carries the argument is the échelle-diagram-plus-seismic-model pipeline. Observed TESS frequencies are folded modulo a large frequency separation Δν, estimated from the star's mean density through Δν ∝ ρ̄^0.46, so that the asymptotic relation ν_{n,ℓ} ≈ Δν(n + ℓ/2 + ε) places radial modes on a recognizable vertical ridge. A working hypothesis fixes the highest-amplitude frequency as a radial mode of an arbitrary order n; CLÉS evolutionary tracks and OSC radial-mode frequencies are then matched to it by minimizing a seismic χ² (with observed-frequency uncertainty taken as 0.1 d⁻¹). The chosen orders are checked twice over: Petersen-diagram frequency ratios and pulsation constan

What would settle it

Time-resolved, high-resolution spectra of HD 68703 that resolve the moving bumps and phase behaviour of its line-profile variations would directly measure the spherical degree ℓ of its strongest modes: a clean ℓ=0 signature at the frequencies called radial would confirm the identifications, while a match to ℓ=1 or ℓ=2 patterns would refute them. For HD 73345, measuring a full orbital radial-velocity cycle would test the binary interpretation that the few-epoch drift currently rests on.

Watch

Extended reading notes

Core claim

The paper's central claim is that the strongest pulsation frequencies in the TESS light curves are radial pressure modes of specific overtone orders in each of the three stars. Échelle diagrams from separations Δν = 6.96, 3.25, and 5.20 d⁻¹ show radial (ℓ=0) ridges; CLÉS models with OSC adiabatic frequencies pick the radial order n via a seismic χ²; Petersen ratios and pulsation constants Q line up. The adopted orders: n=3 and 4 for HD 23734, n=1, 3, and 4 for HD 68703, and n=3, 4, and 5 for HD 73345, with dominant peaks non-radial in the first two stars and radial in HD 68703. Spectroscopy shows no chemically peculiar abundance anomalies: all three are normal A/F stars in the δ Scuti instab

Load-bearing premise

Everything rests on the working hypothesis that the dominant pulsation frequency is a radial mode in evolved main-sequence stars but a non-radial mode in less evolved ones; if a star lands on the wrong side of that divide, the radial orders and the masses, ages, and radii derived from them would be wrong.

Editorial extensions

If this is right

  • All three stars join the δ Scuti class with known radial overtones, so the earlier ground-based null detections are explained as sensitivity limits of the survey rather than true quiescence.
  • Each star gets a set of seismic parameters from the preferred model — masses of about 1.7, 2.0, and 1.9 M☉ and ages of 0.33, 1.29, and 0.86 Gyr for HD 23734, HD 68703, and HD 73345 — ready to be compared with independent evolutionary and cluster ages.
  • HD 68703, whose line-profile variability is strong, becomes a natural target for time-series spectroscopy aimed at direct non-radial mode detection; its radial modes n=1, 3, and 4 are the unambiguous part of its pulsation spectrum.
  • For HD 73345, the Praesepe cluster age (759 Myr) and the seismic age (863 Myr) can be used together; if the binary interpretation is right, its luminosity is slightly overestimated and its evolutionary position will shift once the companion's light is accounted for.
  • The survey-level conclusion: other chemically peculiar candidates previously dismissed as non-pulsators from the ground deserve re-observation with space photometry of the kind used here.

Reading between the lines

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

  • If the highest-amplitude-is-radial hypothesis holds for these three, the same shortcut could be applied to other A/F stars with one or two dominant peaks, turning sparse TESS frequency sets into rough mass and age estimates without a full mode identification — a cheap way to grow the sample of seismically calibrated δ Scuti stars.
  • The detection of rotational modulation in stars shown to be chemically normal hints that rotational signals in δ Scuti light curves are not always tied to chemical spots; star-spot or surface-convection interpretations may apply to normal rotators, which could change how rotational frequencies are separated from pulsation frequencies in similar surveys.
  • The paper proposes follow-up spectroscopy mainly for HD 68703, but the same line-profile technique applied to HD 23734 and HD 73345 would test the tacit assumption that their strongest modes are also radial; verifying ℓ=0 for even one of the pair would validate the methodology used for all three.
  • For HD 73345, a complete orbital solution would turn the single-star seismic model into a binary-star test case: with the companion's mass and light contribution known, the luminosity correction could be computed and the seismic age revised, potentially reconciling the star with the 1σ box its current model sits outside.
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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 / 5 minor

Summary. The paper presents a combined K2/TESS photometric and high-resolution spectroscopic study of three A/F-type stars, HD 23734, HD 68703, and HD 73345. Frequency analysis yields 64, 38, and 26 detected frequencies, respectively, with evidence for rotational modulation and δ Scuti-type pulsation. Spectroscopic parameter and abundance analysis indicates that the three stars are chemically normal, and radial-velocity monitoring suggests that HD 73345 may be a long-period binary. The central asteroseismic claim is that specific TESS frequencies are radial modes of orders n=3 and 4 (HD 23734), n=1, 3, and 4 (HD 68703), and n=3, 4, and 5 (HD 73345), based on échelle diagrams, seismic χ² fitting, Petersen ratios, and Q values. The photometric and spectroscopic characterisation is generally sound, but the radial-mode identification is not internally consistent and needs substantial reworking.

Significance. If the radial-mode identifications are correct, the paper would provide seismic constraints on three δ Scuti stars, including a newly identified pulsator, and contribute to the Nainital-Cape survey follow-up programme. The study has genuine strengths: explicit SNR thresholds for frequency detection (5.2 for TESS, 5.7 for K2), combined multi-sector and multi-mission datasets, detailed abundance analysis, and a clearly presented use of the dynamic échelle method. However, the mode-identification claim is the load-bearing component of the asteroseismic parameters, and the present analysis contains internal inconsistencies (detailed below) that must be resolved before the central claim can be accepted. The atmospheric and rotational characterisation of the three stars is a useful independent contribution.

major comments (3)
  1. [§5.1, Fig. 7 and Tables B1/B3] The claimed consecutive radial modes are not consistent with the adopted large separation used to construct the échelle diagrams. For HD 23734, Fig. 7 adopts Δν = 6.96 d⁻¹, but the two claimed consecutive radial modes, fT7(n=3) = 32.93878 d⁻¹ and fT4(n=4) = 38.94782 d⁻¹, are separated by 6.009 d⁻¹, not 6.96 d⁻¹. In the échelle diagram modulo 6.96 d⁻¹ these two frequencies fall at different fractional positions (≈5.10 and ≈4.15), so they do not define a single ℓ=0 ridge. For HD 73345, the adopted Δν = 5.20 d⁻¹ is inconsistent with the spacings of the claimed n=3, 4, 5 modes: fT12=24.7246, fT3=29.50692, and fT15=34.3951 d⁻¹ give spacings of 4.782 and 4.888 d⁻¹. These are not small discrepancies (≈15% and ≈6–8%), and they directly affect the mode identification. The authors should either derive Δν self-consistently from the identified radial pairs and show that the échelle ridges align, or
  2. [§5.2, Eq. (3)] The seismic χ² minimization is applied to one observed frequency at a time, with the radial order n and the stellar model parameters as free choices. This mode-by-mode approach does not require a single model to reproduce all claimed radial modes simultaneously, and with 26–64 detected frequencies, accidental agreement between a model frequency and some observed peak is plausible. The statement that the models 'align closely' is therefore not an independent confirmation. Moreover, the working hypothesis in §5.2 — that the highest-amplitude frequency is radial for evolved main-sequence stars and non-radial for less evolved, higher-surface-gravity stars — is ad hoc and is not tested against any independent diagnostic. Since the same observed frequencies are used both to choose n and to validate the fit, the mode identification has a circular component. Please provide a simultaneous fit of
  3. [§5.3–5.4, Fig. 8 and Tables B1–B3] The Petersen-ratio and Q-value checks are presented as confirmation of the mode identification, but they use the same mode labels and the same theoretical models that are under test, so they do not provide an independent validation. In addition, the quoted Q ranges are too broad to distinguish high overtones for these stars. For example, in Table B3 the mode labelled F3 for HD 73345 has Q = 0.017 ± 0.002, which falls in the stated Q < 0.018 'third-overtone' range rather than the second-overtone range (0.018–0.021), and F5 = 0.012 ± 0.002 is compatible with third or fourth overtone. The claimed agreement needs to be re-evaluated with a self-consistent Δν and, ideally, with a mode-identification method that is not built on the same model frequencies (e.g., amplitude ratios or multi-colour photometry if available).
minor comments (5)
  1. [Table 6] The 'Seismology' column entries for Δν appear to be the values adopted for the dynamic échelle diagrams rather than values derived directly from the best-fitting seismic models. Please clarify the provenance of these numbers.
  2. [Notation throughout] The use of 'F3', 'F4', etc. in Tables B1–B3 and the phrase 'second and third overtones' in §5.2 is inconsistent with the radial order n used in the abstract and Fig. 7. Please use a single convention and define it clearly.
  3. [Fig. 7 caption] The open green circles are described as radial modes predicted by seismic models, but the text does not explain how these predictions are selected or what their uncertainties are. A legend and a short description of the model parameters would help.
  4. [Appendix B] For HD 73345, many K2 frequencies are listed as '2Nyq - fK', presumably because they are aliases of higher-frequency TESS peaks. The table would be clearer if the alias relation were stated explicitly in a footnote.
  5. [Appendices C and A6] There are a number of typographical errors (e.g., 'All thee spectra' in Fig. C1, 'sectxor' in Fig. A6, and incorrect use of 'e' in several places). A careful copy-edit is needed.

Circularity Check

2 steps flagged · score 5.0 of 10

Partial circularity: radial-mode 'predictions' are fits to the very frequencies they are said to validate, and the echelle Δν is interactively adjusted rather than independently predicted.

  1. fitted input called prediction [Section 5.2, Eq. (3); Fig. 7 caption; Table 6]
    "For each model, we computed the radial mode frequencies (ℓ=0) ... considering various values of the radial overtone number n associated with ν_radialmax. The most likely n value was determined by minimizing the seismic-χ2, following the formulation of Murphy et al. (2021): χ2 = ((ft − fo)/σfo)^2 ... The identified radial modes that align closely with the models are the second and third overtones for HD 23734; the fundamental, second, and third overtones for HD 68703; and the second, third, and fourth overtones for HD 73345."

    Equation (3) targets each observed frequency fo of the candidate radial mode. The model and radial order n are selected by minimizing that χ2, so the resulting model frequencies ft are made to agree with fo by construction. Calling these same model frequencies 'radial modes predicted by seismic models' (Fig. 7) and using the close match as evidence for the mode identification is circular: the 'prediction' is the fitted input. The identification is not independently tested; the same fo that fixed n is then quoted as the observed radial mode. (The internal inconsistency with the adopted Δν, e.g. 38.94782−32.93878=6.009 d−1 vs Δν=6.96 d−1 for HD 23734, further shows the fit is not a self-consistent prediction.)

  2. fitted input called prediction [Section 5.1, Fig. 7; Section 5.4]
    "To obtain an initial estimate of Δν, we computed the mean stellar density ... These values were then used to refine Δν through the dynamic echelle interface (Hey & Ball 2022). ... we identified radial (ℓ=0) and possibly non-radial (ℓ=1) ridges for all three samples."

    The large separation Δν is not an independent output: it is adjusted in an interactive echelle tool to make ridges appear, and the same ridges are then used to label observed frequencies as radial overtones. Later sections cite the 'agreement among the Q values, echelle diagrams, seismic models and frequency ratios' as confirmation, but the echelle component of that agreement uses the interactively chosen Δν. For the claimed consecutive radial pairs the spacings do not match the adopted Δν (HD 23734: 6.009 vs 6.96 d−1; HD 73345: 4.78 and 4.89 vs 5.20 d−1), so the ridge identification is a fitted choice rather than an independent verification.

full rationale

The strongest circularity is in Section 5.2: the radial order n is chosen by matching theoretical radial-mode frequencies to observed frequencies through Eq. (3), and then those same model frequencies are presented as 'predicted' radial modes that validate the identification. This is a fitted-input-called-prediction pattern. The echelle Δν is also refined interactively, so the radial ridges are partly constructed from the data rather than independently predicted. On the other hand, the paper does contain substantial non-circular work: Teff, log g, [M/H], vsin i, and abundances come from spectrum synthesis; the evolutionary status uses Gaia parallaxes and CLES tracks; and the HD 73345 cluster age provides an external comparison. There is no load-bearing self-citation or imported uniqueness theorem; citations to the authors' earlier papers are contextual. The central mode-order claim, however, is not self-contained: it depends on the stated working hypothesis and on fits whose agreement is partly imposed by construction. I therefore assign a partial-circularity score of 5, not higher, because the spectroscopic parameters and external data give the analysis independent content, and not lower because the radial-mode 'validation' loop is genuinely circular.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard asteroseismic scaling relations plus several model assumptions: solar metallicity, fixed overshoot, LTE synthesis, and the working hypothesis that the strongest modes are radial. The free parameters are the seismic masses, ages, and refined delta-nu values, all derived from fitting the observed frequencies. The paper introduces no new entities. The most fragile assumptions are the radial-mode working hypothesis and the below-threshold rotation detection, both acknowledged by the authors.

free parameters (3)
  • Seismic stellar mass M/Msun = HD 23734: 1.67+-0.10; HD 68703: 1.96+-0.10; HD 73345: 1.85+-0.10
    Derived from the chi-square fit of CLES+OSC models to the observed radial-mode frequencies (Section 5.2, Table 6). The mass is adjusted with the radial order n to match the frequencies, so it is a fitted parameter.
  • Seismic age = HD 23734: 0.327+-0.010 Gyr; HD 68703: 1.290+-0.200 Gyr; HD 73345: 0.863+-0.100 Gyr
    Output of the same best-fit evolutionary models that match the identified radial modes. Age is not independently measured and depends on the chosen n and the model assumptions.
  • Large frequency separation delta nu = HD 23734: 6.96 d^-1; HD 68703: 3.25 d^-1; HD 73345: 5.20 d^-1
    Initial estimate from mean density using Eq. (2), then refined interactively through the dynamic echelle interface (Section 5.1). The final value is effectively fitted to produce clean ridges, not derived from first principles.
assumptions (6)
  • standard math Asymptotic relation nu_n,l = delta_nu(n + l/2 + epsilon) (Tassoul 1980)
    Used to construct echelle diagrams (Eq. 1). Standard asymptotic p-mode relation, assumed to hold for low-degree, high-order modes.
  • standard math Scaling relation delta_nu/delta_nu_sun = 0.776 (rho/rho_sun)^0.46
    Used to estimate the initial large separation from mean density (Eq. 2). Empirical scaling from Suarez et al. 2014.
  • domain assumption Seismic models assume solar metallicity Z = 0.014 and overshoot alpha_ov = 0.1
    CLES models are computed with these fixed values for all masses (Section 5.2). The paper does not vary metallicity or overshoot, so the derived masses and ages depend on this choice.
  • domain assumption Local Thermodynamic Equilibrium (LTE) for spectrum synthesis
    Abundance analysis uses SME with Atlas9 models in LTE (Section 4.2.2). The paper notes departures from LTE may explain the oxygen anomaly.
  • ad hoc to paper The highest-amplitude frequencies correspond to radial modes in evolved main-sequence stars and to non-radial modes in less evolved, higher-gravity stars
    This is the working hypothesis introduced in Section 5.2 to break the degeneracy in mode assignment. It is not a standard, proven result and directly determines which frequencies are treated as radial modes.
  • ad hoc to paper The HD 23734 frequency at 2.3406 d^-1 with SNR 4.8 is the rotational frequency
    Despite being below the paper's own TESS detection threshold of SNR 5.2, this peak is adopted as the rotational frequency and used in consistency checks (Section 4.2.3).

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Cite this review

Pith. "Pith review of Asteroseismology of HD 23734, HD 68703, and HD 73345 using K2-TESS Space-based Photometry and High-resolution Spectroscopy." pith.science (2026). https://pith.science/paper/IIGR2KOK

@misc{pith2026250820680,
  author       = {Pith},
  title        = {Pith review of: Asteroseismology of HD 23734, HD 68703, and HD 73345 using K2-TESS Space-based Photometry and High-resolution Spectroscopy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IIGR2KOK}},
  note         = {Machine review of arXiv:2508.20680}
}
abstract

In this paper, we present a comprehensive study of three stars, HD 23734, HD 68703, and HD 73345, which were previously observed as chemically peculiar candidates within the Nainital-Cape survey and reported as null results for the pulsational variability. Frequency analyses of \ktwo\ and \tess\ time-series photometric data reveal the co-existence of rotational modulation and pulsation. We use the spectrum synthesis technique to determine fundamental parameters and chemical composition, which shows that all the three stars are likely to be chemically normal. The evolutionary status of the target stars corresponds to the main-sequence phases and places them within the $\delta$ Scuti instability strip of the Hertzsprung-Russell diagram. The line profile variability is observed in all three stars, especially intriguing in HD\,68703 and a typical signature of the non-radial pulsation, demands further detailed examination. Using \tess\ photometry, we identified the radial modes of orders $n$=3 and 4 for HD\,23734, $n$=1, 3, and 4 for HD\,68703, and $n$=3,4 and 5 for HD\,73345. In addition to the presence of pulsation and rotation, HD\,73345 exhibits a steady increase in radial velocity that we interpret as the star being likely to be part of a long-period binary system. Finally, we propose an extended campaign aimed for the in-depth spectroscopic and spectropolarimetric study of selected pulsating stars monitored under the Nainital-Cape survey project.

Figures

Figures reproduced from arXiv: 2508.20680 by the authors.

Figure 1
Figure 1. Top panel: The window function for HD 23734 based on photometric data from K2 (Campaign 4; black) and TESS (Sectors 42, 43, and 44; green). Middle panel: Comparison of frequency spectra derived from K2 and TESS light curves. For visual clarity, the K2 spectrum has been vertically shifted by 1.8 mmag. Red vertical solid lines mark the integer multiples of the K2 Nyquist frequency, while blue dashed lines indicate fre… view at source ↗
Figure 2
Figure 2. Same as [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Same as [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The Hβ (left panel) and Hα (right panel) line regions for the target stars. The spectrographs used to obtained these profiles are listed in the top of each panel. The observed and synthetic profiles are shown with black and red colors, respectively. MNRAS 000, 000–000 …
Figure 5
Figure 5. Figure 5: Relative abundances of elements derived from spectroscopic analysis. The horizontal black dashed line indicates solar abundances, while the vertical grey dashed lines mark the one-to-one correspondence between names of the element and respective atomic numbers. The unc…
Figure 6
Figure 6. Figure 6: Evolutionary tracks for stellar masses ranging from 1.60 M⊙ to 2.00 M⊙, computed for solar metallicity (Z = 0.014) and overshooting parameter αov = 0.1. Dotted lines denote isochrones corresponding to ages of 0.1, 0.5, 0.8, 1.05, 1.17 and 1.4 Gyr. The open symbols repr…
Figure 7
Figure 7. Figure 7: Echelle diagrams of HD 23734 ( ´ left panel), HD 68703 (middle panel ), and HD 73345 (right panel), constructed using their respective large frequency separations of ∆ν = 6.96, 3.25, and 5.20 d−1 (indicated by vertical lines). For clarity, the frequency range is extend…
Figure 8
Figure 8. Figure 8: Petersen diagram for HD 23734 and HD 73345 (left panel) and HD 68703 (right panel ), computed for Z = 0.014 and αov = 0.1. The crosses and circles represent the frequency ratios of the second overtone ( f3) to higher radial overtones for HD 23734 and HD 73345, respecti…

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