Pith. sign in

REVIEW 3 major objections 4 minor 3 cited by

Modelling $\delta$ Scuti pulsations: A new grid of p, g, and f modes across pre-main-sequence to post-main-sequence evolution

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Young delta Scuti stars should show f and low-order g modes as readily as the fundamental radial mode, and a universal $p_{n1,\ell 0}$--$\Delta\nu$ relation holds across all evolutionary stages.

desk verdict A substantial, carefully built δ Sct grid with solid scaling relations; the f/g-mode observability claim is real but oversold without non-adiabatic growth rates. read the letter →

arxiv 2507.03561 v5 pith:YIO7YISI submitted 2025-07-04 astro-ph.SR

Anuj Gautam , Simon J. Murphy , Timothy R. Bedding This is my paper
classification astro-ph.SR
keywords asteroseismologydeltaScutistarsstellarpulsationsmodeinertiagmodesfevolutionscalingrelations
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 aims to make delta Scuti stars usable as precision clocks for stellar age-dating by supplying a theoretical grid of 25 million pulsation models running from the pre-main-sequence through the post-main-sequence contraction phase. It claims that f modes and low-order g modes, whose mode inertias are comparable to or lower than that of the fundamental radial mode during the late pre-main sequence and early main sequence, should be observable in these stars. It also establishes that the fundamental radial mode frequency follows $p_{n1,\ell 0} = 3.058\,\Delta\nu + 0.276$ d$^{-1}$ across every evolutionary stage with tight scatter. A sympathetic reader would care because mode identification and age inference for intermediate-mass stars have been limited by grids that omit rotation, higher-degree modes, or the pre-main sequence.

What carries the argument

The load-bearing tool is the grid itself: about 20,000 evolutionary tracks sampled at thousands of ages, with adiabatic oscillation frequencies computed for degrees $\ell=0$ to 3, p modes up to radial order 11, g modes down to $-5$, and f modes, including avoided crossings tracked with the standard p/g/f classification scheme. Rotation is included up to $\Omega/\Omega_{\rm crit}=0.3$ via first-order perturbative corrections for p modes and the traditional approximation of rotation for g modes. Mode inertias computed from the eigenfunctions and normalized to the fundamental radial mode carry the observability claim, while the $p_{n1,\ell 0}$--$\Delta\nu$ fits carry the mode-identification claim.

What would settle it

Compute non-adiabatic growth rates for the f and low-order g modes across the grid: low inertia alone does not guarantee observable amplitude if those modes are linearly damped, so a finding that they are strongly damped inside the instability strip would overturn the observability claim.

Watch

Extended reading notes

Core claim

The central claim is that low-inertia f modes ($\ell=2,3$) and low-order g modes are not theoretical curiosities but should appear in the observed pulsation spectra of young delta Scuti stars. During the late pre-main sequence, near the zero-age main sequence, and through most of the main sequence before avoided crossings begin, these modes have mode inertias comparable to or lower than the fundamental radial mode, so their surface amplitudes should be comparable. The paper further claims that a single linear relation $p_{n1,\ell 0} = 3.058\,\Delta\nu + 0.276$ d$^{-1}$ ($R^2 = 0.996$) links the fundamental radial mode frequency to the large frequency separation across all evolutionary stages, with a rotation-corrected version $p_{n1,\ell 0} = 3.005\,\Delta\nu + 0.509\,\Omega/2\pi + 0.232$ d$^{-1}$. Application to HD 3622 and V624 Tau places these modes at the frequencies of unexplained peaks adjacent to the fundamental radial mode, which the grid explains as f and g modes rather than as a poorly modelled p mode.

Load-bearing premise

The grid assumes that adiabatic, first-order, shellular rotation in the stellar evolution and oscillation codes gives accurate frequencies for stars rotating up to 30 percent of critical speed, an assumption the paper itself notes breaks down once mode coupling becomes significant in post-main-sequence models.

Editorial extensions

If this is right

  • Unexplained peaks just below the fundamental radial mode in young delta Scuti stars can be attributed to $\ell=2,3$ f modes and low-order g modes, preventing misidentification.
  • A measured fundamental radial mode frequency gives $\Delta\nu$ directly through $p_{n1,\ell 0} = 3.058\,\Delta\nu + 0.276$ d$^{-1}$, so echelle diagrams can be built with the correct frequency modulus without trial and error.
  • The $\Delta\nu$--mean-density relation $\Delta\nu/\Delta\nu_\odot = 0.857\,(\bar\rho/\bar\rho_\odot)^{0.507}$ holds with about 1% scatter, so density, and hence age, can be read from the large separation once the scaling factor is known.
  • The grid spans the pre-main sequence, so asteroseismic ages for young delta Scuti stars need no longer depend on cluster membership or empirical calibrations.

Reading between the lines

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

  • If f and low-order g modes are observable, their rotational splittings could probe different interior depths than p modes, because the Ledoux constants for g modes and f modes differ strongly from p modes, offering a new way to constrain internal rotation.
  • The same low-inertia argument suggests those modes should be searched for not only near the ZAMS but in stars up to several hundred Myr old, before avoided crossings start to redistribute mode energy.
  • The small but systematic residuals around the $\Delta\nu$--density relation may encode usable information about metallicity and age, even though the paper recommends full frequency modelling for precision work.
  • Amplitude ratios measured from space photometry could serve as a direct observational test of the predicted inertia ratios, without needing fully non-adiabatic models.
Share X Bluesky LinkedIn Reddit HN

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 large grid of adiabatic stellar pulsation models for delta Scuti stars, computed with MESA and GYRE. The grid covers masses 1.4–2.5 M_sun, metallicities Z = 0.001–0.026, and rotation up to Omega/Omega_crit = 0.3, evolved from the pre-main sequence through the main sequence to the post-MS contraction phase. For each model, adiabatic p, g, and f modes (ell = 0–3) are computed, including avoided crossings. The authors derive scaling relations between Delta nu, mean density, and the fundamental radial mode frequency, and they argue that f and low-order g modes have inertias comparable to or lower than the fundamental radial mode, implying that these modes should be observable in young delta Scuti stars. The grid is publicly available, and the paper includes comparisons to two observed stars, HD 3622 and V624 Tau.

Significance. If the claims hold, this grid is a significant community resource: it is far more extensive than previous delta Scuti grids, includes rotation and a full evolutionary range, and publicly releases models and input files. The validation work is a genuine strength: resolution tests, non-adiabatic frequency corrections below 0.4%, consistency checks with earlier scaling relations, and comparisons to observed echelle diagrams all support the reliability of the computed frequencies. The scaling relation p_n1,l0 = 3.058 Delta nu + 0.276 d^-1, with R^2 = 0.996, is a useful empirical tool for mode identification if its regime of validity is clearly stated. However, the most novel scientific claim beyond the grid itself—that f and low-order g modes should be observable—is not adequately supported by the evidence presented, as it rests on mode inertia alone without non-adiabatic stability or visibility calculations. The paper is therefore valuable but requires strengthening of this central claim before publication.

major comments (3)
  1. [Sec. 3.4 (Eq. 14), Sec. 2.3, Sec. 3.3.2]
  2. [Sec. 3.3.2, Fig. 9]
  3. [Fig. 12, Sec. 3.4]
minor comments (4)
  1. [Sec. 4.2, Eq. (18)]
  2. [Sec. 2.1.2]
  3. [Sec. 2.3.1]
  4. [Sec. 5]

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the scaling relations are openly calibrated fits and the observability claim rests on an explicit, unverified assumption rather than on a disguised input.

full rationale

The paper's central deliverable is a grid of adiabatic pulsation frequencies computed with MESA and GYRE; these are external, independently implemented codes and the grid is made public, so the frequency catalogue is not circular. The Δν–ρ relation (Eq. 16) and the p_n1,l0–Δν relation (Eqs. 18–19) are fits to the grid's own output, but the paper presents them as empirical calibrations, not as first-principles predictions, and compares them with previous independent grids and observations (e.g., fΔν=0.85 from Bedding et al. 2020). The exponent 0.507 is validated against the well-known asymptotic expectation 0.5, which is an external anchor. The f/g-mode observability claim is the only step that could look like a prediction, but it is not circular: E/E_ref is computed directly from GYRE eigenfunctions via Eq. 14, and the paper explicitly states that amplitudes cannot be predicted from adiabatic theory and that the conversion A_surf ∝ sqrt(eta/E) requires 'assuming they have similar driving and damping'. That assumption is openly flagged rather than smuggled in, and the non-adiabatic calculations are deferred in Sec. 2.3. It is an unsupported inference (correctness risk), not a circular derivation. Likewise, the HD 3622 and V624 Tau comparisons use p-mode fits and then compare unassigned peaks with model f/g modes; the paper does not claim the f/g modes were used as fit targets. No self-citation chain is load-bearing: the cited Murphy et al. (2023) and Bedding et al. (2020) grids are independent calibrations for the scaling relations and numerical settings, not inputs that force the paper's conclusions. No uniqueness theorem is invoked. Overall, no step reduces by construction to its own input.

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

The paper introduces no new physical entities. Its free parameters are standard stellar modelling inputs (alpha_MLT, overshooting) and fitted scaling coefficients. The heaviest burden is the combined assumption that adiabatic, 1D, shellular-rotation models capture the relevant pulsation physics across all evolutionary phases.

free parameters (4)
  • alpha_MLT = 1.9
    Mixing-length parameter chosen from prior calibrations, not fitted to the grid. The paper tests +/-0.2 and finds up to 10 percent frequency differences during pre-MS, so it is a free input with significant impact.
  • Overshooting f and f0 = f=0.017, f0=0.002 (top); f=0.006, f0=0.001 (bottom)
    Overshooting parameters adopted from Claret & Torres (2019), with single values applied across the whole grid. The paper acknowledges overshooting is mass-dependent, so this is a fixed input with known systematic impact.
  • Delta_nu scaling factor f_Delta_nu = 0.847 +/- 0.015
    Fitted scaling factor in Eq. 17 to the grid's model output. It is a fit, not a prediction, though it is compared with previous values.
  • p_n1,l0-Delta_nu relation coefficients = 3.058, 0.276 (no rotation); 3.005, 0.509, 0.232 (with rotation)
    Linear regression coefficients fitted to the grid's model output in Eqs. 18 and 19. They are presented as empirical fits, not derived from first principles.
assumptions (4)
  • domain assumption Adiabatic approximation for pulsation frequencies
    Section 2.3 states all grid frequencies are adiabatic, with non-adiabatic corrections estimated below 0.4 percent. This is a standard assumption for large grids, but it ignores mode stability and driving.
  • domain assumption Shellular rotation and first-order/TAR treatment in GYRE
    Section 2.3.1 assumes solid-body rotation and uses perturbative or TAR treatments. The paper restricts to Omega/Omega_crit <= 0.3 to remain in this regime, but rapid rotators are excluded.
  • standard math MESA and GYRE codes correctly solve stellar structure and pulsation equations
    The paper relies entirely on MESA r24.03.1 and GYRE v7.2.1. These are community-standard, but no independent verification of the numerical implementations is provided.
  • domain assumption Classical instability strip of Dupret et al. (2004) for selecting models
    Section 4 restricts scaling relation fits to models within the classical instability strip. The strip location depends on the adopted convection treatment, so this selection is model-dependent.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Modelling $\delta$ Scuti pulsations: A new grid of p, g, and f modes across pre-main-sequence to post-main-sequence evolution." pith.science (2026). https://pith.science/paper/YIO7YISI

@misc{pith2026250703561,
  author       = {Pith},
  title        = {Pith review of: Modelling $\delta$ Scuti pulsations: A new grid of p, g, and f modes across pre-main-sequence to post-main-sequence evolution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YIO7YISI}},
  note         = {Machine review of arXiv:2507.03561}
}
abstract

Space-based photometry reveals regular high-frequency patterns in many young $\delta$ Scuti stars. These pulsations provide a powerful means of inferring stellar properties, particularly ages, for young $\delta$ Scuti stars for which traditional age-dating methods are poorly constrained. Realising this potential requires theoretical models that capture the complexities of stellar structure and evolution. We present a comprehensive grid of 25 million stellar pulsation models, computed using the mesa stellar evolution code and the gyre stellar oscillation code, tailored to $\delta$ Scuti stars. The grid spans a wide range of masses, metallicities and rotation velocities, and covers evolutionary phases from the early pre-main-sequence through the main sequence and into the post-main sequence contraction phase. For each model, we computed adiabatic pulsation frequencies for degrees $\ell$ = 0 to 3, capturing p modes, g modes, f modes and their interactions through avoided crossings. We find that f and low-order g modes have mode inertias comparable to or lower than the fundamental radial mode during the late pre-MS and early MS, implying that these modes should be observable. We revisit $\delta$ Scuti scaling relations and map asteroseismic observables, including the large frequency separation ($\Delta\nu$) and phase offset parameter ($\varepsilon$), across age, mass, metallicity, and rotation. This new model grid, which is publicly available, improves upon previous such model grids by facilitating interpretation of $\delta$ Scuti pulsations, allowing for more reliable age estimates and tighter constraints on stellar evolutionary pathways, and planet formation in A- and F-type stars.

Figures

Figures reproduced from arXiv: 2507.03561 by the authors.

Figure 1
Figure 1. Phases of evolution of a typical 1.7-M⊙, solar-metallicity 𝛿 Sct star on the Hertzsprung-Russell diagram. 2 Methodology 2.1 Stellar evolutionary models Stellar evolutionary models were calculated using mesa (Modules for Experiments in Stellar Astrophysics; r24.03.1; Paxton et al. 2011, 2013, 2015, 2018, 2019; Jermyn et al. 2023). This code computes one-dimensional stellar models by solving the fully coupled structur… view at source ↗
Figure 3
Figure 3. Kippenhahn diagrams for 12 stars from our model grid, illustrating how variations in stellar mass and metallicity influence core structure and evolution. These factors affect the size of the convective core, the extent of near-core overshooting, and the timing of the transition to stable hydrogen burning at the ZAMS (indicated by black dashed lines). Shading represents log10 of the net energy generation rate, define… view at source ↗
Figure 4
Figure 4. Evolution of a 1.7-M⊙ star with solar metallicity. Figure 4a shows the pre-MS evolution up to the ZAMS with three panels: the top panel displays the evolutionary track on the HR diagram coloured by log10 of the surface gravity (cm s−2 ), the bottom left panel zooms in to show the ZAMS, while the bottom right panel presents Kippenhahn diagram corresponding to the top panel. Figure 4b shows the MS and post-MS evolutio… view at source ↗
Figures from the paper (13 more)
Figure 5
Figure 5. Figure 5: Percentage of the main-sequence lifetime spent in each evolutionary phase for stellar models across a range of four masses and three metallicities. Each bar represents a star with a given mass (x-axis) and metallicity (panel title), subdivided into pre-main-sequence (P…
Figure 6
Figure 6. Figure 6: Distribution of models across the HR diagram, separated into two panels: pre-MS models (top) and MS models (bottom). Each panel contains four subplots displaying the same models but coloured according to different stellar parameters: log(Age/Myr), equatorial rotation v…
Figure 7
Figure 7. Figure 7: Evolution of stellar pulsation modes as a function of age for a 1.7-M⊙, solar-metallicity star. The top panels show mode frequency evolution, while the bottom panels display frequencies scaled by mean density (normalized to solar values), which makes avoided crossings …
Figure 8
Figure 8. Figure 8: Evolution of stellar pulsation modes as a function of age for a 1.7-M⊙, solar-metallicity star, organized by spherical degree ℓ. Each panel displays modes of a specific degree: ℓ = 0 (radial modes), ℓ = 1 (dipole modes), ℓ = 2 (quadrupole modes), and ℓ = 3 (octupole mo…
Figure 9
Figure 9. Figure 9: Échelle diagrams for HD 3622 and the Pleiades star V624 Tau. The red filled markers indicate the identified modes and the overlaid unfilled markers represent modes from the least squares best-fit model. throughout the bulk and are not just confined to the surface. Thei…
Figure 10
Figure 10. Figure 10: Scaled eigenfunctions for representative f, p, and g modes across evolution. Each subfigure shows the radial (Ψ𝑟 , solid line) and horizontal (Ψℎ, dotted line) components of the scaled eigenfunctions at three evolutionary stages (top to bottom: pre-MS, ZAMS, MS). (a) …
Figure 11
Figure 11. Figure 11: Occurrence of mixed modes throughout the evolution from pre-MS to late MS. Mode evolution for ℓ = 1, 2, 3 is shown in vertically stacked panels. Left-hand panels focus on the pre-MS, where mixed character appears for a short while in certain modes prior to the establi…
Figure 12
Figure 12. Figure 12: Normalized mode inertia throughout the evolution of a 1.7-M⊙, solar-metallicity star. For each mode we plot the fraction 𝐸/𝐸ref, where 𝐸ref is the value for the fundamental radial mode (p1,0). frequencies. Particularly relevant are the connections between large freque…
Figure 13
Figure 13. Figure 13: shows this relation for our grid. From a linear regression (in the log–log scale) of models within the instability strip, we find: Δ𝜈/Δ𝜈⊙ = 0.857 × (𝜌¯/𝜌¯⊙) 0.507 . (16) To facilitate comparison, we adopt Δ𝜈⊙ = 11.655 d −1 or 134.9 𝜇Hz (Kjeldsen & Bedding 1995). The b…
Figure 14
Figure 14. Figure 14: Scaling behaviour of the 𝑓Δ𝜈 relative to the mean stellar density. Each panel shows the dimensionless scaling factor 𝑓Δ𝜈 = (Δ𝜈/Δ𝜈⊙ ) (𝜌¯/𝜌¯⊙ ) −0.5 as a function of the scaled mean density 𝜌¯/𝜌¯⊙, for models located within the classical instability strip of Dupret et …
Figure 15
Figure 15. Figure 15: Relationship between the fundamental radial mode frequency (p𝑛1 ℓ0 ) and the large frequency separation (Δ𝜈) across our grid of models that lie within the instability strip. The points represent individual models spanning pre-MS, MS, and post-MS contraction phases. Th…
Figure 16
Figure 16. Figure 16: Visualization of the ratio between p𝑛1 ℓ0 and large frequency separation Δ𝜈, for models within the classical instability strip (Dupret et al. 2004). The three plots in each panel display trends with stellar parameters shown by colour: (a) equatorial rotation velocity …
Figure 17
Figure 17. Figure 17: The two panels show 𝜀 as a function of Δ𝜈, across models that lie within the classical instability strip. The top and the bottom panels present pre-MS and MS models, respectively. Each plot within a panel shows the dependence of 𝜀 with a different global stellar param…

Discussion (0). Sign in to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Wildly Oscillating Stars -- Unexplained dense ridge-like frequency agglomerations in A and F type pulsators

    astro-ph.SR 2026-06 unverdicted novelty 7.0 of 10

    A subset of A and F pulsating stars exhibit dense unexplained frequency agglomerations forming ridges below the fundamental mode, indicating a pulsational regime not captured by existing models.

  2. Forward Modeling of the $\delta$ Sct Star V1790 Ori: $\Delta \nu$, $\Omega$, Resolution and Non-adiabatic Effects

    astro-ph.SR 2026-07 conditional novelty 6.0 of 10

    For V1790 Ori, the large separation Δν ≈ 82 μHz is needed as a constraint to remove model degeneracy, and the 260.672 μHz peak—once called the fundamental radial mode—changes identity across modeling configurations.

  3. The Longest-period Young Transiting Exoplanets. A Duo of Puffy Giants inside a Debris Disk

    astro-ph.EP 2026-07 conditional novelty 6.0 of 10

    HD 114082 hosts two puffy, moderate-to-low-mass giants on nearly circular, coplanar, near-resonant orbits of 225.55 and ~314 days, the longest-period young transiting exoplanets known.

Reference graph

Works this paper leans on

157 extracted references · 45 canonical work pages · cited by 3 Pith papers

  1. [1]

    A., Morrell N

    Abt H. A., Morrell N. I., 1995, @doi [ ] 10.1086/192182 , https://ui.adsabs.harvard.edu/abs/1995ApJS...99..135A 99, 135

    doi:10.1086/192182 1995

  2. [2]

    Adassuriya J., 2022, PhD thesis, @doi 10.5281/zenodo.6814384 , https://ui.adsabs.harvard.edu/abs/2022PhDT.........2A

    work page doi:10.5281/zenodo.6814384 2022

  3. [3]

    Aerts C., Tkachenko A., 2024, Asteroseismic Modelling of Fast Rotators and its Opportunities for Astrophysics , @doi 10.48550/arXiv.2311.08453 , http://arxiv.org/abs/2311.08453

    arXiv doi:10.48550/arxiv.2311.08453 2024

  4. [4]

    W., 2010, Asteroseismology

    Aerts C., Christensen-Dalsgaard J., Kurtz D. W., 2010, Asteroseismology . Springer Netherlands, @doi 10.1007/978-1-4020-5803-5

    doi:10.1007/978-1-4020-5803-5 2010

  5. [5]

    Aerts C., et al., 2019, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201834762 , 624, A75

    work page doi:10.1051/0004-6361/201834762 2019

  6. [6]

    V., Mombarg J

    Aerts C., Reeth T. V., Mombarg J. S. G., Hey D., 2025, Evolution of the near-core rotation frequency of 2,497 intermediate-mass stars from their dominant gravito-inertial mode, @doi 10.48550/arXiv.2502.17692 , http://arxiv.org/abs/2502.17692

    arXiv doi:10.48550/arxiv.2502.17692 2025

  7. [7]

    H., Pedersen M

    Anders E. H., Pedersen M. G., 2023, @doi [Galaxies] 10.3390/galaxies11020056 , 11, 56

    doi:10.3390/galaxies11020056 2023

  8. [8]

    Antoci V., et al., 2014, @doi [ ] 10.1088/0004-637X/796/2/118 , https://ui.adsabs.harvard.edu/abs/2014ApJ...796..118A 796, 118

    doi:10.1088/0004-637x/796/2/118 2014

Show all 157 references
  1. [9]

    Antoci V., et al., 2019, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stz2787 , 490, 4040

    2019 doi

  2. [10]

    J., Scott P., 2009, @doi [ ] 10.1146/annurev.astro.46.060407.145222 , https://ui.adsabs.harvard.edu/abs/2009ARA&A..47..481A 47, 481

    Asplund M., Grevesse N., Sauval A. J., Scott P., 2009, @doi [ ] 10.1146/annurev.astro.46.060407.145222 , https://ui.adsabs.harvard.edu/abs/2009ARA&A..47..481A 47, 481

    2009

  3. [11]

    A., Daszyńska-Daszkiewicz J., Pamyatnykh A

    Balona L. A., Daszyńska-Daszkiewicz J., Pamyatnykh A. A., 2015, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stv1513 , 452, 3073

    2015 doi

  4. [12]

    R., Murphy S

    Barac N., Bedding T. R., Murphy S. J., Hey D. R., 2022, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stac2132 , 516, 2080

    2022 doi

  5. [13]

    R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2226-8 , 581, 147

    Bedding T. R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2226-8 , 581, 147

    2020 doi

  6. [14]

    R., et al., 2023, @doi [The Astrophysical Journal Letters] 10.3847/2041-8213/acc17a , 946, L10

    Bedding T. R., et al., 2023, @doi [The Astrophysical Journal Letters] 10.3847/2041-8213/acc17a , 946, L10

    2023 doi

  7. [15]

    C., White R

    Beyer A. C., White R. J., 2024, @doi [The Astrophysical Journal] 10.3847/1538-4357/ad6b0d , 973, 28

    2024 doi

  8. [16]

    Bildsten L., Ushomirsky G., Cutler C., 1996, @doi [The Astrophysical Journal] 10.1086/177012 , 460, 827

    1996 doi

  9. [17]

    M., Kurtz D

    Bowman D. M., Kurtz D. W., 2018, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/sty449 , 476, 3169

    2018 doi

  10. [18]

    Breger M., et al., 2011, @doi [Monthly Notices of the Royal Astronomical Society] 10.1111/j.1365-2966.2011.18508.x , 414, 1721

    2011

  11. [19]

    Breger M., et al., 2012, @doi [Astronomische Nachrichten] 10.1002/asna.201111640 , 333, 131

    2012 doi

  12. [20]

    Brogaard K., et al., 2012, @doi [ ] 10.1051/0004-6361/201219196 , https://ui.adsabs.harvard.edu/abs/2012A&A...543A.106B 543, A106

    2012 doi

  13. [21]

    L., et al., 2005, @doi [The Astrophysical Journal] 10.1086/426704 , 619, 1072

    Buzasi D. L., et al., 2005, @doi [The Astrophysical Journal] 10.1086/426704 , 619, 1072

    2005 doi

  14. [22]

    Cantiello M., Braithwaite J., 2019, @doi [The Astrophysical Journal] 10.3847/1538-4357/ab3924 , 883, 106

    2019 doi

  15. [23]

    Chen X., et al., 2022, @doi [The Astrophysical Journal Supplement Series] 10.3847/1538-4365/aca284 , 263, 34

    2022 doi

  16. [24]

    210, Delta Scuti and Related Stars

    Christensen-Dalsgaard J., 2000, in Breger M., Montgomery M., eds, Astronomical Society of the Pacific Conference Series Vol. 210, Delta Scuti and Related Stars. p. 187

    2000

  17. [25]

    Claret A., Torres G., 2016, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201628779 , 592, A15

    2016 doi

  18. [26]

    Claret A., Torres G., 2017, @doi [The Astrophysical Journal] 10.3847/1538-4357/aa8770 , 849, 18

    2017 doi

  19. [27]

    Claret A., Torres G., 2018, @doi [The Astrophysical Journal] 10.3847/1538-4357/aabd35 , 859, 100

    2018 doi

  20. [28]

    Claret A., Torres G., 2019, @doi [ ] 10.3847/1538-4357/ab1589 , https://ui.adsabs.harvard.edu/abs/2019ApJ...876..134C 876, 134

    2019 doi

  21. [29]

    H., et al., 2002, @doi [Astronomy & Astrophysics] 10.1051/0004-6361:20020161 , 385, 921

    Dall T. H., et al., 2002, @doi [Astronomy & Astrophysics] 10.1051/0004-6361:20020161 , 385, 921

    2002 doi

  22. [30]

    Daszyńska-Daszkiewicz J., Walczak P., Pamyatnykh A., Szewczuk W., Niewiadomski W., 2023, @doi [The Astrophysical Journal Letters] 10.3847/2041-8213/acade2 , 942, L38

    2023 doi

  23. [31]

    Dhouib H., Prat V., Van Reeth T., Mathis S., 2021, @doi [Astronomy and Astrophysics] 10.1051/0004-6361/202140615 , 652, A154

    2021 doi

  24. [32]

    C., 2022, @doi [The Astrophysical Journal] 10.3847/1538-4357/ac3980 , 924, 130

    Dornan V., Lovekin C. C., 2022, @doi [The Astrophysical Journal] 10.3847/1538-4357/ac3980 , 924, 130

    2022 doi

  25. [33]

    Dupret M.-A., Grigahcène A., Garrido R., Gabriel M., Scuflaire R., 2004, @doi [Astronomy & Astrophysics] 10.1051/0004-6361:20031740 , 414, L17

    2004 doi

  26. [34]

    A., Goode P

    Dziembowski W. A., Goode P. R., 1992, @doi [ ] 10.1086/171621 , https://ui.adsabs.harvard.edu/abs/1992ApJ...394..670D 394, 670

    1992 doi

  27. [35]

    Eckart C., 1963, @doi [Physics of Fluids] 10.1063/1.1706859 , https://ui.adsabs.harvard.edu/abs/1963PhFl....6.1037E 6, 1037

    1963 doi

  28. [36]

    S., 1926, The Internal Constitution of the Stars

    Eddington A. S., 1926, The Internal Constitution of the Stars . https://ui.adsabs.harvard.edu/abs/1926ics..book.....E

    1926

  29. [37]

    Espinosa Lara F., Rieutord M., 2011, @doi [ ] 10.1051/0004-6361/201117252 , https://ui.adsabs.harvard.edu/abs/2011A&A...533A..43E 533, A43

    2011 doi

  30. [38]

    Farag E., et al., 2024, An Expanded Set of Los Alamos OPLIB Tables in MESA : Type -1 Rosseland -mean Opacities and Solar Models , @doi 10.3847/1538-4357/ad4355 , http://arxiv.org/abs/2406.02845

    2024 arXiv

  31. [39]

    W., Alexander D

    Ferguson J. W., Alexander D. R., Allard F., Barman T., Bodnarik J. G., Hauschildt P. H., Heffner-Wong A., Tamanai A., 2005, @doi [ ] 10.1086/428642 , https://ui.adsabs.harvard.edu/abs/2005ApJ...623..585F 623, 585

    2005 doi

  32. [40]

    B., Cortés T

    Forteza S. B., Cortés T. R., García R. A., 2018, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201731803 , 614, A46

    2018 doi

  33. [41]

    C., Michel E., Lebreton Y., 2006, @doi [ ] 10.1051/0004-6361:20053791 , https://ui.adsabs.harvard.edu/abs/2006A&A...446..611F 446, 611

    Fox Machado L., P \'e rez Hern \'a ndez F., Su \'a rez J. C., Michel E., Lebreton Y., 2006, @doi [ ] 10.1051/0004-6361:20053791 , https://ui.adsabs.harvard.edu/abs/2006A&A...446..611F 446, 611

    2006 doi

  34. [42]

    Frandsen S., et al., 2001, @doi [Astronomy & Astrophysics] 10.1051/0004-6361:20010950 , 376, 175

    2001 doi

  35. [43]

    Garc \' a Hern \'a ndez A., et al., 2017, @doi [ ] 10.1093/mnrasl/slx117 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.471L.140G 471, L140

    2017 doi

  36. [44]

    García Hernández A., et al., 2009, @doi [Astronomy and Astrophysics] 10.1051/0004-6361/200911932 , 506, 79

    2009 doi

  37. [45]

    García Hernández A., et al., 2013, @doi [Astronomy and Astrophysics] 10.1051/0004-6361/201220256 , 559, A63

    2013 doi

  38. [46]

    García Hernández A., Martín-Ruiz S., Monteiro M. J. P. F. G., Suárez J. C., Reese D. R., Pascual-Granado J., Garrido R., 2015, @doi [The Astrophysical Journal] 10.1088/2041-8205/811/2/L29 , 811, L29

    2015 doi

  39. [47]

    L., et al., 2010, @doi [Publications of the Astronomical Society of the Pacific] 10.1086/650399 , 122, 131

    Gilliland R. L., et al., 2010, @doi [Publications of the Astronomical Society of the Pacific] 10.1086/650399 , 122, 131

    2010 doi

  40. [48]

    Goldstein J., Townsend R. H. D., 2020, @doi [ ] 10.3847/1538-4357/aba748 , https://ui.adsabs.harvard.edu/abs/2020ApJ...899..116G 899, 116

    2020 doi

  41. [49]

    O., 1986, in Osaki Y., ed., Hydrodynamic and Magnetodynamic Problems in the Sun and Stars

    Gough D. O., 1986, in Osaki Y., ed., Hydrodynamic and Magnetodynamic Problems in the Sun and Stars. p. 117

    1986

  42. [50]

    J., Dupret M

    Goupil M. J., Dupret M. A., Samadi R., Boehm T., Alecian E., Suarez J. C., Lebreton Y., Catala C., 2005, @doi [Journal of Astrophysics and Astronomy] 10.1007/BF02702333 , https://ui.adsabs.harvard.edu/abs/2005JApA...26..249G 26, 249

    2005 doi

  43. [51]

    R., Pamyatnykh A

    Guo Z., Bedding T. R., Pamyatnykh A. A., Kurtz D. W., Li G., Gautam A., Murphy S. J., Aerts C., 2024, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stae2423 , 535, 2927

    2024 doi

  44. [52]

    A., 2021, @doi [Frontiers in Astronomy and Space Sciences] 10.3389/fspas.2021.653558 , 8, 653558

    Guzik J. A., 2021, @doi [Frontiers in Astronomy and Space Sciences] 10.3389/fspas.2021.653558 , 8, 653558

    2021

  45. [53]

    R., 2002, @doi [ ] 10.1046/j.1365-8711.2002.05401.x , https://ui.adsabs.harvard.edu/abs/2002MNRAS.333..251H 333, 251

    Handler G., Shobbrook R. R., 2002, @doi [ ] 10.1046/j.1365-8711.2002.05401.x , https://ui.adsabs.harvard.edu/abs/2002MNRAS.333..251H 333, 251

    2002

  46. [54]

    Hasanzadeh A., Safari H., Ghasemi H., 2021, @doi [ ] 10.1093/mnras/stab1411 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.505.1476H 505, 1476

    2021 doi

  47. [55]

    Heger A., Langer N., 2000, @doi [The Astrophysical Journal] 10.1086/317239 , 544, 1016

    2000 doi

  48. [56]

    S., Bodenheimer P., 1965, @doi [ ] 10.1086/148357 , https://ui.adsabs.harvard.edu/abs/1965ApJ...142..841H 142, 841

    Henyey L., Vardya M. S., Bodenheimer P., 1965, @doi [ ] 10.1086/148357 , https://ui.adsabs.harvard.edu/abs/1965ApJ...142..841H 142, 841

    1965 doi

  49. [57]

    M., Perez Hernandez F., Michel E., Belmonte J

    Hernandez M. M., Perez Hernandez F., Michel E., Belmonte J. A., Goupil M. J., Lebreton Y., 1998, , https://ui.adsabs.harvard.edu/abs/1998A&A...338..511H 338, 511

    1998

  50. [58]

    210, Delta Scuti and Related Stars

    Houdek G., 2000, in Breger M., Montgomery M., eds, Astronomical Society of the Pacific Conference Series Vol. 210, Delta Scuti and Related Stars. p. 454

    2000

  51. [59]

    A., Rogers F

    Iglesias C. A., Rogers F. J., 1993, @doi [ ] 10.1086/172958 , https://ui.adsabs.harvard.edu/abs/1993ApJ...412..752I 412, 752

    1993 doi

  52. [60]

    A., Rogers F

    Iglesias C. A., Rogers F. J., 1996, @doi [ ] 10.1086/177381 , https://ui.adsabs.harvard.edu/abs/1996ApJ...464..943I 464, 943

    1996 doi

  53. [61]

    S., Anders E

    Jermyn A. S., Anders E. H., Lecoanet D., Cantiello M., 2022, @doi [The Astrophysical Journal Supplement Series] 10.3847/1538-4365/ac7cee , 262, 19

    2022 doi

  54. [62]

    S., et al., 2023, @doi [ ] 10.3847/1538-4365/acae8d , https://ui.adsabs.harvard.edu/abs/2023ApJS..265...15J 265, 15

    Jermyn A. S., et al., 2023, @doi [ ] 10.3847/1538-4365/acae8d , https://ui.adsabs.harvard.edu/abs/2023ApJS..265...15J 265, 15

    2023 doi

  55. [63]

    A., Bedding T

    Keen M. A., Bedding T. R., Murphy S. J., Schmid V. S., Aerts C., Tkachenko A., Ouazzani R. M., Kurtz D. W., 2015, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stv2107 , 454, 1792

    2015 doi

  56. [64]

    L., Murphy S

    Kerr R., Kraus A. L., Murphy S. J., Krolikowski D. M., Offner S. S. R., Tofflemire B. M., Rizzuto A. C., 2022a, @doi [The Astrophysical Journal] 10.3847/1538-4357/ac9b45 , 941, 49

    doi

  57. [65]

    L., Murphy S

    Kerr R., Kraus A. L., Murphy S. J., Krolikowski D. M., Bedding T. R., Rizzuto A. C., 2022b, @doi [The Astrophysical Journal] 10.3847/1538-4357/aca0dd , 941, 143

    doi

  58. [66]

    C., 1970, A Simple Method for the Solution of the Stellar Structure Equations Including Rotation and Tidal Forces

    Kippenhahn R., Thomas H. C., 1970, A Simple Method for the Solution of the Stellar Structure Equations Including Rotation and Tidal Forces . https://ui.adsabs.harvard.edu/abs/1970stro.coll...20K

    1970

  59. [67]

    R., 1995, Amplitudes of stellar oscillations: the implications for asteroseismology., @doi 10.48550/arXiv.astro-ph/9403015 , https://ui.adsabs.harvard.edu/abs/1995A&A...293...87K

    Kjeldsen H., Bedding T. R., 1995, Amplitudes of stellar oscillations: the implications for asteroseismology., @doi 10.48550/arXiv.astro-ph/9403015 , https://ui.adsabs.harvard.edu/abs/1995A&A...293...87K

    1995 doi arXiv

  60. [68]

    P., 1967, @doi [ ] 10.1086/149359 , https://ui.adsabs.harvard.edu/abs/1967ApJ...150..551K 150, 551

    Kraft R. P., 1967, @doi [ ] 10.1086/149359 , https://ui.adsabs.harvard.edu/abs/1967ApJ...150..551K 150, 551

    1967 doi

  61. [69]

    W., 2006, @doi [Communications in Asteroseismology] 10.1553/cia147s6 , 147, 6

    Kurtz D. W., 2006, @doi [Communications in Asteroseismology] 10.1553/cia147s6 , 147, 6

    2006 doi

  62. [70]

    Kurtz D., 2022, Asteroseismology across the HR diagram, @doi 10.48550/arXiv.2201.11629 , http://arxiv.org/abs/2201.11629

    2022 doi arXiv

  63. [71]

    W., Saio H., Takata M., Shibahashi H., Murphy S

    Kurtz D. W., Saio H., Takata M., Shibahashi H., Murphy S. J., Sekii T., 2014, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stu1329 , 444, 102

    2014 doi

  64. [72]

    Leclerc A., Laibe G., Delplace P., Venaille A., Perez N., 2022, @doi [The Astrophysical Journal] 10.3847/1538-4357/ac99d9 , 940, 84

    2022 doi

  65. [73]

    Ledoux P., 1951, @doi [ ] 10.1086/145477 , https://ui.adsabs.harvard.edu/abs/1951ApJ...114..373L 114, 373

    1951 doi

  66. [74]

    Lee U., 1993, @doi [The Astrophysical Journal] 10.1086/172368 , 405, 359

    1993 doi

  67. [75]

    Lee U., Saio H., 1997, @doi [The Astrophysical Journal] 10.1086/304980 , 491, 839

    1997 doi

  68. [76]

    A., Zdravkov T., Breger M., 2010, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/200912914 , 509, A90

    Lenz P., Pamyatnykh A. A., Zdravkov T., Breger M., 2010, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/200912914 , 509, A90

    2010 doi

  69. [77]

    R., Murphy S

    Li G., Van Reeth T., Bedding T. R., Murphy S. J., Antoci V., Ouazzani R.-M., Barbara N. H., 2020, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stz2906 , 491, 3586

    2020 doi

  70. [78]

    L., 1998, @doi [Space Science Reviews] 10.1023/A:1005048124341 , 84, 285

    Linsky J. L., 1998, @doi [Space Science Reviews] 10.1023/A:1005048124341 , 84, 285

    1998 doi

  71. [79]

    Lopes I., 2000, @doi [The Astrophysical Journal] 10.1086/317033 , 542, 1071

    2000 doi

  72. [80]

    C., Guzik J

    Lovekin C. C., Guzik J. A., 2017, @doi [The Astrophysical Journal] 10.3847/1538-4357/aa8e01 , 849, 38

    2017 doi

  73. [81]

    J., et al., 2021, @doi [ ] 10.1093/mnras/stab1368 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.505.2427L 505, 2427

    Lyttle A. J., et al., 2021, @doi [ ] 10.1093/mnras/stab1368 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.505.2427L 505, 2427

    2021 doi

  74. [82]

    Maeder A., Meynet G., 2000, @doi [ ] 10.1146/annurev.astro.38.1.143 , https://ui.adsabs.harvard.edu/abs/2000ARA&A..38..143M 38, 143

    2000 doi

  75. [83]

    Mathis S., Prat V., 2019, @doi [Astronomy and Astrophysics] 10.1051/0004-6361/201935639 , 631, A26

    2019 doi

  76. [84]

    Meynet G., Maeder A., 1997, Astronomy and Astrophysics, 321, 465

    1997

  77. [85]

    Michel E., et al., 2017, in European Physical Journal Web of Conferences. p. 03001 ( @eprint arXiv 1705.03721 ), @doi 10.1051/epjconf/201716003001

    2017 arXiv

  78. [86]

    M., 2022, @doi [Frontiers in Astronomy and Space Sciences] 10.3389/fspas.2022.952296 , 9

    Mirouh G. M., 2022, @doi [Frontiers in Astronomy and Space Sciences] 10.3389/fspas.2022.952296 , 9

    2022

  79. [87]

    M., Angelou G

    Mirouh G. M., Angelou G. C., Reese D. R., Costa G., 2019, @doi [Monthly Notices of the Royal Astronomical Society: Letters] 10.1093/mnrasl/sly212 , 483, L28

    2019 doi

  80. [88]

    J., Fossati L., Bedding T

    Murphy S. J., Fossati L., Bedding T. R., Saio H., Kurtz D. W., Grassitelli L., Wang E. S., 2016, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stw705 , 459, 1201

    2016 doi

  81. [89]

    J., Paunzen E., Bedding T

    Murphy S. J., Paunzen E., Bedding T. R., Walczak P., Huber D., 2020a, @doi [ ] 10.1093/mnras/staa1271 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.495.1888M 495, 1888

    doi

  82. [90]

    J., Saio H., Takada-Hidai M., Kurtz D

    Murphy S. J., Saio H., Takada-Hidai M., Kurtz D. W., Shibahashi H., Takata M., Hey D. R., 2020b, @doi [ ] 10.1093/mnras/staa2667 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.498.4272M 498, 4272

    doi

  83. [91]

    J., Joyce M., Bedding T

    Murphy S. J., Joyce M., Bedding T. R., White T. R., Kama M., 2021, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stab144 , 502, 1633

    2021 doi

  84. [92]

    J., Bedding T

    Murphy S. J., Bedding T. R., White T. R., Li Y., Hey D., Reese D., Joyce M., 2022, @doi [ ] 10.1093/mnras/stac240 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.511.5718M 511, 5718

    2022 doi

  85. [93]

    J., Bedding T

    Murphy S. J., Bedding T. R., Gautam A., Joyce M., 2023, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stad2849 , p. stad2849

    2023 doi

  86. [94]

    J., Bedding T

    Murphy S. J., Bedding T. R., Gautam A., Kerr R. P., Mani P., 2024, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stae2226 , 534, 3022

    2024 doi

  87. [95]

    Niu J.-S., Xue H.-F., 2024, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/202348757 , 682, L8

    2024 doi

  88. [96]

    Osaki Y., 1975, , https://ui.adsabs.harvard.edu/abs/1975PASJ...27..237O 27, 237

    1975

  89. [97]

    Ouazzani R.-M., Goupil M.-J., 2012, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201117151 , 542, A99

    2012 doi

  90. [98]

    W., Dupret M.-A., 2015, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201525734 , 579, A116

    Ouazzani R.-M., Roxburgh I. W., Dupret M.-A., 2015, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201525734 , 579, A116

    2015 doi

  91. [99]

    A., 2000, Pulsational instability domain of Delta Scuti variables, @doi 10.48550/arXiv.astro-ph/0005276 , http://arxiv.org/abs/astro-ph/0005276

    Pamyatnykh A. A., 2000, Pulsational instability domain of Delta Scuti variables, @doi 10.48550/arXiv.astro-ph/0005276 , http://arxiv.org/abs/astro-ph/0005276

    2000 doi arXiv

  92. [100]

    Paparó M., et al., 2013, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201321792 , 557, A27

    2013 doi

  93. [101]

    Paxton B., Bildsten L., Dotter A., Herwig F., Lesaffre P., Timmes F., 2011, @doi [ ] 10.1088/0067-0049/192/1/3 , https://ui.adsabs.harvard.edu/abs/2011ApJS..192....3P 192, 3

    2011 doi

  94. [102]

    Paxton B., et al., 2013, @doi [ ] 10.1088/0067-0049/208/1/4 , https://ui.adsabs.harvard.edu/abs/2013ApJS..208....4P 208, 4

    2013 doi

  95. [103]

    Paxton B., et al., 2015, @doi [ ] 10.1088/0067-0049/220/1/15 , https://ui.adsabs.harvard.edu/abs/2015ApJS..220...15P 220, 15

    2015 doi

  96. [104]

    Paxton B., et al., 2018, @doi [ ] 10.3847/1538-4365/aaa5a8 , https://ui.adsabs.harvard.edu/abs/2018ApJS..234...34P 234, 34

    2018 doi

  97. [105]

    Paxton B., et al., 2019, @doi [ ] 10.3847/1538-4365/ab2241 , https://ui.adsabs.harvard.edu/abs/2019ApJS..243...10P 243, 10

    2019 doi

  98. [106]

    G., et al., 2021, @doi [Nature Astronomy] 10.1038/s41550-021-01351-x , 5, 715

    Pedersen M. G., et al., 2021, @doi [Nature Astronomy] 10.1038/s41550-021-01351-x , 5, 715

    2021 doi

  99. [107]

    Perrot M., Delplace P., Venaille A., 2019, Topological transition in stratified fluids, @doi 10.48550/arXiv.1810.03328 , http://arxiv.org/abs/1810.03328

    2019 doi arXiv

  100. [108]

    M., et al., 2006, @doi [The Astrophysical Journal] 10.1086/497981 , 636, 1087

    Peterson D. M., et al., 2006, @doi [The Astrophysical Journal] 10.1086/497981 , 636, 1087

    2006 doi

  101. [109]

    M., 2017, @doi [Astronomy and Astrophysics] 10.1051/0004-6361/201629637 , 598, A105

    Prat V., Mathis S., Lignières F., Ballot J., Culpin P. M., 2017, @doi [Astronomy and Astrophysics] 10.1051/0004-6361/201629637 , 598, A105

    2017 doi

  102. [110]

    W., 1974, @doi [Annual Review of Astronomy and Astrophysics] 10.1146/annurev.aa.12.090174.001353 , 12, 257

    Preston G. W., 1974, @doi [Annual Review of Astronomy and Astrophysics] 10.1146/annurev.aa.12.090174.001353 , 12, 257

    1974

  103. [111]

    Cambridge University Press, Cambridge ; New York

    Prialnik D., 2010, An introduction to the theory of stellar structure and evolution, 2nd ed edn. Cambridge University Press, Cambridge ; New York

    2010

  104. [112]

    M., Michel E., 1999, Astronomy and Astrophysics, 346, 586

    Pérez Hernández F., Claret A., Hernández M. M., Michel E., 1999, Astronomy and Astrophysics, 346, 586

    1999

  105. [113]

    D., Foster H., Telting J

    Reed M. D., Foster H., Telting J. H., Østensen R. H., Farris L. H., Oreiro R., Baran A. S., 2014, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stu412 , 440, 3809

    2014 doi

  106. [114]

    R., 2022, Frontiers in Astronomy and Space Sciences, 9

    Reese D. R., 2022, Frontiers in Astronomy and Space Sciences, 9

    2022

  107. [115]

    Reese D., Lignières F., Rieutord M., 2008, @doi [Astronomy & Astrophysics] 10.1051/0004-6361:20078075 , 481, 449

    2008 doi

  108. [116]

    R., Lignières F., Ballot J., Dupret M.-A., Barban C., Veer-Menneret C

    Reese D. R., Lignières F., Ballot J., Dupret M.-A., Barban C., Veer-Menneret C. v., MacGregor K. B., 2017, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201321264 , 601, A130

    2017 doi

  109. [117]

    R., Mirouh G

    Reese D. R., Mirouh G. M., Espinosa Lara F., Rieutord M., Putigny B., 2021, @doi [ ] 10.1051/0004-6361/201935538 , https://ui.adsabs.harvard.edu/abs/2021A&A...645A..46R 645, A46

    2021 doi

  110. [118]

    J., 2000, @doi [Astronomy and Astrophysics Supplement Series] 10.1051/aas:2000221 , 144, 469

    Rodríguez E., López-González M. J., 2000, @doi [Astronomy and Astrophysics Supplement Series] 10.1051/aas:2000221 , 144, 469

    2000 doi

  111. [119]

    E., Hernández A

    Rodríguez-Martín J. E., Hernández A. G., Suárez J. C., Rodón J. R., 2020, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/staa2378 , 498, 1700

    2020 doi

  112. [120]

    E., 2007, @doi [Astronomy and Astrophysics] 10.1051/0004-6361:20065224 , 463, 671

    Royer F., Zorec J., Gómez A. E., 2007, @doi [Astronomy and Astrophysics] 10.1051/0004-6361:20065224 , 463, 671

    2007 doi

  113. [121]

    Saio H., 1981, @doi [ ] 10.1086/158708 , https://ui.adsabs.harvard.edu/abs/1981ApJ...244..299S 244, 299

    1981 doi

  114. [122]

    W., Takata M., Shibahashi H., Murphy S

    Saio H., Kurtz D. W., Takata M., Shibahashi H., Murphy S. J., Sekii T., Bedding T. R., 2015, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stu2696 , 447, 3264

    2015 doi

  115. [123]

    Saux A. L., Leclerc A., Laibe G., Delplace P., Venaille A., 2025, A core-sensitive mixed \ f\ /\ g\ mode of the Sun predicted by wave topology and hydrodynamical simulation, @doi 10.48550/arXiv.2506.09572 , http://arxiv.org/abs/2506.09572

    2025 doi arXiv

  116. [124]

    Scuflaire R., 1974, , https://ui.adsabs.harvard.edu/abs/1974A&A....36..107S 36, 107

    1974

  117. [125]

    J., Murphy S

    Scutt O. J., Murphy S. J., Nielsen M. B., Davies G. R., Bedding T. R., Lyttle A. J., 2023, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stad2621 , 525, 5235–5244

    2023 doi

  118. [126]

    H., Panda S

    Singh K. H., Panda S. K., Hanasoge S. M., Dhanpal S., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2504.08229 , https://ui.adsabs.harvard.edu/abs/2025arXiv250408229S p. arXiv:2504.08229

    2025 doi arXiv

  119. [127]

    Smalley B., et al., 2017, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stw2903 , 465, 2662

    2017 doi

  120. [128]

    R., 2010, @doi [Annual Review of Astronomy and Astrophysics] 10.1146/annurev-astro-081309-130806 , 48, 581

    Soderblom D. R., 2010, @doi [Annual Review of Astronomy and Astrophysics] 10.1146/annurev-astro-081309-130806 , 48, 581

    2010 doi

  121. [129]

    W., Palla F., 2004, The Formation of Stars

    Stahler S. W., Palla F., 2004, The Formation of Stars . https://ui.adsabs.harvard.edu/abs/2004fost.book.....S

    2004

  122. [130]

    W., Shu F

    Stahler S. W., Shu F. H., Taam R. E., 1980, @doi [The Astrophysical Journal] 10.1086/158377 , 241, 637

    1980 doi

  123. [131]

    G., M \"u llner M., Vorobyov E

    Steindl T., Zwintz K., Barnes T. G., M \"u llner M., Vorobyov E. I., 2021, @doi [ ] 10.1051/0004-6361/202140818 , https://ui.adsabs.harvard.edu/abs/2021A&A...654A..36S 654, A36

    2021 doi

  124. [132]

    Steindl T., Zwintz K., Vorobyov E., 2022, @doi [Nature Communications] 10.1038/s41467-022-32882-0 , 13, 5355

    2022 doi

  125. [133]

    F., 1979, @doi [ ] 10.1086/156802 , https://ui.adsabs.harvard.edu/abs/1979ApJ...227..935S 227, 935

    Stellingwerf R. F., 1979, @doi [ ] 10.1086/156802 , https://ui.adsabs.harvard.edu/abs/1979ApJ...227..935S 227, 935

    1979 doi

  126. [134]

    C., Garc \' a Hern \'a ndez A., Moya A., Rodrigo C., Solano E., Garrido R., Rod \'o n J

    Su \'a rez J. C., Garc \' a Hern \'a ndez A., Moya A., Rodrigo C., Solano E., Garrido R., Rod \'o n J. R., 2014, @doi [ ] 10.1051/0004-6361/201322270 , https://ui.adsabs.harvard.edu/abs/2014A&A...563A...7S 563, A7

    2014 doi

  127. [135]

    Takata M., 2006a, @doi [ ] 10.1093/pasj/58.4.759 , https://ui.adsabs.harvard.edu/abs/2006PASJ...58..759T 58, 759

    doi

  128. [136]

    Takata M., 2006b, @doi [ ] 10.1093/pasj/58.5.893 , https://ui.adsabs.harvard.edu/abs/2006PASJ...58..893T 58, 893

    doi

  129. [137]

    Tassoul M., 1980, @doi [ ] 10.1086/190678 , https://ui.adsabs.harvard.edu/abs/1980ApJS...43..469T 43, 469

    1980 doi

  130. [138]

    S., 2005, @doi [ ] 10.1051/0004-6361:20052933 , https://ui.adsabs.harvard.edu/abs/2005A&A...443..627T 443, 627

    Th \'e ado S., Vauclair S., Cunha M. S., 2005, @doi [ ] 10.1051/0004-6361:20052933 , https://ui.adsabs.harvard.edu/abs/2005A&A...443..627T 443, 627

    2005 doi

  131. [140]

    Townsend R. H. D., 2003b, @doi [Monthly Notices of the Royal Astronomical Society] 10.1046/j.1365-8711.2003.06640.x , 343, 125

    2003

  132. [141]

    Townsend R., 2013, @doi [Proceedings of the International Astronomical Union] 10.1017/S1743921313014257 , 9, 153

    2013 doi

  133. [142]

    Townsend R. H. D., Teitler S. A., 2013, @doi [ ] 10.1093/mnras/stt1533 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.435.3406T 435, 3406

    2013 doi

  134. [143]

    Townsend R. H. D., Goldstein J., Zweibel E. G., 2018, @doi [ ] 10.1093/mnras/stx3142 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.475..879T 475, 879

    2018 doi

  135. [144]

    Uesugi A., Fukuda I., 1982, VizieR Online Data Catalog, 3063, III/63B

    1982

  136. [145]

    K., 1986, @doi [The Astrophysical Journal] 10.1086/184700 , 306, L37

    Ulrich R. K., 1986, @doi [The Astrophysical Journal] 10.1086/184700 , 306, L37

    1986 doi

  137. [146]

    https://ui.adsabs.harvard.edu/abs/1989nos..book.....U

    Unno W., Osaki Y., Ando H., Saio H., Shibahashi H., 1989, Nonradial oscillations of stars. https://ui.adsabs.harvard.edu/abs/1989nos..book.....U

    1989

  138. [147]

    Uytterhoeven K., et al., 2011, @doi [ ] 10.1051/0004-6361/201117368 , https://ui.adsabs.harvard.edu/abs/2011A&A...534A.125U 534, A125

    2011 doi

  139. [148]

    R., Lund M

    Verma K., Raodeo K., Basu S., Silva Aguirre V., Mazumdar A., Mosumgaard J. R., Lund M. N., Ranadive P., 2019, @doi [ ] 10.1093/mnras/sty3374 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.483.4678V 483, 4678

    2019 doi

  140. [149]

    R., et al., 2011a, @doi [The Astrophysical Journal] 10.1088/2041-8205/742/1/L3 , 742, L3

    White T. R., et al., 2011a, @doi [The Astrophysical Journal] 10.1088/2041-8205/742/1/L3 , 742, L3

    doi

  141. [150]

    R., Bedding T

    White T. R., Bedding T. R., Stello D., Christensen-Dalsgaard J., Huber D., Kjeldsen H., 2011b, @doi [The Astrophysical Journal] 10.1088/0004-637X/743/2/161 , 743, 161

    doi

  142. [151]

    L., Aguirre Børsen-Koch V., Rørsted J

    Winther M. L., Aguirre Børsen-Koch V., Rørsted J. L., Stokholm A., Verma K., 2023, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stad1802 , 525, 1416

    2023 doi

  143. [152]

    P., 1992, Astronomy and Astrophysics, 265, 115

    Zahn J. P., 1992, Astronomy and Astrophysics, 265, 115

    1992

  144. [153]

    Zorec J., Royer F., 2012, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201117691 , 537, A120

    2012 doi

  145. [154]

    Zwintz K., et al., 2024, @doi [Astronomy and Astrophysics] 10.1051/0004-6361/202348236 , 683, A49

    2024 doi

  146. [155]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

  147. [156]

    N., 2013, Journal of Improbable Astronomy, 1, 1

    Author A. N., 2013, Journal of Improbable Astronomy, 1, 1

    2013

  148. [157]

    D., 2015, Journal of Interesting Stuff, 17, 198

    Jones C. D., 2015, Journal of Interesting Stuff, 17, 198

    2015

  149. [158]

    B., 2014, The Example Journal, 12, 345 (Paper I)

    Smith A. B., 2014, The Example Journal, 12, 345 (Paper I)

    2014

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.