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

This paper analyzes TESS light curves of three late O-type supergiant stars (HD 188001, HD 192639, and HD 195592) to search for periodic signatures, rotational modulation, and potential evidence of Rossby waves (r modes). The authors use the generalized Lomb-Scargle periodogram and the weighted wavelet Z-transform to identify frequencies, then compare observed frequencies with theoretical predictions from stellar evolution and pulsation models (LPCODE and LP-PUL) and the Rossby wave dispersion relation.

Key results:

• All three stars exhibit a comparable set of low-frequency oscillations, most classified as g-mode pulsations (l = 1 or l = 2), consistent with their evolutionary state near the end of core hydrogen burning.

• Evidence of rotational modulation is found in all three stars, with approximately uniform frequency spacings interpreted as rotational splitting: ∆f = 0.0576 d−1 for HD 188001, ∆f = 0.05185 d−1 for HD 192639, and ∆f = 0.08185 d−1 for HD 195592.

• Derived rotation periods are 14.5 ± 4.2 d (HD 188001), 16.1 ± 2.6 d (HD 192639), and 6.1 ± 1.0 d (HD 195592), leading to inclination angles of 90°, 90°, and 20°, respectively.

• Some remaining oscillation patterns are consistent with Rossby modes, including tesseral and sectoral configurations: e.g., (l, m) = (3, 2) for HD 188001; (2, 2), (4, 2), (3, 3), (7, 3) for HD 192639; and (2, 2), (3, 2), (3, 3), (5, 3), (5, 4) for HD 195592.

• The observed frequency patterns (σ = mΩ) suggest that high-order r modes may be excited, and these waves could contribute to the red-noise component commonly observed in the periodograms of massive supergiants.

• The authors conclude that Rossby waves may be excited in rotating O-type supergiants, suggesting these large-scale inertial oscillations could play a role in the observed low-frequency variability, though a comprehensive theoretical treatment is deferred to future studies.

Improvements to AI Systems Based on This Paper:

1. Enhanced Stellar Oscillation Classification

• The AI can now automatically classify low-frequency oscillations in massive stars (O/B supergiants) as g-modes, r-modes, or rotational modulation by comparing observed frequencies against theoretical grids from LPCODE/LP-PUL and the Rossby wave dispersion relation.

• It can output probability scores for each mode type (e.g., l=1 vs. l=2) and flag candidate r-mode signatures (tesseral/sectoral patterns) with confidence intervals.

2. Robust Rotational Period and Inclination Inference

• The system can derive stellar rotation periods and inclination angles from uniform frequency spacings (rotational splitting) in TESS light curves, even with sparse or noisy data, using Bayesian priors informed by the three stars’ results (e.g., 6–16 d periods, 20°–90° inclinations).

• It can automatically correct for projection effects and provide uncertainty bounds (e.g., ±2–4 d) without manual tuning.

3. Red-Noise Decomposition for Massive Supergiants

• The AI can separate red-noise components from coherent signals in periodograms, attributing excess low-frequency power to high-order r modes (σ = mΩ) rather than assuming pure stochastic noise.

• It can quantify the fractional contribution of Rossby waves to the total variability, enabling better physical interpretation of supergiant light curves.

4. Cross-Mission Light-Curve Harmonization

• The system can adapt its frequency analysis pipeline to different space telescopes (TESS, Kepler, PLATO) by automatically adjusting for cadence, windowing, and systematics, using the wavelet Z-transform’s time-frequency localization to handle gaps and non-stationarity.

5. Theoretical Model Emulation

• The AI can serve as a fast surrogate for LPCODE/LP-PUL stellar evolution and pulsation models, predicting expected frequency ranges for g- and r-modes given stellar mass, age, and rotation—without running full simulations—enabling rapid screening of thousands of stars.

6. Automated Candidate Selection for Follow-Up

• It can rank stars by likelihood of hosting detectable Rossby waves (based on rotation rate, spectral type, and evolutionary stage) and suggest optimal observational windows (e.g., long TESS sectors) to maximize r-mode detection.

What the Improved AI System Can Do Specifically:

• Given a new O-type supergiant light curve, it outputs: (a) a list of significant frequencies with mode classifications (g/r/rotational), (b) best-fit rotation period and inclination with error bars, (c) a red-noise model that separates stochastic and wave-driven components, and (d) a comparison to theoretical predictions for core-hydrogen-burning stars.

• It can also generate synthetic light curves with injected r-modes to test detection limits, improving survey design for future missions.

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.