Gravity modes and potential evidence for Rossby Waves in late O-type supergiants

Aldana Alberici Adam; Alejandra Christen; Alejandro H. Corsico; Alex Lobel; Gunther F. Avila Marin; Julieta Sanchez Arias; Lydia S. Cidale; Michaela Kraus; Suryani Guha

Gravity modes and potential evidence for Rossby Waves in late O-type supergiants

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read TESS light curves of three late O-type supergiants reveal rotationally split g-modes and candidate Rossby waves.

desk verdict Careful TESS analysis of three O supergiants, but the Rossby-wave interpretation rests on a frequency spacing that could equally be a spot or harmonic series. read the letter →

arxiv 2608.11010 v2 pith:JGUTQAZJ submitted 2026-08-11 astro-ph.SR

Lydia S. Cidale , Alejandra Christen , Aldana Alberici Adam , Suryani Guha , Alex Lobel , Gunther F. Avila Marin , Michaela Kraus , Alejandro H. Corsico

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Julieta Sanchez Arias

This is my paper · ORCID

classification astro-ph.SR

keywords RossbywavesO-typesupergiantsstellarpulsationsg-modesrotationalsplittingTESSphotometryasteroseismologyrednoise

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports that the low-frequency variability seen in TESS light curves of three late O-type supergiants—HD 188001, HD 192639, and HD 195592—is not just stochastic red noise but contains coherent, rotation-related oscillations. The periodograms show a nearly constant frequency spacing in each star, which the authors interpret as rotational splitting of g-mode pulsations (mostly $\ell=1$ or $\ell=2$). Using the splitting formula $\Delta f = m(1-C_\ell) f_{\rm rot}$, they derive rotation periods of roughly 14.5, 16.1, and 6.1 days, and they find that the residual independent frequencies are consistent with the dispersion relation of global Rossby waves, $\sigma = -2m\Omega/[\ell(\ell+1)] + m\Omega$. If this interpretation survives longer baselines, it would mean that Rossby waves are excited in evolved massive stars and that part of the broadband 'red noise' seen in such stars is actually made of discrete rotationally driven modes.

What carries the argument

The load-bearing identities are the rotational-splitting formula $\Delta f = m(1-C_\ell) f_{\rm rot}$ (with $C_\ell=0.166$ for two stars and $0.5$ for the third) and the inertial-frame Rossby dispersion relation $\sigma = -2m\Omega/[\ell(\ell+1)] + m\Omega$, where Rossby waves are large-scale waves in a rotating fluid whose restoring force is the Coriolis force. The splitting formula converts a measured constant frequency spacing into a rotation frequency, and the dispersion relation is used to match residual observed frequencies to specific $(\ell,m)$ Rossby modes through a graphical comparison. The period search combines a generalised Lomb-Scargle periodogram with a weighted wavelet Z-transform, followed by iterative pre-whitening to isolate significant frequencies, and the g-mode identifications are anchored by stellar evolution models and adiabatic pulsation calculations.

What would settle it

A direct measurement of the rotation period of HD 188001, HD 192639, or HD 195592—from time-resolved spectroscopy of line-profile variations, from a longer TESS baseline that resolves the frequency spacing well beyond $1.5/\Delta T$, or from an independent asteroseismic analysis—that disagrees with the 14.5, 16.1, or 6.1 day values would falsify the rotational-splitting interpretation and, with it, the Rossby-mode identifications that depend on the derived rotation frequency.

Watch

Extended reading notes

Core claim

The authors' central claim is that each of the three stars shows an approximately uniform frequency spacing in its TESS periodogram, which they identify as the rotational splitting of g-mode oscillations (mostly $\ell=1$ or $\ell=2$), and that after accounting for these modes plus harmonics and combination frequencies, the remaining independent frequencies match the inertial-frame Rossby-wave dispersion relation $\sigma = -2m\Omega/[\ell(\ell+1)] + m\Omega$ for modes such as $(\ell,m)=(3,2)$, $(3,3)$, and $(5,4)$. From the splitting they derive rotation periods of $14.5\pm4.2$ days for HD 188001, $16.1\pm2.6$ days for HD 192639, and $6.1\pm1.0$ days for HD 195592, with inclination angles near $90^\circ$ for the first two and about $20^\circ$ for the third. They further argue that the co-existence of g-modes and Rossby candidates, plus a pattern of frequencies at integer and half-integer multiples of the splitting, points to rotational modulation and suggests that Rossby waves may contribute to the red-noise component observed in massive supergiants.

Load-bearing premise

The load-bearing premise is that the nearly constant frequency spacing seen in each star's periodogram is rotational splitting of g-modes, rather than a corotating spot, binary motion, or an instrumental artifact; if that premise fails, the rotation periods and every Rossby-mode identification built on them collapse.

Editorial extensions

If this is right

If the frequency spacing is rotational splitting, the derived rotation periods ($14.5$, $16.1$, and $6.1$ days) and inclination angles give direct photometric rotation constraints for these stars.
The residual frequencies matching the Rossby dispersion relation imply that the low-frequency variability of O-type supergiants is not purely stochastic; part of it is a set of discrete, rotationally driven modes, which could contribute to the observed red noise.
The g-modes that fit the adopted stellar models are predicted by late main-sequence evolutionary tracks, so these 'supergiants' may still be core hydrogen-burning stars whose supergiant appearance is set by their winds.
A longer TESS baseline, with frequency resolution better than $1.5/\Delta T$, would test whether the equally spaced frequency sets and the Rossby candidates persist and sharpen.

Reading between the lines

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

If Rossby waves are truly excited in these stars, they could act as a mechanism for angular momentum transport in the near-surface layers of massive stars, a process the paper mentions but does not model.
Applying the same analysis to a larger TESS sample of late O-type and B-type supergiants would test whether the constant-spacing pattern and Rossby candidates are a general property of evolved massive stars rather than a coincidence in three objects.
Spectroscopic follow-up targeting line-profile variability at the predicted Rossby frequencies could independently confirm the modes, because Rossby waves perturb surface temperature and pressure.
The HD 188001 result is the least secure because its spacing ($0.0576$ d$^{-1}$) is only marginally above the restrictive Rayleigh resolution ($0.055$ d$^{-1}$); an independent measurement of its rotation period would settle whether the quoted $14.5$ day period is real.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Here's my take. This is an honest, careful observational study of three late O supergiants with TESS light curves. What's new: first systematic frequency decomposition of these stars in TESS, with period lists from two complementary methods, phase-folded diagrams, and g-mode identification against LPCODE models. The authors are appropriately cautious, calling the Rossby evidence 'potential' and 'tentative' throughout, and they do list alternative explanations in the discussion. That intellectual honesty is real.

The soft spot is the load-bearing interpretation. The entire Rossby identification depends on treating the fitted equal spacing Δf as rotational splitting via Eq. (5). But the authors' own tables show that essentially all detected frequencies are integer or half-integer multiples of Δf. That is exactly the pattern produced by a long-lived co-rotating spot or a harmonic series, and the paper does not quantitatively exclude those alternatives. For HD 188001, the spacing is barely resolved, just above the 1.5/ΔT criterion. For HD 192639, there is an internal inconsistency: with R=19.8 R☉ and P_rot=16.1 d, the equatorial velocity is about 62 km/s, but the adopted vsini is 82 km/s, so the star cannot appear equator-on (i≈90°) as listed. That error undercuts the r-mode identification for that star. Throughout, there is no false-alarm probability for the r-mode matches, and the S/N threshold was lowered to 4 to keep candidates alive.

None of this makes the paper worthless. The frequency lists and g-mode matches are useful, and the red-noise connection is plausible. But the Rossby result is not independently established. If the spacing is not rotational splitting, all three Rossby identifications lose their basis.

I would send this to peer review: the observational work deserves referee scrutiny, and the authors need to be pushed on the statistical front and on the spot/harmonic alternative. The paper is a solid candidate after major revision, not as is. For my own work, I would not cite the Rossby detection yet; I might cite the frequency lists. I would bring it to reading group as a case study in how a tentative detection can be vulnerable to interpretation.

Referee Report

4 major / 4 minor

Summary. The paper analyses TESS light curves of three late O-type supergiants (HD 188001, HD 192639, and HD 195592) using generalized Lomb-Scargle periodograms and weighted wavelet Z-transforms, with iterative pre-whitening and Monte Carlo frequency uncertainties. The authors identify a set of low-frequency peaks in each star, note an approximately constant frequency spacing Δf, interpret that spacing as rotational splitting via Eq. (5), derive rotation periods, classify most frequencies as l=1 or l=2 g-modes with the help of LPCODE/LP-PUL models, and then identify residual frequencies as Rossby-wave candidates using the dispersion relation Eq. (4). The central claim is that the detected evenly spaced frequency sets are rotationally split g-modes and that the residual pattern is consistent with Rossby waves, which would make the derived rotation periods and inclination angles physically meaningful.

Significance. If the central claim were robust, the paper would provide the first systematic evidence for Rossby waves in late O-type supergiants and would connect the low-frequency photometric variability of these stars to coherent rotation-driven oscillations rather than purely stochastic red noise. The authors use two complementary period-search methods, explicitly quote Monte Carlo frequency uncertainties, exploit multi-sector TESS observations spanning about five years, and compare against non-rotating LPCODE/LP-PUL pulsation models; they also repeatedly use cautious phrasing such as 'potential evidence' and 'tentative'. These are genuine strengths. However, the identification chain from Δf to f_rot to the r-mode assignments is not yet statistically or physically secured, and the derived parameters contain an internal inconsistency for HD 192639. The result is therefore plausible but not established at the level needed for its strong conclusions.

major comments (4)

[§5.2, Table 3] The rotation solution for HD 192639 is internally inconsistent: with R=19.8 R_sun and P_rot=16.1 d, the equatorial velocity is 2πR/P ≈62 km/s, which is less than the adopted vsin i=82 km/s. Since sin i ≤1, this is impossible at any inclination, yet Table 3 lists i≈90°. The r-mode identifications for this star, built on f_rot=0.0622 d^-1 from Eq. (5), therefore cannot be considered supported by the current analysis.
[§5.1, Eq. (5)] The load-bearing assumption that the fitted spacing Δf is rotational splitting is not tested against the alternatives listed in §6. Tables D.1 and D.2 show that essentially all detected frequencies are integer or half-integer multiples of Δf; a long-lived co-rotating spot or a harmonic series produces the same pattern without invoking g-mode splitting. For HD 188001, Δf=0.0576 d^-1 is only comparable to 1.5/ΔT=0.055 d^-1, so the 'constant spacing' is barely resolved. Because f_rot is derived from Δf via Eq. (5) and enters every r-mode identification through Eq. (4), this ambiguity is load-bearing for the central claim.
[§6, Figs. 4, 7, 10] The r-mode matches are not an independent confirmation: for high ℓ, Eq. (4) reduces to σ≈mΩ = mΔf once f_rot is set by Δf, so the graphical agreement in Figs. 4, 7, and 10 partly reproduces the same fitted spacing. No false-alarm probability is given for the matches, and several candidate frequencies are detected in only one sector (e.g., f2 for HD 188001 in sector 14, Table C.1). A quantitative test, such as a Monte Carlo false-alarm estimate over the searched (ℓ,m) grid, is needed before the 'potential evidence' can be distinguished from chance alignment.
[§3.1] The detection threshold was lowered to S/N≥4 because the recommended TESS threshold of S/N≥5 could exclude low-frequency RWs. While this is transparently stated, no estimate is given of how many spurious frequencies this admits, and the residual noise window is a broad 5 d^-1. Given that several r-mode candidates are single-sector detections and the rotation periods have large uncertainties, the significance of the r-mode identifications should be quantified under the adopted threshold.

minor comments (4)

[Abstract] The abstract names the third target as HD 159952, while the body and tables consistently use HD 195592.
[§4.1] The term 'thermodes' is introduced without a definition; its relationship to toroidal modes should be clarified at first use.
[Table D.2] The note says 'The obtained period is in column 4', but in Table D.2 the period appears in column 5; the column numbering in the note should be corrected.
[§5.2 and Table D.1] The text refers to 'f15' as identified in Table D.1, but Table D.1 does not use the f_i labels from Table C.2; aligning the row labels between the two tables would improve readability.

Circularity Check

2 steps flagged · score 6.0 of 10

Rossby-mode 'matches' are constructed from the fitted spacing Δf: f_rot is derived from Δf via Eq. (5), and Eq. (4) then returns multiples of the same Δf that the tables already use to describe the observed frequencies; the agreement is a restatement of the fit, not an independent test.

fitted input called prediction [Sect. 5.1, Eq. (5), and Fig. 4]
"Assuming that the observed frequency separation, Δf, arises from rotational splitting, we estimated the rotational frequency using the relation, Δf=m(1−C_l) f_rot ... We obtained f_rot =0.0691 d−1 ... The search for potential RWs was done using Ω=2π f_rot in Eq. (4) for various values of ℓ and |m|≤ℓ."

Δf is not independently predicted; it is obtained by mean-square optimization over the observed frequencies. f_rot is then algebraically fixed by Δf through Eq. (5) with an assumed splitting coefficient, and Eq. (4) converts f_rot into a grid of candidate r-mode frequencies. Because Eq. (4) for high ℓ reduces to σ≈mΩ, the candidate grid is essentially integer multiples of the same Δf (or rational multiples for the specific ℓ,m chosen). The observed frequencies are then compared graphically with this grid and pronounced consistent; but the grid was constructed from the very spacing that was fitted to those frequencies, so the agreement is a restatement of the fit rather than an independent prediction of the Rossby interpretation.
self definitional [Sect. 5.2 and Table D.1 note; also Table D.2 note]
"all the observed frequencies appear to be organised as integers or half-integer multiples of the derived frequency separation, which is also indicative of an underlying rotational modulation. ... The identified g modes appear to cluster around integer and half-integer multiplets of Δf (f_e = m/2 Δf with m=1 to 30 ...)."

In Tables D.1 and D.2 the 'theoretical' comparison column is literally f_e = m/2 Δf, the half-integer grid to which the observed frequencies have already been shown to belong. The r-mode labels (ℓ,m) are assigned to entries of this same grid via Eq. (4) after choosing f_rot from Δf. Thus the claimed consistency with the Rossby dispersion relation is established by construction: any observed frequency near a half-integer multiple of the fitted Δf can be assigned some (ℓ,m). The dispersion relation itself is standard external physics, but it is not used here to predict new frequencies that are independent of the fitted spacing.

full rationale

The core r-mode identification is partially circular. The paper fits an approximately constant frequency spacing Δf directly from the observed periodograms, derives the stellar rotation frequency f_rot through the assumed splitting relation Eq. (5), and then tests the Rossby dispersion relation Eq. (4) using Ω=2π f_rot. Since Eq. (4) with high ℓ reduces to σ≈mΩ, the predicted r-mode frequencies are multiples of the same Δf that was fitted to the data. The paper's own tables reinforce this: the observed frequencies cluster around integer and half-integer multiples of Δf, and the 'theoretical' frequencies are written as f_e=m/2 Δf. Matching these two grids is therefore not an independent confirmation; it is a relabeling of the fitted spacing. The g-mode identifications, by contrast, retain independent content: the LPCODE/LP-PUL frequencies are computed from stellar parameters and evolutionary tracks without fitting to the observed modes, and matching some observed frequencies within the Rayleigh resolution is a real (if not unique) test. Likewise, the Rossby dispersion relation itself is standard external physics from Haurwitz, Papaloizou & Pringle, and Provost et al., and the paper's methodological self-citations (e.g., Alberici Adam et al. 2023 for period-search recommendations, and the Kourniotis et al. 2025 comparison) are not load-bearing for the central claim. However, the specific r-mode candidates in Figs. 4, 7, and 10 and Tables D.1–D.2 reduce by construction to the fitted Δf, so the 'potential evidence for Rossby waves' is not independent of its input. The internal inconsistency noted for HD 192639 (v_rot≈62 km/s below the adopted vsini=82 km/s while listing i≈90°) is a correctness concern rather than a circularity, but it compounds the fragility of the r-mode interpretation. Overall, partial circularity in the central Rossby identification warrants a score of 6.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim relies on a fitted frequency spacing, an assumed splitting coefficient, selected evolutionary tracks, and a lowered detection threshold. No new physical entities are introduced; all wave types are established phenomena. The main burden is that the r-mode frequencies are computed from the same fitted spacing used to identify them.

free parameters (7)

Delta f (HD 188001) = 0.0576 d^-1
Frequency spacing derived by mean-square optimization over selected observed frequencies in Sect 5.1; used to derive f_rot and to identify harmonic/multiplet structure.
Delta f (HD 192639) = 0.05185 d^-1
Same mean-square fitting procedure in Sect 5.2; used to derive f_rot and to label g-mode and r-mode candidates.
Delta f (HD 195592) = 0.08185 d^-1
Same mean-square fitting procedure in Sect 5.3; used to derive f_rot and to label g-mode and r-mode candidates.
f_rot (HD 188001, HD 192639, HD 195592) = 0.0691, 0.0622, 0.1637 d^-1
Derived from the fitted Delta f through Eq. 5 with assumed C_l; carries the uncertainty of the Delta f fit and the mode-degree choice.
Splitting coefficient C_l = 0.166 for HD 188001 and HD 192639; 0.5 for HD 195592
Assumed mode degree for the rotational splitting: C_l=0.166 (l=2) and C_l=0.5 (l=1); choosing a different degree changes f_rot and all Rossby predictions.
Evolutionary track initial mass = 50, 40, 30 Msun for HD 188001, HD 192639, HD 195592
Chosen by matching the stars' HR positions to LPCODE tracks (Fig. 1); the g-mode frequency grid used for identification depends on this choice.
S/N detection threshold = 4
Adopted instead of the recommended 5 to retain low-frequency r-mode candidates (Sect 3.1); a hand-chosen selection that affects which frequencies enter the analysis.

assumptions (5)

domain assumption Uniform rotation is assumed for the Rossby dispersion relation and the rotational splitting interpretation.
Used before Eq. 4 and in Sect 5; differential rotation would shift r-mode frequencies and change the splitting pattern.
domain assumption g-mode eigenfrequencies can be computed from non-rotating LPCODE models, with rotation treated only as a first-order split.
Sect 6 states (Omega/Omega_g)^2 is 1-12%; for HD 195592 at 12% the neglect of rotation in the eigenfrequencies is not clearly negligible.
ad hoc to paper The nearly constant observed frequency spacing is rotational splitting rather than another harmonic or alias mechanism.
Central interpretation in Sects 5.1-5.3; the authors call it tentative and note the spacing is near the Rayleigh resolution for HD 188001.
domain assumption Adopted stellar parameters (Teff, logg, R, vsini) from Gormaz-Matamala et al. 2022 and Holgado et al. 2022 are correct.
Table 1 inputs; errors in vsini or R directly propagate to the rotation period upper limits and inclination estimates.
domain assumption LPCODE model calibration (Z=0.01, alpha_MLT=1.822, f_OV=0.0174) applies to these stars.
Sect 4.2; the g-mode frequency tables used for identification depend on these choices.

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Cite this review

Pith. "Pith review of Gravity modes and potential evidence for Rossby Waves in late O-type supergiants." pith.science (2026). https://pith.science/paper/JGUTQAZJ

@misc{pith2026260811010,
  author       = {Pith},
  title        = {Pith review of: Gravity modes and potential evidence for Rossby Waves in late O-type supergiants},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JGUTQAZJ}},
  note         = {Machine review of arXiv:2608.11010}
}

read the original abstract

The properties of O-type supergiant stars remain largely unexplored. By analysing their light variations, we can unravel underlying physical phenomena, such as binarity, stellar pulsations, and rotation modes. This study aims to analyse the TESS light curves of 3 O-type supergiants to identify periodic signatures and gain deeper insights into their internal dynamics and structure. Our primary goal is to search for the presence of rotational modulation and possible evidence of Rossby waves. A period search was performed and we explored phase diagrams and searched for rotational splitting. If the observed wave frequencies were consistent with the dispersion relation of global Rossby waves, we identified them as potential signatures of this mechanism. We used a graphical method to compare the observed and predicted frequencies. The analysed stars (HD 188001, HD 192639, and HD 159952) exhibit a comparable set of frequencies. We classify most of them as g-mode oscillations (either l=1 or l=2), in agreement with the evolutionary state of the objects. In all cases, we find evidence of rotational modulation. The remaining oscillation patterns may be consistent with Rossby modes, including both tesseral and sectoral configurations. The angle of inclination of the rotation axis was estimated using stellar parameters available in the literature, together with the rotational period derived in this work. We also discuss a possible connection between the observed low-frequency waves and the red-noise component commonly observed in the periodogram of photometric time series of massive supergiants. Our results provide evidence of g-mode oscillations modulated by rotation. In addition, we find that Rossby waves may be excited in rotating O-type supergiants, which suggests that these large-scale inertial oscillations could play a role in the observed low-frequency variability of such stars.