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arxiv: 2606.07125 · v1 · pith:BHBEPTNPnew · submitted 2026-06-05 · 🌌 astro-ph.SR

Revealing mixed modes in compressible hydrodynamical simulations of red giant stars

Nils B. de Vries , Arthur Le Saux , Isabelle Baraffe , Thomas Guillet , Richard H. D. Townsend , Armand Leclerc , Adrien Morison This is my paper

Pith reviewed 2026-06-27 21:00 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords mixed modesred giant starshydrodynamical simulationsstellar oscillationsangular momentum transportmode amplitudesMUSIC code
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The pith

Two-dimensional hydrodynamical simulations constrain mixed mode amplitudes in a red giant star for the first time.

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

This paper uses the MUSIC code to run compressible hydrodynamical simulations of a 1.3 solar mass red giant in two dimensions, with the outer boundary truncated at 90 and 98 percent of the stellar radius. The goal is to directly measure the amplitudes of mixed modes, which combine gravity-wave behavior in the core with acoustic behavior in the envelope. These amplitudes are needed to assess how efficiently the modes can transport angular momentum and explain the slow core rotation observed in evolved stars. The simulations show good frequency agreement with linear codes for most modes and provide estimates of kinetic energies and surface velocities that can be compared to observations.

Core claim

The authors find that modes with frequencies below 50 microHz have the largest kinetic energies in both simulations, contrary to empirical predictions that peak near 312.8 microHz. In the simulation truncated at 0.98 stellar radii, the extrapolated surface velocities match empirical predictions, forming a bell-shaped curve peaking near 700 microHz. Excellent agreement is found between the simulated mode frequencies and those from GYRE and Dedalus solvers for p-dominated modes, with some discrepancies for g-dominated modes in the 60 to 240 microHz range.

What carries the argument

Compressible hydrodynamical simulations using the MUSIC code on radially truncated domains, validated against linear oscillation solvers GYRE and Dedalus for frequency and eigenfunction agreement.

If this is right

  • The largest kinetic energies being at low frequencies implies that these modes could have a significant effect on angular momentum transport in the interior.
  • The extrapolated surface velocities being comparable to predictions in the 0.98 truncation run suggests the simulations capture observable mode properties.
  • Mixed modes can be identified and their properties measured directly in non-linear hydrodynamical simulations rather than relying solely on linear theory.
  • Low-frequency modes have small surface velocities, making them hard to observe but potentially important for internal dynamics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the truncation assumption holds, extending these simulations to include more of the envelope could refine the surface velocity estimates.
  • These results open the possibility of using hydro simulations to test non-linear interactions between modes that linear theory cannot capture.
  • The discrepancy in g-dominated modes points to potential numerical challenges in simulating gravity waves in the core that future work could address.

Load-bearing premise

The two truncated domains produce mixed-mode amplitudes and kinetic energies that are representative of the full untruncated star without dominant boundary artifacts.

What would settle it

A simulation with a domain extending to a larger fraction of the stellar radius or the full star yielding substantially different kinetic energy distributions for low-frequency modes would indicate that the current truncations introduce significant artifacts.

Figures

Figures reproduced from arXiv: 2606.07125 by Adrien Morison, Armand Leclerc, Arthur Le Saux, Isabelle Baraffe, Nils B. de Vries, Richard H. D. Townsend, Thomas Guillet.

Figure 1
Figure 1. Figure 1: Snapshots of the radial (left) and meridional (middle) velocities normalised by the respective rms velocity at every radius and the temperature perturbation (right) compared to the meridional average temperature. The velocities and temperature perturbations are larger in the RGext98 simulation compared to the RGext90 simulation throughout the simulation domain [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Spectra of P[ˆvr](ν, r, ℓ). In panel a) we show an Echelle diagram, with the linear modes overplotted in red. Filled ´ symbols indicate modes located at that frequency, while spectral reflections are plotted in open symbols. In the other three panels we show frequency-radius spectra at fixed values of ℓ, note the different color scales for these. In the frequency-radius diagrams we plot the buoyancy freque… view at source ↗
Figure 3
Figure 3. Figure 3: The simulation spectrum P[ˆvr](ν, r, ℓ) at the chosen ℓ and frequency is plotted as a function of radius in solid-black with square black markers. This signal includes both the mode and the convective signal. On top of the simulation results the radial displacement eigenfunctions obtained from linear theory are plotted in blue, orange and purple, corresponding to regions where the mode acts as a g-mode wit… view at source ↗
Figure 4
Figure 4. Figure 4: Kinetic energies (top row) and extrapolated surface velocities (bottom row) of both the RGext90 (left column) and RGext98 (right column) simulations in blue circles, orange squares and grey diamonds for ℓ = 0, 1.797, 2.18 respectively. The kinetic energies are computed within the truncated region of the simulation. Both the kinetic energies and surface velocities are compared to empirical estimates using t… view at source ↗
Figure 5
Figure 5. Figure 5: The MUSIC initial conditions are obtained from this 1D initial model, where we have ensured that it re￾produces the N2 profile of the 1D MESA model whilst maintaining hydrostatic equilibrium. This results in mi￾nor deviations in the temperature and density profiles. For both simulations the fractional deviations from the 1D MESA model are O(10−3 ) in most of the domain, peaking towards the inner boundary w… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the frequencies of the modes ob￾tained using the dedalus eigenvalue solver plotted in red, black and orange circles, corresponding to p-, g- and mixed modes respectively. The frequencies found using gyre are over plotted in blue triangles. model are performed using gyre only. The inner bound￾ary condition is set to REGULAR and outer boundary condition to VACUUM, i.e. vanishing surface density… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the radial displacement eigenfunc￾tions obtained from linear theory using the dedalus eigen￾value solver and gyre. The eigenfunction obtained from the dedalus eigenvalue solver is plotted in solid-blue, -or￾ange and -purple, corresponding to the g-mode, p-mode, and evanescent regions respectively. The gyre eigenfunction is overlaid in dashed-black, showing excellent agreement for the modes. a… view at source ↗
read the original abstract

Mixed modes are observed in many low-mass evolved stars. They provide information about core rotation rates of these stars, which are lower than predicted by stellar evolution models. The mixed modes themselves have been invoked as an angular momentum transport mechanism, but estimating their transport efficiency requires knowledge of their amplitudes. We constrain, for the first time, the mixed mode amplitudes in 2D hydrodynamical simulations of a $1.3M_\odot$ red giant using the code \textsc{music}. We perform two simulations with outer radial truncations at fractional radii $r_o/r_\star = 0.90$ and $r_o/r_\star = 0.98$. We compare the modes in the simulation with those found using both \textsc{gyre} and a \textsc{dedalus} eigenvalue solver. Excellent frequency agreement is found for all p-dominated modes, with minor discrepancies for g-dominated modes, especially in the frequency range $[60, \ 240]\ \mu\mathrm{Hz}$. We find excellent eigenfunction agreement for all modes except those in this frequency range. According to empirical predictions the largest kinetic energies are located around $\nu_{\mathrm{max}} = 312.8\ \mu\mathrm{Hz}$, but in both simulations the modes with frequencies $\nu <50\ \mu\mathrm{Hz}$ have the largest kinetic energies. In the simulation with $r/r_\star = 0.98$, the simulated modes have extrapolated surface velocities comparable to the empirical predictions, with highest surface velocities in a bell-shaped curve peaking around $\nu = 700 \ \mu\mathrm{Hz}$. The extrapolated surface velocities of the low frequency modes are small, and thus hard to observe, but their large kinetic energies deeper in the interior could significantly impact angular momentum transport, which has not yet been investigated.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports the first constraints on mixed-mode amplitudes from 2D compressible hydrodynamical simulations of a 1.3 M⊙ red giant using MUSIC, performed with outer truncations at r_o/r⋆ = 0.90 and 0.98. Frequencies and eigenfunctions are compared to independent GYRE and Dedalus linear solvers, showing excellent agreement for p-dominated modes but discrepancies for g-dominated modes in [60, 240] μHz. Kinetic energies peak at ν < 50 μHz (contrary to empirical ν_max), and surface velocities are extrapolated for the 0.98 run to compare with observations.

Significance. If truncation effects can be shown to be sub-dominant, the work supplies the first direct numerical amplitudes for mixed modes in nonlinear hydro simulations, with external validation from two independent linear solvers. This could inform angular-momentum transport efficiency estimates in red-giant models.

major comments (2)
  1. [Simulation setup and truncation description] The central claim that the reported mixed-mode amplitudes and kinetic energies are representative of the full star rests on the untested assumption that boundary artifacts from the two truncated domains (r_o/r⋆ = 0.90 and 0.98) are negligible. No convergence test against a less-truncated domain is presented, and the largest KE at ν < 50 μHz together with g-mode discrepancies in [60, 240] μHz could arise from the omitted outer envelope where p-mode displacement peaks.
  2. [Mode identification and post-processing] The extraction of eigenfunctions and kinetic energies from the hydrodynamical runs is not described in sufficient detail to assess whether the post-processing isolates linear mixed-mode properties or is affected by nonlinear or compressible effects; this is load-bearing for the amplitude and surface-velocity claims.
minor comments (2)
  1. Clarify the precise method used to extrapolate surface velocities from the r_o/r⋆ = 0.98 run, especially for the low-frequency modes whose extrapolated values are stated to be small.
  2. The abstract states 'excellent eigenfunction agreement for all modes except those in this frequency range'; quantify the level of agreement (e.g., overlap integrals or L2 norms) rather than using qualitative descriptors.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major comment below and have revised the manuscript to incorporate additional details and discussion where needed.

read point-by-point responses

  1. Referee: The central claim that the reported mixed-mode amplitudes and kinetic energies are representative of the full star rests on the untested assumption that boundary artifacts from the two truncated domains (r_o/r⋆ = 0.90 and 0.98) are negligible. No convergence test against a less-truncated domain is presented, and the largest KE at ν < 50 μHz together with g-mode discrepancies in [60, 240] μHz could arise from the omitted outer envelope where p-mode displacement peaks.

    Authors: We performed two simulations with different outer truncations (0.90 and 0.98 r⋆) precisely to test sensitivity to the boundary location. The result that kinetic energies are largest for ν < 50 μHz holds in both runs, and the 0.98 run yields extrapolated surface velocities consistent with empirical expectations. While a simulation with still smaller truncation would be desirable, computational cost precludes it at present. The consistency across the two domains together with the close match to GYRE and Dedalus for p-dominated modes indicates that the reported trends are not dominated by truncation artifacts. We have added a dedicated subsection discussing possible truncation effects and their limited influence on the low-frequency KE peak. revision: partial

  2. Referee: The extraction of eigenfunctions and kinetic energies from the hydrodynamical runs is not described in sufficient detail to assess whether the post-processing isolates linear mixed-mode properties or is affected by nonlinear or compressible effects; this is load-bearing for the amplitude and surface-velocity claims.

    Authors: We agree that the post-processing procedure requires more explicit description. In the revised manuscript we have expanded the relevant methods section to detail the extraction pipeline: the temporal filtering applied to isolate oscillatory signals, the projection onto radial and horizontal components, the computation of kinetic energy integrals, and the rationale that the extracted quantities correspond to linear eigenmodes (supported by the frequency and eigenfunction agreement with the independent linear solvers). We also note the limitations arising from nonlinearity and compressibility and how they are mitigated by the comparison to linear theory. revision: yes

Circularity Check

0 steps flagged

No circularity; external GYRE/Dedalus comparisons supply independent validation of frequencies and eigenfunctions.

full rationale

The paper runs MUSIC hydro simulations on truncated domains and directly compares extracted mode frequencies and eigenfunctions to independent linear solvers (GYRE and Dedalus). Reported agreement for p-dominated modes and noted discrepancies for g-dominated modes constitute external benchmarks rather than internal fits or self-definitions. No equations reduce a derived quantity to a fitted parameter by construction, no load-bearing self-citations appear, and no ansatz or uniqueness claim is smuggled via prior author work. The truncation assumption is an untested modeling choice but does not create a circular derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

No new free parameters, axioms beyond standard stellar hydrodynamics, or invented entities are introduced; the work relies on established codes and solvers.

axioms (1)
  • domain assumption Compressible hydrodynamics and linear mode analysis assumptions standard in stellar oscillation theory apply to the truncated 2D domains.
    Invoked when extracting modes and comparing to eigenvalue solvers.

pith-pipeline@v0.9.1-grok · 5885 in / 1286 out tokens · 22281 ms · 2026-06-27T21:00:20.399125+00:00 · methodology

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