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K-dwarf Radius Inflation and a 10-Gyr Spin-down Clock Unveiled through Asteroseismology of HD 219134 from the Keck Planet Finder

T0 review · 3 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The paper derives a mass of 0.763 solar masses, a radius of 0.748 solar radii, and an age of 10.151 Gyr for the K dwarf HD 219134 from 25 detected oscillation modes, making it the first main-sequence star cooler than 5000 K with an…

desk verdict Solid frequency extraction and a genuinely new seismic age for the coolest K dwarf yet, but the 4σ radius discrepancy makes both the radius-inflation and spin-down claims conditional rather than established. read the letter →

arxiv 2502.00971 v2 pith:EO2N76RV submitted 2025-02-03 astro-ph.SR astro-ph.EP

Yaguang Li , Daniel Huber , J. M. Joel Ong , Jennifer van Saders , R. R. Costa , Jens Reersted Larsen , Sarbani Basu , Timothy R. Bedding
show 21 more authors
Fei Dai Ashley Chontos Theron W. Carmichael Daniel Hey Hans Kjeldsen Marc Hon Tiago L. Campante Mário J. P. F. G. Monteiro Mia Sloth Lundkvist Nicholas Saunders Howard Isaacson Andrew W. Howard Steven R. Gibson Samuel Halverson Kodi Rider Arpita Roy Ashley D. Baker Jerry Edelstein Chris Smith Benjamin J. Fulton Josh Walawender
This is my paper · ORCID
classification astro-ph.SRastro-ph.EP
keywords KdwarfstarsLate-typeAsteroseismologyStellarradiimassesrotationRadialvelocityInterferometry
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 reports the first asteroseismic detection in the K3 dwarf HD 219134 using four nights of radial-velocity data from the Keck Planet Finder, extracting 25 oscillation frequencies and using them to derive a stellar mass of $0.763\pm0.020\,M_\odot$, a radius of $0.748\pm0.007\,R_\odot$, and an age of $10.151\pm1.520$ Gyr. This makes HD 219134 the first main-sequence star cooler than 5000 K with an asteroseismic age, giving a rare anchor point for gyrochronology in old, cool dwarfs. The age is used to show that a weakened-magnetic-braking model of angular momentum loss, fed with asteroseismically constrained composition and mixing length, reproduces the observed 41.3-day rotation period. The authors also find that their asteroseismic radius is 4% smaller than a recent interferometric radius, a $4\sigma$ discrepancy they cannot attribute to interferometry, modeling choices, magnetic fields, or tidal heating, and they state that the derived quantities are conditional until it is resolved. Finally, they confirm that oscillation amplitudes in K dwarfs scale as $(L/M)^{1.5}$, steeper than the $(L/M)^{0.7}$ relation for G dwarfs.

What carries the argument

The load-bearing tool is asteroseismic frequency modeling built on the asymptotic relation $\nu_{n,\ell}\simeq\Delta\nu(n+\ell/2+\epsilon)-\delta\nu_{0,\ell}$. The large separation $\Delta\nu=182.799\pm0.069\,\mu$Hz fixes the mean density, while the small separation $\delta\nu_{0,2}=10.90\pm0.41\,\mu$Hz, which is sensitive to the core hydrogen gradient, is the age clock. Because $\delta\nu_{0,2}$ in a K dwarf is almost exactly 1 cycle/day, it is entangled with daily sidelobes in the spectral window; the authors use Gold deconvolution of the power spectrum to disentangle true $\ell=0{-}3$ ridges, then fit 25 modes with five independent evolutionary-modeling pipelines that differ in atmospheric boundary conditions, opacities, mixing-length treatment, and surface corrections. For the spin-down test, the machinery is a two-zone rotational evolution model with a Rossby-number-dependent weakened magnetic braking prescription, calibrated against open clusters and asteroseismic field stars and tested with solar-calibrated versus asteroseismically constrained helium and mixing length.

What would settle it

A decisive test is an independent radius measurement accurate to better than 1%, either from a new interferometric angular diameter with a second instrument or from an asteroseismic radius that does not rely on the surface term; if the true radius is $0.783\,R_\odot$ rather than $0.748\,R_\odot$, the evolutionary models are wrong and the 10.15 Gyr age, the rotation-model agreement, and the revised planet radii all collapse, while a true radius near $0.748\,R_\odot$ would clear the models and point to interferometric systematics.

Watch

Extended reading notes

Core claim

The central claim is that HD 219134 can be asteroseismically modeled to give a mass of $0.763\pm0.020\,M_\odot$, a radius of $0.748\pm0.007\,R_\odot$, and an age of $10.151\pm1.520$ Gyr, making it the first main-sequence star cooler than 5000 K with an asteroseismic age. The age is read primarily from the small frequency separation $\delta\nu_{0,2}$, which tracks the hydrogen profile in the core. The authors emphasize that this age is robust to surface physics and to the choice of classical constraints, but that the radius is not a direct seismic measurement: it is the radius of a 1D evolutionary model whose interior matches the oscillation frequencies. They then report that this model radius is 4% smaller than the $0.783\pm0.005\,R_\odot$ radius inferred from interferometry, a $4\sigma$ discrepancy they cannot explain with interferometric systematics, atmospheric boundary conditions, mixing-length choices, magnetic fields, or tidal heating. In the paper's own words, the subsequent rotation-evolution results and planet properties are only conditional until that discrepancy is understood.

Load-bearing premise

Everything hangs on the assumption that one-dimensional evolutionary models of the star's interior and envelope are accurate; the paper itself calls that into question by reporting a 4σ radius mismatch with interferometry and labeling its own derived quantities conditional.

Editorial extensions

If this is right

  • HD 219134 becomes the coolest benchmark star ($T_{\rm eff}\approx4850$ K) with an asteroseismic age older than 4.2 Gyr, so any future gyrochronology calibration for old K dwarfs must reproduce its 41.3-day rotation period at 10.15 Gyr.
  • The weak-braking models with asteroseismically constrained helium and mixing length reproduce the observed rotation, while a long core-envelope coupling timescale ($\alpha_{\rm ce}\approx12$) is disfavored; this constrains angular momentum transport in K dwarfs.
  • The masses and radii of the two transiting super-Earths are revised downward (b: $4.59\,M_\oplus$, $1.542\,R_\oplus$; c: $4.23\,M_\oplus$, $1.455\,R_\oplus$), placing them on the Earth-like 30% Fe plus 70% MgSiO$_3$ composition track.
  • K-dwarf oscillation amplitudes follow a $(L/M)^{1.5}$ scaling in radial velocity, not the $(L/M)^{0.7}$ G-dwarf relation, implying that the $\nu_{\rm max}$ scaling relation may also differ in cool dwarfs.
  • The 4% radius discrepancy, if real, is a direct sign that 1D envelope models misplace the outer layers of K dwarfs, and it is the reason the paper labels its own age, rotation, and planet results conditional.

Reading between the lines

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

  • If the interferometric radius survives scrutiny, the most economical fix is that the outer boundary condition of 1D models, whether atmosphere, mixing length, or both, is wrong for cool dwarfs; that would shift radii more than ages, since the age is set by the core diagnostic $\delta\nu_{0,2}$.
  • A steeper $(L/M)^{1.5}$ amplitude scaling suggests that $\nu_{\rm max}$ in K dwarfs may also deviate from the solar-calibrated scaling; if so, seismic radii and distances for cool dwarfs that rely on $\nu_{\rm max}$ would need a temperature-dependent correction.
  • The paper's Rossby number estimate ($\mathrm{Ro}/\mathrm{Ro}_\odot\approx0.83$) sits about $1\sigma$ below the braking-quenching threshold, so HD 219134 may be caught near the spin-down stall; a few more old K dwarfs with asteroseismic ages could map whether this stall happens at a single Rossby number or shifts with mass and metallicity.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reports the first asteroseismic detection and modeling of the K3 V planet host HD 219134 using four nights of Keck Planet Finder radial velocities. Twenty-five oscillation frequencies are extracted with the help of Gold deconvolution, and five independent evolutionary-modeling pipelines yield a consistent set of fundamental parameters: M = 0.763 ± 0.020 (stat) M_sun, R = 0.748 ± 0.007 (stat) R_sun, and an age of 10.151 ± 1.520 (stat) Gyr. The asteroseismic radius is 4% (4σ) smaller than the interferometric radius of 0.783 ± 0.005 R_sun from Elliott et al. (2025), a discrepancy the authors cannot explain after exploring interferometric systematics, atmospheric boundary conditions, mixing length, magnetic fields, and tidal heating. The paper uses the asteroseismic age together with an independent rotation period (41.3 ± 2.8 d) to test angular-momentum-loss models, claiming that weakened magnetic braking reproduces the observed rotation, and it also revises the masses and radii of the transiting super-Earths and analyzes oscillation amplitudes.

Significance. If the asteroseismic age and radius are reliable, this would be the first asteroseismic age for a main-sequence star cooler than 5000 K and a valuable benchmark for gyrochronology and angular-momentum-loss models at ages beyond the current open-cluster calibrators. The paper has notable strengths: five independent modeling pipelines with diverse input physics; explicit propagation of statistical and systematic uncertainties; a candid and detailed discussion of the radius discrepancy; and public release of the radial-velocity time series. The mode frequencies and the internal consistency across teams are valuable even if the final age is model-dependent. However, the central claim of a '10-Gyr spin-down clock' is currently conditional on the accuracy of 1D evolutionary models that fail a 4σ test against the best interferometric radius, and the paper itself concedes in §8 that all derived quantities are only conditional pending an explanation of this discrepancy.

major comments (3)
  1. [§4 and §8] The central age claim rests on evolutionary models whose accuracy is directly challenged by the 4σ radius discrepancy with the Elliott et al. (2025) interferometric radius. As the paper states in §4.2, the asteroseismic radius is not directly seismically constrained but is the radius of a 1D model whose interior matches the frequencies; the age is an output of the same models. A 4% radius failure is exactly the kind of model inaccuracy that could bias the age, especially for a main-sequence star whose age diagnostic (δν0,2) is sensitive to core structure and hence to the model's mass-radius relation. The manuscript should provide a concrete test showing that the age remains robust when the radius discrepancy is resolved, for example by repeating the modeling with the interferometric radius imposed as a constraint, or by identifying a physics change that removes the radius discrepancy and recomputing the age. Without such a test, the 10.151 Gyr age and all rotation-model conclusions built on it remain unsupported, as the paper's own §8 conditional language acknowledges.
  2. [§3.1] The choice of the Ligi et al. (2019) effective temperature (4854 ± 66 K) over the more precise Elliott et al. (2025) value (4678 ± 45 K) is justified only by 'maximis[ing] compatibility between inputs and stellar models.' This is a model-compatibility criterion, not an accuracy criterion. The paper notes that using the Elliott Teff makes the asteroseismic radius disagree with the Elliott interferometric radius by more than 3σ, but it does not report what mass, radius, and age would result from the Elliott Teff. Since Teff is a key classical constraint, the sensitivity of the quoted age to this choice must be quantified. If the age shifts by more than the stated 1.5 Gyr uncertainty when the alternative Teff is used, the quoted age is not robust.
  3. [§5.3 and Figure 9] The claim that weakened magnetic braking models 'accurately reproduce the observed rotation period' is not a discriminating test. Figure 9(b) explicitly shows that standard magnetic braking also reproduces HD 219134's rotation period at the asteroseismic age, and the text states that 'both the standard and weakened braking models adequately explain the current observations.' The star's derived Rossby number, Ro/Ro⊙ = 0.83 ± 0.07, is only 1σ below the critical value Rocrit/Ro⊙ = 0.93, so the data do not statistically establish that the star is in the weakened-braking regime. The gyrochronology implication is therefore weaker than the title suggests: the paper demonstrates consistency with one calibrated model family, not that the age anchors a distinct spin-down clock. The authors should either soften the interpretation or provide a quantitative metric (e.g., a model comparison such as ΔBIC or a posterior predictive check) showing that the weakened-braking model is preferred over standard braking.
minor comments (4)
  1. [Abstract and §8] The abstract states 'age of 10.151 ± 1.520 (stat) ± 0.810 (sys) Gyr' while Table 3 and §5 report age 10.2 ± 1.5 (stat) ± 1.0 (sys); the statistical uncertainty in Table 2 Team 1 is also listed as 1.5 Gyr. Please harmonize these numbers and state explicitly which systematic uncertainty estimate is adopted.
  2. [Table 1 and §2] The mode-lifetime assumption τ = 3 days is described as 'conservative,' but no test of sensitivity to τ is provided. Since frequency uncertainties enter the seismic modeling and hence the quoted age uncertainty, a short discussion of how σ(ν) changes for τ = 1–5 days would strengthen the error budget.
  3. [References] The reference 'Elliott et al., A. 2025, in preparation' is cited as the source of the key interferometric radius and Teff. A paper in preparation is not a stable reference for a central quantity; if the data are from a preprint or a published work, cite that source, or give the reader access to the measurement details.
  4. [§2] The Gold deconvolution implementation reference (M. Morháč et al. 2003) and the GitHub link are given, but the choice of regularization parameters and the number of iterations are not described. For reproducibility, please state these algorithmic details or point to the forthcoming paper in more specific terms.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the asteroseismic radius and age are genuine model predictions made without inputting the interferometric radius, and the rotation-model agreement is calibrated on independent clusters and field stars.

full rationale

The central derivation is not circular. The asteroseismic modeling inputs are the oscillation frequencies (Table 1), the Ligi Teff, and spectroscopic [Fe/H]; Section 3.1 states: 'We deliberately excluded the bolometric flux and radius as direct constraints, despite their high precision, to avoid potential inconsistencies.' The radius and age are therefore model outputs, not refits of the interferometric radius, and the 4-sigma comparison with the Elliott (2025) interferometric radius is a genuine external test. Section 4.2's admission that the quoted radii are 'the radii of 1D models possessing interior structures consistent with the asteroseismic constraints, rather than radii directly constrained using seismology' is a transparency caveat about model dependence, not a definitional reduction: the interferometric radius was never an input. The rotation-model test in Sections 5.2-5.3 calibrates fK, Rocrit, and alpha_ce on open clusters, Kepler field stars with asteroseismic ages, and the Sun; HD 219134 is not in that calibration sample, and the predicted Prot at the asteroseismic age is compared with the independently measured 41.3 +/- 2.8 d period. That is an out-of-sample prediction. The paper also honestly notes in Section 5.3 that standard magnetic braking 'adequately explain[s] the current observations' too, so the weakened-braking match is not unique; this is a limitation of test power, not circularity. Self-citations (e.g., Li et al. 2023 surface correction; Hon et al. 2024b; Ong & Basu 2019; van Saders et al. 2016; Saunders et al. 2024) are used as external calibrations or prior empirical relations and are not the load-bearing derivation: five independent modeling teams with varied input physics converge, and the rotation calibration uses published cluster ages and field-star ages. Finally, Section 8 explicitly concedes that all derived quantities are 'only conditional' pending an explanation of the radius discrepancy, showing that the claims are not being insulated from falsification. No step reduces, by equation or by self-citation, to its own inputs.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central results depend on standard stellar modeling parameters (α_MLT, Y_init) fitted to the oscillation frequencies, and on calibrated rotation model parameters (fK, Rocrit, αce) fitted to external cluster data. No new physical entities are introduced. The key non-standard input is the choice of the Ligi Teff over the Elliott Teff for modeling, which materially affects the derived radius and age.

free parameters (6)
  • Mixing length parameter α_MLT = α_MLT/α_MLT,⊙ ≈ 0.95 to 1.03 across teams (Team 1: 0.95±0.05)
    Treated as free parameter in several teams; affects the model radius and age.
  • Initial helium abundance Y_init = 0.27 ± 0.02
    Free parameter fitted in all teams; affects age and structure.
  • Rotation model fK = 5.655
    Calibrated to open cluster and field star rotation data; scales magnetic braking strength in Eq. 8.
  • Rotation model Rocrit/Ro⊙ = 0.93
    Calibrated Rossby threshold for weakened magnetic braking; affects whether the star is in the stalled spin-down regime.
  • Core-envelope coupling exponent αce = 3.8
    Calibrated to reproduce rotation evolution of clusters; controls core-envelope angular momentum exchange timescale.
  • Assumed mode lifetime τ = 3 days
    Assumed for frequency uncertainty estimation (Eq. 2); not independently measured.
assumptions (5)
  • domain assumption Stellar evolution models (MESA, GARSTEC, YREC) with standard microphysics (OPAL opacities, nuclear reaction rates) accurately represent the interior of HD 219134.
    Invoked throughout §3; the asteroseismic age and radius are outputs of these models.
  • standard math The asymptotic relation (Eq. 1) and the interpretation of échelle ridges as ℓ=0-3 modes are correct for this star.
    Used in §2 to identify the 25 modes; the 1 c/d sidelobe degeneracy makes this non-trivial.
  • ad hoc to paper The adopted Ligi et al. (2019) interferometric Teff (4854 K) is the appropriate modeling input, rather than the Elliott et al. (2025) value (4678 K).
    §3.1 chooses the Ligi value to 'maximise compatibility' with models; using Elliott Teff yields >3σ inconsistency with the Elliott radius.
  • domain assumption The weakened magnetic braking prescription (van Saders et al. 2016, Eq. 7) with Rossby threshold applies to K dwarfs at this age.
    Used in §5.2 to predict HD 219134's rotation period; the model parameters are calibrated on hotter stars and clusters.
  • ad hoc to paper Mode lifetime τ=3 days is a conservative estimate for frequency uncertainties.
    Used in Eq. 2 to compute σ(ν); the actual mode lifetime is not measured.

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Cite this review

Pith. "Pith review of K-dwarf Radius Inflation and a 10-Gyr Spin-down Clock Unveiled through Asteroseismology of HD 219134 from the Keck Planet Finder." pith.science (2026). https://pith.science/paper/EO2N76RV

@misc{pith2026250200971,
  author       = {Pith},
  title        = {Pith review of: K-dwarf Radius Inflation and a 10-Gyr Spin-down Clock Unveiled through Asteroseismology of HD 219134 from the Keck Planet Finder},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EO2N76RV}},
  note         = {Machine review of arXiv:2502.00971}
}
abstract

We present the first asteroseismic analysis of the K3\,V planet host HD~219134, based on four consecutive nights of radial velocities collected with the Keck Planet Finder. We applied Gold deconvolution to the power spectrum to disentangle modes from sidelobes in the spectral window, and extracted 25 mode frequencies with spherical degrees $0\leq\ell\leq3$. We derive the fundamental properties using five different evolutionary-modeling pipelines and report a mass of 0.763 $\pm$ 0.020 (stat) $\pm$ 0.007 (sys) M$_\odot$, a radius of 0.748 $\pm$ 0.007 (stat) $\pm$ 0.002 (sys) R$_\odot$, and an age of 10.151 $\pm$ 1.520 (stat) $\pm$ 0.810 (sys) Gyr. Compared to the interferometric radius 0.783 $\pm$ 0.005~R$_\odot$, the asteroseismic radius is 4\% smaller at the 4-$\sigma$ level -- a discrepancy not easily explained by known interferometric systematics, modeling assumptions on atmospheric boundary conditions and mixing lengths, magnetic fields, or tidal heating. HD~219134 is the first main-sequence star cooler than 5000~K with an asteroseismic age estimate and will serve as a critical calibration point for stellar spin-down relations. We show that existing calibrated prescriptions for angular momentum loss, incorporating weakened magnetic braking with asteroseismically constrained stellar parameters, accurately reproduce the observed rotation period. Additionally, we revised the masses and radii of the super-Earths in the system, which support their having Earth-like compositions. Finally, we confirm that the oscillation amplitude in radial velocity scales as $(L/M)^{1.5}$ in K dwarfs, in contrast to the $(L/M)^{0.7}$ relation observed in G dwarfs. These findings provide significant insights into the structure and angular momentum loss of K-type stars.

Figures

Figures reproduced from arXiv: 2502.00971 by the authors.

Figure 1
Figure 1. H–R diagram showing the footprint of asteroseis￾mology conducted using space-based photometry (e.g. W. J. Chaplin et al. 2015; T. L. Campante et al. 2015; M. N. Lund et al. 2016, 2017; A. Serenelli et al. 2017; J. Yu et al. 2018; Y. Li et al. 2020; E. Hatt et al. 2023; L. Gonz´alez-Cuesta et al. 2023; J. Zhou et al. 2024; M. N. Lund et al. 2024) and ground-based radial velocity (RV) measurements (e.g. H. Kjeldsen et… view at source ↗
Figure 2
Figure 2. Asteroseismic observations of HD 219134 over four consecutive nights using the Keck Planet Finder. Top: Radial-ve￾locity time series after filtering out signals with periods longer than 1.2 hours. Bottom: Power spectrum of the RV time series, weighted by the reported RV uncertainties, displaying a clear power excess around 4500 µHz. The inset shows the spectral window. 2. OSCILLATION FREQUENCIES We obtained approxim… view at source ↗
Figure 3
Figure 3. Echelle diagrams showing structures of regular fre- ´ quency spacings. Panel a: replicated ´echelle diagram of the original power spectrum. Panel b: ´echelle diagram of the power spectrum, deconvolved from the spectral window and then convolved with a 1 µHz width Gaussian filter for clar￾ity. Panel c: collapsed ´echelle diagram, summing the power along the y-axis of panel b. Panel d: same as panel b, but highlightin… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Stellar mass, radius and age derived from five in￾dependent asteroseismic modeling teams. The asteroseismic radius is compared against the interferometric radius based on an angular diameter measurement from A. Elliott et al. (2025). has a BT magnitude of 6.861 ± 0.015…
Figure 5
Figure 5. Figure 5: Stellar evolutionary models from zero-age to ter￾minal-age main sequence, calculated by Team 1, presented on the C–D diagram (top; δν0,2 vs. ∆ν) and the H–R dia￾gram (bottom). The models are color-coded by stellar age. The position of HD 219134 is marked by a star symb…
Figure 6
Figure 6. Figure 6: Probability contours of stellar properties presented in the space of radius, αMLT and Yinit, based on models calcu￾lated by Team 1. These contours are derived from constraints provided by asteroseismic observations. spheric boundary conditions and surface correction pr…
Figure 7
Figure 7. Figure 7: Time series of log R ′ HK measured by three different instruments spanning 20 years (HARPS, F. Motalebi et al. 2015; HIRES and APF, L. J. Rosenthal et al. 2021; H. Isaac￾son et al. 2024). ich & S. Soter 1966; F. Dai et al. 2024): τd ≈ 30 Gyr  Q′ ⋆ 106  M⋆/M⊙ Mp/M⊕ …
Figure 8
Figure 8. Figure 8: Calibrators of gyrochrones shown on the Prot–Teff diagram. The open cluster data include Pleiades (L. M. Rebull et al. 2016), Praesepe (S. T. Douglas et al. 2017, 2019), NGC 6811 (J. L. Curtis et al. 2019), NGC 752 (M. A. Agueros et al. ¨ 2018), NGC 6819 (S. Meibom et …
Figure 9
Figure 9. Figure 9: Rotation evolutionary models projected to older ages. These are calibrated based on asteroseismic field stars and open clusters hotter than 4500 K. The calibrators within the Teff ∈ [4650, 4900] K range are shown in triangles. The evolutionary tracks include models wit…
Figure 10
Figure 10. Figure 10: Chromospheric activity-age relation. The sample includes solar twins (D. Lorenzo-Oliveira et al. 2018), the Kepler asteroseismic sample (C. Karoff et al. 2013; T. S. Metcalfe et al. 2016; O. L. Creevey et al. 2017), and the TESS asteroseismic sample (D. Huber et al. 2…
Figure 11
Figure 11. Figure 11: The mass–radius diagram of exoplanets with Rp < 1.8 R⊕, using planet properties from the NASA Ex￾oplanet Archive (NASA Exoplanet Science Institute 2020). Ultra-short-period planets are defined following F. Dai et al. (2019), and are expected to be bare rocky cores who…
Figure 12
Figure 12. Figure 12: Oscillation amplitudes in radial velocity as a function of L/M (top) and Teff (bottom) for main-sequence dwarfs, color-coded by chromospheric activity. The power spectrum of HD 219134 appears to show a dip in the center of the oscillation region that is remark￾ably si…

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Forward citations

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Reference graph

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