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Impact of rotation on the amplitude of acoustic modes in solar-like stars: Insights from hydrodynamical simulations

Using fully compressible hydrodynamical simulations, this study demonstrates that increasing rotation rates in solar-like stars systematically reduce acoustic mode amplitudes by inhibiting convective excitation and enhancing damping, thereby explaining the observed lack of detectable modes in rapidly rotating, magnetically active stars.

Original authors: Arthur Le Saux, Leïla Bessila, Stéphane Mathis

Published 2026-04-30

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CC BY 4.0

Original authors: Arthur Le Saux, Leïla Bessila, Stéphane Mathis

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a star like our Sun as a giant, glowing drum. Just like a drumhead vibrates when you hit it, these stars "ring" with sound waves traveling through their insides. These vibrations, called acoustic modes or p-modes, are like the star's heartbeat. By listening to the pitch and volume of these heartbeats, astronomers can figure out what the star is made of, how old it is, and how big it is. This field is called asteroseismology.

For a long time, astronomers noticed something strange: while most stars with "sloshing" hot gas on their surfaces (convection) should be ringing loudly, many of the fastest-spinning stars were strangely quiet. They were either very faint or completely silent.

The Big Question
Why do fast-spinning stars go quiet? A recent theory suggested that spinning too fast acts like a brake on the churning gas inside the star. If the gas can't churn as vigorously, it can't hit the "drum" as hard, and the sound waves get weaker.

The Experiment: A Digital Star
To test this, the authors built a virtual star inside a supercomputer. They didn't just make a simple model; they created a fully detailed, 3D-like simulation (technically called "2.5D") of a star exactly like our Sun, but they spun it at different speeds:

Not spinning at all (0x).
Spinning at our Sun's speed (1x).
Spinning 3, 5, and even 8 times faster than our Sun.

They used a special code called MUSIC that treats the star's gas as a real, compressible fluid, allowing them to hear the actual sound waves the simulation produced.

What They Found
The results were clear and dramatic, like turning down the volume knob on a radio:

The Volume Drops: As they increased the spin speed, the "volume" (amplitude) of the star's sound waves dropped significantly.
- At 1x speed, the sound was about 20% quieter.
- At 3x speed, it was 30% quieter.
- At 8x speed (very fast!), the sound was 77% quieter.
- Analogy: Imagine trying to run through a crowd. If you run slowly, you can push people aside easily. If you spin around wildly while running, you get tangled up and can't move forward as effectively. The star's spinning gas gets "tangled," making it harder to generate the powerful pushes needed to create loud sound waves.
The Sound Dampens Faster: Not only was the initial "hit" weaker, but the sound also died out faster. In the fastest-spinning models, the vibrations were dampened (silenced) about 50% faster than in the non-spinning model.
- Analogy: It's like hitting a drum that is covered in thick foam. Even if you hit it with the same force, the sound dies out almost instantly because the foam absorbs the energy. The rapid spin seems to add a layer of "foam" that swallows the sound.

Why This Matters
The study confirms that rotation is a major reason why fast-spinning stars are hard to detect with current telescopes. If a star is spinning too fast, its internal "heartbeat" becomes so faint that our instruments might miss it entirely.

The authors conclude that to understand these stars correctly, we can't just look at their frequency (pitch); we must also account for how their spin changes the volume and how quickly the sound fades. This helps explain why we see so many "silent" fast-spinning stars in our galaxy.

A Note on the Simulation
The authors were careful to mention that their computer model had some limitations (like being a simplified version of a 3D star), but the trend they found—faster spin equals quieter stars—was consistent and robust. They are now planning to run even more complex 3D simulations to refine the details, but the main message is already clear: Spin kills the sound.

1. Problem Statement

Solar-like oscillations (acoustic $p$ -modes) are crucial for asteroseismology, allowing the probing of stellar internal structure and dynamics. However, observations from the Kepler mission revealed a significant anomaly: a large fraction of solar-like stars, particularly those that are rapidly rotating and magnetically active, show no detectable acoustic modes despite possessing convective envelopes necessary for their excitation.

Recent theoretical work (Bessila et al., 2025) hypothesized that rotation inhibits the stochastic excitation of these modes by suppressing convective motions, thereby reducing the power injected into the modes. However, this prediction had not yet been tested against non-linear, global hydrodynamical simulations. Furthermore, the interplay between rotation, excitation, and mode damping (dissipation) remained unquantified in a global context.

2. Methodology

The authors employed fully compressible hydrodynamical simulations using the MUSIC code to model a solar-like star ( $1 M_\odot$ , 4.6 Gyr old).

Simulation Setup:
- Geometry: 2.5D simulations (azimuthal symmetry assumed, $\theta \in [0, \pi]$ ) to balance the need for rotation physics with computational cost.
- Domain: Radial range $r \in [0.3, 0.98] R_{star}$ , covering the radiative interior and the convective envelope (base at $0.722 R_{star}$ ).
- Physics: Solves fully compressible Navier-Stokes equations including the Coriolis force. Magnetic fields and centrifugal forces were neglected to isolate the impact of rotation on convection.
- Rotation Rates: Five simulations were performed with uniform rotation rates: $\Omega = 0, 1, 3, 5,$ and $8 \Omega_\odot$ (where $\Omega_\odot \approx 413$ nHz).
- Initialization: Models were initialized using a 1D MESA stellar evolution model.
Analysis Techniques:
- Mode Identification: Acoustic modes were identified by computing power spectra of the radial velocity ( $P[\hat{v}_r^2]$ ) and matching peaks to eigenfrequencies from a 1D GYRE model.
- Amplitude Measurement: Mode amplitudes were measured at $r = 0.9 R_{star}$ for angular degrees $\ell \in [0, 5]$ .
- Damping Rate Estimation: Damping rates ( $\eta$ ) were derived by fitting Lorentzian profiles to the power spectrum peaks to measure the linewidth ( $\Gamma$ ), using the relation $\Gamma = \eta / 2\pi$ .
- Theoretical Comparison: Results were compared against the theoretical stochastic excitation model of Bessila et al. (2025), which utilizes Rotating Mixing-Length Theory (R-MLT) and assumes a Lorentzian eddy-time correlation function.

3. Key Contributions

First Global Analysis: This study presents the first dedicated analysis of solar-like oscillations in global, rotating stellar simulations, moving beyond previous local or anelastic approximations that filtered out acoustic waves.
Validation of Correlation Functions: The authors empirically validated the theoretical assumption that a Lorentzian eddy-time correlation function (rather than Gaussian) is required to model the rotational suppression of $p$ -mode excitation.
Decoupling Excitation and Damping: The study separates the effects of rotation on mode excitation (power injection) and mode damping, providing a complete physical picture of amplitude reduction.

4. Key Results

A. Convective Flow Morphology

Alignment with Rotation: As the rotation rate increases (Rossby number decreases), convective motions align with the rotation axis, forming Taylor-Proudman columns, particularly at high latitudes.
Velocity Suppression: The root-mean-square (RMS) convective velocity decreases with increasing rotation rate, particularly near the base of the convection zone. This trend aligns with R-MLT predictions, though the non-rotating case showed unexpectedly low velocities in 2.5D geometry (a known 2D vs. 3D artifact).

B. Acoustic Mode Amplitudes

Systematic Decline: There is a clear, systematic decrease in the amplitude of low-degree ( $\ell \leq 5$ $ℓ \leq 5$ ) acoustic modes as rotation increases.
- $\Omega = 1 \Omega_\odot$ : Amplitude reduced by 21%.
- $\Omega = 3 \Omega_\odot$ : Amplitude reduced by 29%.
- $\Omega = 5 \Omega_\odot$ : Amplitude reduced by 53%.
- $\Omega = 8 \Omega_\odot$ : Amplitude reduced by 77%.
Comparison with Theory: The measured amplitude reduction closely matches the theoretical prediction of reduced power injection for $\Omega \leq 5 \Omega_\odot$ . For the fastest rotator ( $8 \Omega_\odot$ ), the simulation shows a stronger reduction than predicted, potentially due to the development of anti-solar differential rotation (poles rotating faster than the equator) in the simulations, which Biscarrat et al. (2025) showed can further suppress excitation.

C. Mode Damping

Enhanced Damping: The study found that damping rates ( $\eta$ $η$ ) increase with rotation.
- For the fastest rotator ( $8 \Omega_\odot$ ), the damping rate increased by approximately 51% compared to the non-rotating case.
Combined Effect: The observed amplitude reduction is the result of a "double whammy": a decrease in the power injected by convection and an increase in the damping of the modes.

D. Power Injection Validation

By using the measured kinetic energy spectra and eddy-time correlation functions from the simulations to calculate injected power, the authors confirmed that:

The Lorentzian correlation function is the correct choice for modeling rotational effects.
The injected power decreases significantly with rotation, consistent with the amplitude trends.

5. Significance and Implications

Explaining Non-Detections: The results provide a robust physical explanation for the "missing" acoustic modes in rapidly rotating stars observed by Kepler. The suppression is not due to a lack of convection, but rather the rotation-induced inhibition of the turbulent power available to excite the modes, compounded by increased damping.
Asteroseismic Interpretation: The study emphasizes that rotation must be explicitly accounted for when interpreting asteroseismic data. Ignoring rotational effects on mode amplitudes could lead to incorrect inferences about stellar internal structure or magnetic activity.
Future Missions: These findings are critical for the upcoming PLATO mission (launch 2026), which will observe tens of thousands of solar-like oscillators. Understanding the rotation-amplitude relationship is essential for maximizing the scientific return from these observations.
Methodological Advance: The work demonstrates the capability of fully compressible hydrodynamical codes (like MUSIC) to bridge the gap between theoretical stochastic excitation models and observational asteroseismology.

Limitations & Future Work:
The authors note that the 2.5D geometry may artificially enhance mean flows and alter convective energetics compared to full 3D simulations. They plan to extend this work to 3D simulations to confirm the differential rotation profiles and the quantitative trends in the non-rotating limit. Additionally, future studies will investigate the combined effects of magnetic fields and differential rotation.