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Competition between gravity waves excited by convection and tides in stars that host a companion

This study models the competition between gravity waves excited by convection and tides in stars with companions, finding that stochastic convective excitation generally dominates over tidal excitation (except for close-in stellar companions around late-type stars), implying that the presence of a companion is unlikely to significantly alter internal angular momentum transport in the host star's radiative layers.

Original authors: M. Esseldeurs, J. Ahuir, L. Amard, S. Mathis, L. Decin

Published 2026-03-30

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CC BY 4.0

Original authors: M. Esseldeurs, J. Ahuir, L. Amard, S. Mathis, L. Decin

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 as a giant, spinning ball of hot gas. Deep inside, it's not just a smooth, uniform swirl; it has layers, like an onion. Some layers are churning with hot gas (convection), while others are calm and stable (radiation).

For a long time, astronomers have been puzzled by a mystery: How does the spin of the star's core get transferred to its outer layers? Why don't the cores spin wildly fast while the outsides spin slowly?

Scientists knew two main things could act like a "conveyor belt" to move this spin (angular momentum) around:

Internal Waves: Think of these as ripples in a pond, but inside the star. These are called Gravity Waves.
Companions: Many stars have a "buddy"—another star or a giant planet orbiting close by. This buddy pulls on the star with gravity, creating tides (like the Moon pulls on Earth's oceans).

The Big Question

The authors of this paper asked a simple but crucial question: Which of these two forces is the real boss?

Is the star's internal churning (convection) creating enough waves to move the spin around? Or is the gravitational tug of a nearby planet or star (the tide) doing the heavy lifting?

The Experiment: A Cosmic Tug-of-War

The researchers built a computer model to simulate stars of different sizes (like our Sun and slightly bigger stars) at different ages. They pitted the two forces against each other:

Team Convection (The Internal Storm): Imagine the star's outer layer as a boiling pot of soup. The bubbles rising and falling create tiny, random ripples (waves) that travel into the star's calm interior. These ripples carry spin energy.
Team Tides (The External Puller): Imagine a giant hand (the companion star or planet) grabbing the star and pulling it. This creates a "bulge" and sends rhythmic waves into the star's interior, also carrying spin energy.

They calculated how much "spin energy" each team could transport.

The Results: Who Won?

The answer was surprisingly clear for most scenarios: Team Convection wins by a landslide.

Here is the breakdown using simple analogies:

1. The "Jupiter" Scenario (Planetary Companions)
Imagine a star with a Jupiter-sized planet orbiting it.

The Result: The planet's gravitational pull is like a gentle breeze. The star's internal boiling (convection) is like a hurricane.
The Analogy: Trying to move a heavy boulder with a gentle breeze (the planet) when a hurricane (convection) is already pushing it is pointless. The planet's waves are too weak to matter. Even if the planet is very close, it rarely changes how the star spins inside.

2. The "Solar" Scenario (Stellar Companions)
Imagine a star with another star orbiting it.

The Result: This is a stronger opponent. A second star is like a strong wind.
The Catch: Even a second star usually can't beat the hurricane of convection unless they are extremely close—like, "hugging" close.
The Exception: If the two stars are very close and the host star has expanded into a giant (like a Red Giant), the tides can become strong enough to compete. But for most of a star's life, the internal churning still rules.

3. The "Big Star" Scenario (Early Type Stars)
For stars bigger than our Sun, the internal structure is different (they have a boiling core instead of a boiling outer layer).

The Result: In these stars, the internal waves are so powerful that even a second star orbiting very close can't compete. The internal "engine" is just too strong.

Why Does This Matter?

This is great news for astronomers trying to understand how stars evolve.

Simpler Models: Before this, scientists worried they needed to account for every single planet and star nearby to understand how a star spins. Now they know: You can mostly ignore the companions.
The "Black Box" Solution: When building computer models of stars, they can focus on the internal waves caused by convection. They don't need to add complex math for every planet in the system, which makes the models faster and easier to run.
The Mystery Remains (Sort of): While we now know which waves are dominant, we still don't fully understand why the spin moves so efficiently. But at least we know it's the star's own internal weather doing the work, not its neighbors.

The Bottom Line

Think of a star as a spinning top.

Convection is the hand spinning the top from the inside.
Tides are someone gently tapping the side of the top.

This paper tells us that for almost all stars, the hand spinning from the inside is doing 99% of the work. The gentle taps from a nearby planet or star are barely noticeable. So, when studying how stars spin and evolve, we can mostly focus on what's happening inside the star, not who is orbiting it.

1. Problem Statement

Asteroseismology has revealed that internal angular momentum transport in stars is significantly more efficient than predicted by standard stellar evolution models (which consider only radial shellular differential rotation and meridional circulation). Two primary mechanisms are proposed to explain this: magnetic fields and Internal Gravity Waves (IGWs).

Stochastic Excitation: IGWs are naturally excited by turbulent convection at the radiative-convective interface.
Tidal Excitation: In binary systems or star-planet systems, gravitational tides from a companion can also excite IGWs at the same interface.

The Core Question: Do tidally excited IGWs compete with, or even dominate over, stochastically excited IGWs in transporting angular momentum? If tides are significant, current models of stellar rotation evolution must account for the presence of companions; if not, models can be simplified.

2. Methodology

The authors developed a theoretical framework to compute and compare the energy luminosity ( $L_E$ ) and angular momentum luminosity ( $L_L$ ) transported by both excitation mechanisms across various stellar masses and evolutionary stages.

Stellar Models: They utilized stellar evolutionary models for host stars with initial masses of $1 M_\odot$ (late-type) and $2 M_\odot$ (early-type), covering phases from the Pre-Main Sequence (PMS) through the Main Sequence (MS), Red Giant Branch (RGB), Horizontal Branch (HB), Asymptotic Giant Branch (AGB), to White Dwarf (WD).
Excitation Models:
- Stochastic: Based on the Press (1981) model, refined by Lecoanet & Quataert (2013). The flux depends on convective velocity ( $v_c$ ), density ( $\rho$ ), and the Brunt-Väisälä frequency gradient ( $dN^2/d\ln r$ ) at the radiative-convective interface.
- Tidal: Based on the formalism of Ahuir et al. (2021a), considering the tidal potential from a companion. They assumed circular, coplanar orbits and focused on the dominant quadrupolar term ( $l=m=2$ ).
Competition Metric: The authors derived analytical expressions for the ratio of tidal to stochastic angular momentum luminosities ( $L_L^T / L_L^S$ ). They identified critical mass ( $M_{crit}$ ) and critical orbital period ( $P_{orb,crit}$ ) thresholds where tidal excitation equals stochastic excitation.
Assumptions: The study assumes progressive waves (damped before reflection) and neglects rotation effects on wave propagation (Coriolis force) and magnetic fields in the primary calculation, treating them as necessary future refinements.

3. Key Contributions

Quantitative Comparison: First systematic quantification of the relative contributions of tidal vs. stochastic IGW excitation across the full stellar evolutionary timeline for both planetary and stellar companions.
Critical Thresholds: Derivation of critical companion masses and orbital periods required for tides to dominate angular momentum transport.
Evolutionary Dependence: Detailed analysis of how the internal structure (convective core vs. convective envelope) of the host star dictates the efficiency of wave excitation.

4. Key Results

A. Late-Type Stars ( $1 M_\odot$ )

Planetary Companions: For a Jupiter-mass companion, stochastic excitation dominates tidal excitation throughout the entire stellar evolution, even at short orbital periods. Tidal effects only become comparable to stochastic effects during the early RGB phase if the orbital period is shorter than ~1 day.
Stellar Companions: For a solar-mass companion, tidal excitation becomes competitive during the MS and RGB phases only for very close orbits (< 3–10 days). During the HB phase, tidal excitation remains sub-dominant unless the companion is inside the stellar Roche limit.
Critical Mass: An Earth-mass companion never generates sufficient tidal IGW luminosity to compete with stochastic excitation. A Jupiter-mass companion only competes at the very beginning of the RGB for ultra-short periods.

B. Early-Type Stars ( $2 M_\odot$ )

Structural Difference: These stars possess a convective core and a radiative envelope during the MS. Stochastic excitation is driven by the convective core.
Dominance of Stochastic Excitation: Tidal excitation is negligible compared to stochastic excitation throughout the entire evolution for both planetary and stellar companions.
Transition Gap: A brief dip in stochastic luminosity occurs during the transition from MS to RGB when the convective core vanishes and the convective envelope has not yet formed, but tides do not fill this gap significantly.

C. General Trends

Scaling: The ratio of tidal to stochastic luminosity scales with the square of the mass ratio ( $q^2$ ), the tenth power of the stellar radius ( $R_\star^{10}$ ), and the inverse sixth power of the semi-major axis ( $a^{-6}$ ).
Evolutionary Impact: As stars evolve into giants (RGB/AGB), their radii expand, increasing tidal forcing ( $F \propto R_\star^5$ ). However, the increase in convective velocity and density at the interface in the stochastic model generally maintains the dominance of stochastic excitation, except in extreme close-binary configurations.

5. Significance and Implications

Simplification of Stellar Models: The study concludes that for the vast majority of stars hosting companions (including those with hot Jupiters or wide binary stars), tidal excitation of IGWs does not significantly alter internal angular momentum transport.
Modeling Strategy: Stellar evolution codes that already include stochastic IGW transport (e.g., MESA, STAREVOL) do not need to systematically include tidal IGW excitation to accurately model internal rotation profiles. The presence of a companion can be neglected for the purpose of internal wave-driven transport.
Remaining Complexity: While tidal IGW excitation is negligible, tidal torques (equilibrium tide and tidal inertial waves) acting on the convective envelope remain crucial. These torques drive the orbital evolution and set the boundary conditions (rotation gradient) that determine where the IGWs deposit or extract angular momentum.
Future Work: The authors note that rotation (Coriolis force) and magnetic fields significantly alter wave propagation and damping (creating gravito-inertial waves). These effects, which require complex multi-dimensional hydrodynamical simulations, are the next necessary step to refine these conclusions, particularly for rapidly rotating stars.

Conclusion: The stochastic excitation of gravity waves by convection is the dominant mechanism for internal angular momentum transport in stars with companions. Tidal excitation only becomes relevant in extreme, short-period binary systems involving evolved stars, suggesting that the internal rotational evolution of most stars can be modeled independently of their companion's tidal wave excitation.