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High-degree gravity modes in the single sdB star HD4539

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The K2 light curve of the sdB star HD 4539 contains g-modes of angular degree up to l=12, claimed as the first l=12 modes seen in an sdB star.

desk verdict Careful K2 analysis with robust l<=8 sequences, but the l=12 'first detection' claim outruns the evidence. read the letter →

arxiv 1908.03558 v1 pith:TDFESVSJ submitted 2019-08-09 astro-ph.SR

R. Silvotti , M. Uzundag , A.S. Baran , R.H. Ostensen , J.H. Telting , U. Heber , M.D. Reed , M. Vuckovic This is my paper · ORCID
classification astro-ph.SR
keywords subdwarfBstarsg-modepulsationsasteroseismologyK2photometryhigh-degreemodesperiodspacinghybridpulsatorHD4539
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

Using 78.7 days of K2 short-cadence photometry, this paper extracts 169 pulsation frequencies from the subdwarf B star HD 4539, 124 of them robust. The central claim is that the g-mode spectrum contains high-degree modes with angular degree up to at least $\ell=12$, and that this is the first time $\ell=12$ modes have been seen in an sdB star; sequences of consecutive modes with $\ell\ge4$ up to at least $\ell=8$ are clearly recognized. The identification works because the star shows clean, evenly spaced period sequences and no rotational splitting, so the asymptotic period-spacing relation can assign a degree to each sequence. If the claim holds, HD 4539 becomes an unusually rich laboratory for testing asteroseismic models of hot subdwarf interiors, and because a few p-modes are also present, it is a hybrid pulsator that could probe both the core and the envelope. The paper also redetermines the atmospheric parameters and uses radial velocities to exclude companions above a few Jupiter masses for periods below about 300 days.

What carries the argument

The load-bearing object is the asymptotic period-spacing relation for high-order g-modes, $\Delta P_\ell = \Delta\Pi / \sqrt{\ell(\ell+1)}$, which predicts that modes of angular degree $\ell$ are evenly spaced in period with a spacing that shrinks as $\ell$ grows. The paper derives a single reduced period spacing $\Delta\Pi\approx 362.76$ s from the clean $\ell=1$ and $\ell=2$ sequences and then uses that value to generate the expected spacings for higher $\ell$, converting observed sequences of evenly spaced periods in echelle diagrams into degree assignments. This relation, together with a two-step prewhitening frequency extraction at 5.4$\sigma$ significance (plus 4$\sigma$ candidates), is what carries the claim of high-degree modes up to $\ell=12$.

What would settle it

A direct test is to re-fit the crowded short-period region with all candidate degrees allowed simultaneously and check whether the assigned $\ell=12$ sequence (e.g., peaks near 1019.9, 968.0, 942.1, 877.0, 855.8, and 835.4 $\mu$Hz) aligns on the predicted $\Delta P_{12}\approx29$ s period spacing to within the ~0.15 $\mu$Hz frequency resolution; if those peaks instead align with $\ell=7$, 9, or 10 spacings, the first-$\ell=12$ claim fails. A longer-duration observation, for example with TESS, would also show whether the suspected $\ell=12$ modes remain coherent and continue the sequence at longer periods.

Watch

Extended reading notes

Core claim

HD 4539 is a long-period V1093 Her-type sdB pulsator whose K2 amplitude spectrum is unusually dense. Measured period spacings for the $\ell=1$ and $\ell=2$ sequences give a reduced period spacing $\Delta\Pi\approx 362.76$ s; assuming the asymptotic relation $\Delta P_\ell = \Delta\Pi / \sqrt{\ell(\ell+1)}$, modes with $\ell=4,5,6,7,8,9,10$, and $12$ are identified from their evenly spaced periods, with amplitudes down to a few ppm. The paper states this is the first detection of $\ell=12$ modes in an sdB star and the first clear recognition of sequences of consecutive modes with $\ell\ge4$ up to at least $\ell=8$; in the crowded short-period region, however, many peaks are also consistent with $\ell=7$, $9$, or $10$, and only about 29% of the identified modes receive a unique robust $\ell\le8$ assignment. The absence of rotational splitting points to a rotation period longer than the 78.7-day run, a pole-on orientation, or both. The star also shows a few p-modes, making it a hybrid pulsator close to the cool boundary of the g-mode instability strip.

Load-bearing premise

The highest-degree labels assume that every g-mode sequence follows the same asymptotic period-spacing law, and in the crowded short-period region a peak labelled $\ell=12$ can often be relabelled $\ell=7$, 9, or 10 without contradicting the data.

Editorial extensions

If this is right

  • If the $\ell=12$ identifications are correct, pulsation models for sdB stars must explain a g-mode excitation window reaching angular degree 12 at amplitudes of only a few ppm, adding a strong constraint on mode driving and damping.
  • Because HD 4539 also shows p-modes, the same star can in principle tie the period-spacing core diagnostic to envelope p-mode frequencies, making it a benchmark hybrid for seismic modeling.
  • The absence of rotational splitting and the stability of several single peaks imply a very slow rotation and/or a near pole-on orientation; this removes multiplet confusion and makes HD 4539 a clean object for verifying mode identifications in other stars.
  • The measured reduced period spacing and the overtone ranges for each degree provide direct input for future model fits that aim to recover the star's internal structure and evolutionary state.
  • The radial-velocity data exclude companions above a few Jupiter masses out to about 300 days, supporting a genuinely single-star status that is relevant to the question of how single sdB stars form.

Reading between the lines

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

  • High-degree g-modes at the few-ppm level may be common among bright, slowly rotating sdB pulsators; if so, HD 4539 could be the prototype of a class rather than an isolated case, and the same period-spacing search could be applied systematically to other K2 and TESS targets.
  • A quantitative model comparison using amplitudes and phases, not just period spacings, could resolve the $\ell=7/9/10/12$ degeneracies in the crowded region; this would be a natural follow-up that the paper does not perform.
  • The large number of high-degree modes implies strong horizontal wavenumber diversity; multi-band or spectroscopic observations could test the geometric cancellation predicted for $\ell=12$ modes, linking photometric and spectroscopic mode visibility.
  • If the absence of rotational splitting is due to a very long rotation period, the star offers a clean environment to search for slow effects such as magnetic frequency shifts or nonlinear mode interactions in future longer light curves.
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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

2 major / 4 minor

Summary. This paper presents a detailed asteroseismic analysis of the bright subdwarf B pulsator HD 4539 using 78.7 days of K2 short-cadence photometry, combined with new low- and high-resolution spectroscopy. The authors extract 169 pulsation frequencies (124 considered robust) and identify g-mode sequences with harmonic degrees l=1, 2, 4, 5, 6, 7, 8, 9, 10, and 12, claiming the first detection of l=12 g-modes in an sdB star. They also derive atmospheric parameters from spectroscopy (Teff=22,800±160 K, log g=5.20±0.02, log(N(He)/N(H))=-2.34±0.05) and SED fitting (Teff=23,470+650-210 K, R=0.26±0.01 Rsun, M=0.40±0.08 Msun), detect pulsation-induced radial velocity variations of ~150 m/s, and place upper limits on a potential companion mass. The paper argues that the absence of rotational splitting implies a very long rotation period and/or a very low inclination.

Significance. If the l=12 identification holds, this is a genuinely novel result: high-degree g-modes have rarely been seen in any pulsating star, and never before in an sdB star. The paper's strengths include a careful two-step prewhitening procedure with explicit detection thresholds, a strong internal consistency check between the l=1 and l=2 period spacings (reduced spacings of 362.75 s and 362.77 s), and complementary spectroscopic analyses that substantially improve the star's fundamental parameters. The claimed l≤8 sequences, many with unique labels, provide useful targets for future seismic modeling. However, the headline l=12 detection currently rests on mode identifications that are mostly tentative or ambiguous, and no statistical test is offered to show that the apparent ~29 s l=12 spacing could not arise by chance in a crowded period spectrum. Thus the paper's central new claim is not yet falsifiable, and the significance of the result depends on strengthening this evidence.

major comments (2)
  1. [Table 1; Section 2.3; Fig. 4] The claim, stated in the abstract and Section 5, that HD 4539 shows g-modes up to l=12 is not supported by unique identifications. In Table 1, the l=12 assignments are either marked 'TI' (e.g., f31, f41, f47, f59, f68, f83, f90, f105) or have alternative lower-degree solutions (e.g., f26, f48, f52, f53, f63, f64, f71, f73, f86, f92, f93, f95, f96, f98, f99, f100). Several of these are 4.0σ candidate detections shown in brackets (f52, f73, f86, f93, f98), which Section 2.1 states are 'considered only as candidates.' Section 2.3 explicitly acknowledges that the high concentration of peaks makes mode identification very difficult, and the Fig. 4 caption says the l=12 sequence is only partially recognized. The paper provides no quantitative test, such as a false-alarm probability or Monte Carlo simulation, of whether the expected l=12 spacing of ~29 s could arise by chance among the dense peaks in the short-period region. Without such a test, the first-detection claim is not falsifiable. Please either add a statistical uniqueness/chance-alignment analysis or downgrade the l=12 detection to a candidate interpretation throughout the paper.
  2. [Section 2.3, Eq. (1)] The paper applies the asymptotic period-spacing relation ΔP_l = ΔΠ / sqrt(l(l+1)) to modes with l=12 and radial order n≈37–69, where n is only ~3–6 times l. The asymptotic approximation strictly requires n≫l, and its accuracy for these relatively low-n, high-l modes is not demonstrated. A small deviation from the asymptotic spacing in this regime would break the sequence alignment and alter the identification. Please include a quantitative check of the asymptotic relation (e.g., against a stellar model or a higher-order asymptotic expansion) or discuss the expected size of the deviation and its effect on the l≥9 identifications.
minor comments (4)
  1. [Throughout] There are several typographical errors: 'treshold' (Section 2.1) should be 'threshold', 'wavelenghts' (Section 3) should be 'wavelengths', and 'Harps-N' (Section 4) should be 'HARPS-N'. The reference 'Vandenburg & Johnson 2014' should be 'Vanderburg & Johnson 2014'.
  2. [Fig. 4 caption] The sentence 'The high concentration of peaks at short periods implies that modes with high degree, up to at least l=12, must be present in this star' is an inference rather than a direct statement of what the figure shows; the caption should clarify which sequences are directly identified and which are inferred.
  3. [Section 2.3] The echelle diagrams in Fig. 5 show only identified modes; the paper should state how many of the 169 detected frequencies remain unidentified and whether those unidentified modes could host additional sequences, since this affects the completeness of the proposed identifications.
  4. [References] The citation 'Charpinet et al. 2019, A&A, submitted' is not a complete reference; please update it with the final publication status or remove it if it is not needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the high-degree mode identifications are tested against an asymptotic period-spacing ladder derived from the independently identified l=1 and l=2 sequences.

full rationale

The paper's central derivation is self-contained and non-circular. Section 2.3 first identifies the l=1 and l=2 sequences directly from evenly spaced periods (Delta P1=256.5 s, Delta P2=148.1 s), checks them against the asymptotic relation (both give Delta Pi about 362.76 s), and only then computes the expected spacings for l>2: 'from which we can compute the expected period spacing for the modes with higher degree.' The l=4-12 identifications in Table 1 and Figs 3-5 are matched to this a-priori ladder; the ladder is not fitted to the high-degree peaks, so the high-degree claim is not an input renamed as a prediction. The l=12 cases are admittedly tentative and degenerate (TI flags and alternative l=7/9/10 solutions), and Fig. 4 says identification is 'very difficult' in the dense short-period region; this is a statistical-confidence/robustness limitation, not circularity. Self-citations (Baran et al. 2015 for the 5.4-sigma K2 false-alarm threshold; Telting et al. 2014a for earlier l=8 detections) are independent calibration/context results and are not load-bearing for the l=12 claim. No equation or fitted parameter is recycled as a derived result.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard asteroseismic scalings and on the measured ΔΠ from the same star's low-degree modes. The listed free parameters are fitted thresholds or scaling quantities used for identification; no new physical entities are introduced.

free parameters (3)
  • Reduced period spacing ΔΠ = 362.76 s (mean of 362.75 and 362.77 s from l=1 and l=2)
    Measured from the l=1 and l=2 period spacings (256.5 s and 148.1 s) of the same star and used to predict ΔP_l for l>2. Internal consistency check: ratio 256.5/148.1 ≈ sqrt(3). This is a calibration quantity for the degree assignments.
  • Detection thresholds (5.4σ, 4.0σ) = 5.4σ for robust detections, 4.0σ for candidate detections
    Chosen thresholds following Baran et al. (2015); they determine which peaks enter Table 1 and thus affect the mode list, but they are standard and not fitted to the central claim.
  • Atmospheric parameters (Teff, log g, He/H) = 22,800 K, 5.20, -2.34
    Fitted from three ALFOSC spectra with an LTE grid; used for the SED fit and radius/mass determination. The paper acknowledges formal errors only, with systematics potentially an order of magnitude larger.
assumptions (5)
  • standard math For high-order g-modes in the asymptotic limit, the period spacing is ΔP_l = ΔΠ / sqrt(l(l+1)) with constant ΔΠ.
    Invoked in Section 2.3 to identify sequences and assign degrees. Standard asteroseismic theory for sdB stars.
  • domain assumption The evenly spaced frequency sequences observed are consecutive overtones n=1,2,3,... with no significant mode trapping or missing modes affecting the spacing in the identified sequences.
    Section 2.3 and Figs. 2-4: mode identification assumes the sequences are complete enough to assign n; the paper notes no clear trapping in l=1 and l=2 sequences, but lower-order modes may be missing.
  • domain assumption The 5.4σ threshold corresponds to a 95% confidence level for K2 data (Baran et al. 2015).
    Section 2.1: used as the detection criterion for the 124 robust frequencies. This calibration is adopted from prior work by one of the authors.
  • domain assumption Rotation splitting is absent or unresolved, so each peak in the amplitude spectrum corresponds to a single (l, m=0) mode and not an unresolved multiplet.
    Section 2.2: the interpretation of single peaks and the lack of multiplets underpins the period-spacing identification; the paper argues for a very long rotation period or pole-on geometry.
  • domain assumption LTE model atmospheres (Heber et al. 2000 grid) are adequate for the atmospheric parameter determination.
    Section 3: the authors note systematic errors from model assumptions can be an order of magnitude larger than the formal fitting errors.

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Cite this review

Pith. "Pith review of High-degree gravity modes in the single sdB star HD4539." pith.science (2026). https://pith.science/paper/TDFESVSJ

@misc{pith2026190803558,
  author       = {Pith},
  title        = {Pith review of: High-degree gravity modes in the single sdB star HD4539},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TDFESVSJ}},
  note         = {Machine review of arXiv:1908.03558}
}
read the original abstract

HD4539 (alias PG0044+097 or EPIC220641886) is a bright (V=10.2) long-period V1093 Her-type subdwarf B (sdB) pulsating star that was observed by the Kepler spacecraft in its secondary (K2) mission. We use the K2 light curve (78.7 days) to extract 169 pulsation frequencies, 124 with a robust detection. Most of these frequencies are found in the low-frequency region typical of gravity (g-)modes, but some higher frequencies corresponding to pressure (p-)modes are also detected. Therefore HD4539 is a hybrid pulsator and both the deep and surface layers of the star can potentially be probed through asteroseismology. The lack of any frequency splitting in its amplitude spectrum suggests that HD4539 has a rotation period longer than the K2 run and/or that it is seen pole-on. From asymptotic period spacing we see many high-degree modes, up to l=12, in the spectrum of HD4539, with amplitudes as low as a few ppm. A large fraction of these modes can be identified and for ~29% of them we obtain a unique and robust identification corresponding to l<=8. Our study includes also a new determination of the atmospheric parameters of the star. From low-resolution spectroscopy we obtain Teff=22,800+-160 K, logg=5.20+-0.02 and log(N(He)/N(H))=-2.34+-0.05. By fitting the SED we obtain Teff=23,470+650-210 K, R_star=0.26+-0.01 Rsun and M_star=0.40+-0.08 Msun. Moreover, from 11 high-resolution spectra we see the radial velocity variations caused by the stellar pulsations, with amplitudes of ~150~m/s for the main modes, and we can exclude the presence of a companion with a minimum mass higher than a few Jupiter masses for orbital periods below ~300 days.

Figures

Figures reproduced from arXiv: 1908.03558 by the authors.

Figure 1
Figure 1. The 2-step procedure that we used to extract the pul￾sation frequencies. Top panel: the main frequencies (those with an amplitude higher than 5.4 σ, 124 in total) are extracted from the amplitude spectrum of the data. Bottom panel: once the 124 main frequencies have been subtracted from the data, secondary frequencies (45 in total, those with an amplitude between 4 and 5.4 σ) are extracted from the amplitude spectru… view at source ↗
Figure 2
Figure 2. Period spacing for the modes with l=1,2: both se￾quences are well defined [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Period spacing for the modes with 4≤l≤8. Note the clean sequence of modes with l=4 (between ∼2260 and ∼3230 s), l=5 (∼2050–2450 s, with 5 consecutive modes), l=6 (∼1680– 2240 s, with at least 9 consecutive modes) and l=8 (∼1550– 1850 s). The modes with l=7 are not active in this region and can be seen at shorter periods in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: Echelle diagrams of the modes with l=1,2,4,5,6,7,8,9,10,12. The size of each point is proportional to the amplitude of that mode. An offset of 105 s was applied to the upper right panel (l=2) just for clarity. MNRAS 000, 1–13 (2019) [PITH_FULL_IMAGE:figures/full_fig_p…
Figure 6
Figure 6. Figure 6: Summary of all identified g-modes. Dotted segments correspond to the modes with only 50% confidence level (reported in brackets in [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Sliding FTs of some of the main pulsation modes. From from top left to bottom right f163, f160, f157 and f154 (l=1); f132 and f130 (l=2); f109 (l=6); f6-f11 and f1 (p-modes). We see that some modes, like f130, f132 and partially f163 are stable both in frequency and am…
Figure 8
Figure 8. Figure 8: Atmospheric parameters of HD 4539 as obtained from the sum of 3 ALFOSC spectra. lar diameter Θ= 6.38+0.06 −0.10 ×10−11 rad and zero interstel￾lar reddening (E(B–V)<0.009). If we combine the angular diameter with the Gaia DR2 parallax $=5.384±0.132 mas (or d=185.7+4.7 …
Figure 9
Figure 9. Figure 9: Spectral energy distribution of HD 4539. Colored data points represent the filter-averaged fluxes, which were converted from observed magnitudes (the filter widths are indicated by dashed horizontal lines), while the gray solid line represents a synthetic spectrum comp…
Figure 10
Figure 10. Figure 10: Upper panel: radial velocities of HD 4539 and best sinusoidal fit using the 3 highest-amplitude pulsation frequencies from [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: Upper limits to the mass of a hypothetical companion to HD 4539 as a function of orbital period. The upper panel is obtained using the RV data (upper panel of [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]

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Works this paper leans on

50 extracted references · 50 canonical work pages

  1. [1]

    Baran A., Pigulski A., Kozie D., Og oza W., Silvotti R., Zo a S., 2005, , 360, 737

    work page 2005

  2. [2]

    Baran A., Koen C., Pokrzywka B., 2015, , 448, L16

    work page 2015

  3. [3]

    Baschek B., Sargent W.\,L.\,W, Searle L., 1972, , 173, 611

    work page 1972

  4. [4]

    et al., 2014, , 569, A123

    Bloemen S. et al., 2014, , 569, A123

    work page 2014

  5. [5]

    et al., 2010, Science, 327, 977

    Borucki W.\,J. et al., 2010, Science, 327, 977

    work page 2010

  6. [6]

    et al., 2007, , 374, 664

    Cenarro A.\,J. et al., 2007, , 374, 664

    work page 2007

  7. [7]

    Charpinet S., Fontaine G., Brassard P., Dorman B., 1996, , 471, L103

    work page 1996

  8. [8]

    Charpinet S., Fontaine G., Brassard P., Chayer P., 1997, , 483, L123

    work page 1997

Show all 50 references
  1. [9]

    Charpinet S., Brassard P., Van Grootel V., Fontaine G., 2014, ASPC, 481, 179

    2014

  2. [10]

    et al., 2013, VizieR Online Data Catalog, 2328

    Cutri R.\,M. et al., 2013, VizieR Online Data Catalog, 2328

    2013

  3. [11]

    Charpinet S., Giammichele N., Zong W., Van Grootel V., Brassard P., Fontaine G., 2018, Open Astronomy, 27, 112

    2018

  4. [12]

    et al., 2019, , submitted

    Charpinet S. et al., 2019, , submitted

    2019

  5. [13]

    Kjeldsen, T.\,R

    Dziembowski W.\,A., Balona L.\,A., Goupil M.-J., Pamyatnykh A.\,A., 1998, ``The First MONS Workshop: Science with a Small Space Telescope'', Eds.: H. Kjeldsen, T.\,R. Bedding, Aarhus Universitet, p. 127

    1998

  6. [14]

    ESA, 1997, The Hipparcos and Tycho Catalogues, ESA SP-1200

    1997

  7. [15]

    Fontaine G., Brassard P., Charpinet S., Green E.\,M., Chayer P., Bill \`e res M., Randall S.\,K., 2003, , 597, 518

    2003

  8. [16]

    Fontaine G., Brassard P., Charpinet S., Green E.\,M., Randall S.\,K., Van Grootel V., 2012, , 539, A12

    2012

  9. [17]

    Gaia Collaboration et al., 2018, , 616, A1

    2018

  10. [18]

    Geier S., Heber U., 2012, , 543, A149

    2012

  11. [19]

    et al., 2010, PASP, 122, 131

    Gilliland R.\,L. et al., 2010, PASP, 122, 131

    2010

  12. [20]

    et al., 2003, , 583, L31

    Green E.\,M. et al., 2003, , 583, L31

    2003

  13. [21]

    Heber U., Langhans G., 1986, ESASP, 263, 279

    1986

  14. [22]

    Heber U., Reid I.\,N., Werner K., 2000, , 363, 198

    2000

  15. [23]

    Heber U., 2016, PASP, 128, 966

    2016

  16. [24]

    Heber U., Irrgang A., Schaffenroth J., 2018, Open Astronomy, 27, 35

    2018

  17. [25]

    et al., 2014, PASP, 126, 398

    Howell S.\,B. et al., 2014, PASP, 126, 398

    2014

  18. [26]

    Jeffery C.S., Saio H., 2006, 371, 659

    2006

  19. [27]

    Kern J.\,W., Reed M.\,D., Baran A.\,S., stensen R.\,H.,Telting J.\,H., 2017, , 465, 1057

    2017

  20. [28]

    Kern J.\,W., Reed M.\,D., Baran A.\,S., Telting J.\,H., stensen R.\,H., 2018, , 474, 4709

    2018

  21. [29]

    Kilkenny D., Koen C., O'Donoghue D., Stobie R.\,S., 1997, , 285, 640

    1997

  22. [30]

    et al., 2012, , 542, A24

    Mantegazza L. et al., 2012, , 542, A24

    2012

  23. [31]

    Ochsenbein F., Bauer P., Marcout J., 2000, , 143, 23O

    2000

  24. [32]

    et al., 2010, , 513, A6

    stensen R.\,H. et al., 2010, , 513, A6

    2010

  25. [33]

    et al., 2011, , 414, 2860

    stensen R.\,H. et al., 2011, , 414, 2860

    2011

  26. [34]

    stensen R.\,H., Reed M.\,D., Baran A.\,S., Telting J.\,H., 2014, , 564, L14

    2014

  27. [35]

    Pesnell W.\,D., 1985, , 292, 238

    1985

  28. [36]

    Randall S.\,K., Fontaine G., Brassard P., Bergeron, P., 2005, , 161, 456

    2005

  29. [37]

    et al., 2011, , 414, 2885

    Reed M.\,D. et al., 2011, , 414, 2885

    2011

  30. [38]

    Foster H., Telting J.\,H., stensen R.\,H., Farris L.\,H., Oreiro R., Baran A.\,S., 2014, , 440, 3809

    Reed M.\,D. Foster H., Telting J.\,H., stensen R.\,H., Farris L.\,H., Oreiro R., Baran A.\,S., 2014, , 440, 3809

    2014

  31. [39]

    et al., 2018, Open Astronomy, 27, 157

    Reed M.\,D. et al., 2018, Open Astronomy, 27, 157

    2018

  32. [40]

    Saffer R.\,A., Bergeron P., Koester D., Liebert J., 1994, , 432, 351

    1994

  33. [41]

    Sale S.\,E., Schoenaers C., Lynas-Gray A.\,E., 2008, ASPC, 392, 109

    2008

  34. [42]

    Schindewolf M., N\'emeth, P., Heber U., Battich T., Miller Bertolami M.\,M., Irrgang A., Latour M., 2018, , 620, A36

    2018

  35. [43]

    Schneider D., Irrgang A., Heber U., Nieva, M.\,F., Przybilla N., 2018, , 618, A86

    2018

  36. [44]

    in Asteroseismology, 151, 67

    Schoenaers C., Lynas-Gray A.\,E., 2007, Comm. in Asteroseismology, 151, 67

    2007

  37. [45]

    Schuh S., Huber J., Dreizler S., Heber U., O'Toole S.\,J., Green E.\,M., Fontaine G., 2006, , 445, L31

    2006

  38. [46]

    Skrutskie M.\,F. et al. 2006, , 131, 1163

    2006

  39. [47]

    et al., 2014a, , 570, A129

    Telting J.\,H. et al., 2014a, , 570, A129

  40. [48]

    Telting J.\,H., stensen R.\,H., Reed M., Farris L., Baran A., Oreiro R., O'Toole S., 2014b, ASPC, 481, 287

  41. [49]

    Vandenburg A., Johnson J.\,A., 2014, , 126, 948

    2014

  42. [50]

    Zong W., Charpinet S., Fu J.-N., Vauclair G., Niu J.-S., Su J., 2018, , 853, 98

    2018

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