---
title: "Read the interior of a star"
description: "Follow radial waves into saved signals, analyze real TESS and Kepler observations, and compare licensed stellar structures."
canonical_url: "https://sandboxphysics.com/stories/stellar-seismology/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/stellar-seismology/"
last_modified: "2026-11-04"
---

AC26

# Read the interior of a star

Sandbox Physics · 2026-11-03

A star’s surface carries many rhythms at once. Follow their waves through a layered sphere, then learn to read the same patterns in real space-telescope data.

1. L1

   ## [Why stars ring](https://sandboxphysics.com/stories/stellar-seismology/why-stars-ring/)

   A star’s changing brightness carries many rhythms. Their frequency pattern reveals how waves travel through its hidden interior.

2. L1

   ## [Standing waves inside a sphere](https://sandboxphysics.com/stories/stellar-seismology/radial-standing-waves/)

   Derive radial acoustic modes from a regular center and a pressure-release boundary, then calculate frequencies and node positions.

3. L2

   ## [Sound crossing a layered star](https://sandboxphysics.com/stories/stellar-seismology/layered-acoustic-interiors/)

   Calculate how a sound-speed boundary changes radial modes, verify the numerical solution, and see why one frequency leaves many interiors possible.

4. L3

   ## [From a light curve to stellar modes](https://sandboxphysics.com/stories/stellar-seismology/lightcurves-modes-and-windows/)

   Follow a saved stochastic signal through exposure, gaps, spectral estimation and conditional frequency inference, with reproducible coverage checks.

5. L3

   ## [Test a red giant model with TESS data](https://sandboxphysics.com/stories/stellar-seismology/tess-red-giant-model/)

   Fit HD128279 lightcurves and compare the modes with new calculations from eight native structures, testing windows, noise and surface corrections.

6. L4

   ## [Read core rotation from mixed modes](https://sandboxphysics.com/stories/stellar-seismology/mixed-modes-core-rotation/)

   Read Li 2024’s mode fitting and near-degeneracy test, convert catalog rotation units correctly, and connect mixed-mode identities to surface corrections.

[Move the internal boundary and compare the modes](https://sandboxphysics.com/labs/stellar-oscillation-modes/)

## Sources and calculation scope

1. [GYRE v7.1: Boundary conditions](https://gyre.readthedocs.io/en/v7.1/ref-guide/osc-equations/bound-conditions.html)

   Central regularity and the Lagrangian free-surface pressure condition in stellar models; distinguish these from the fixed-radius Eulerian pressure-release condition of this gravity-free cavity.

2. [GYRE7.2.1 official release and source](https://github.com/rhdtownsend/gyre/releases/tag/v7.2.1)

   Pinned solver release used to recompute full adiabatic degree0/1/2 frequencies, inertia and pressure/gravity nodes from the eight original structures. Build recipe, original SHA256s and actual execution receipts accompany the scientific package.

3. [MESA School 2026, Lab 3: Asteroseismology](https://mesastar.org/summer-school-2026-labs/monday/lab-3/)

   Official classroom treatment of oscillation frequencies, sound-travel integrals and model evolution. The controllable constant-density cavity here is a separate declared teaching model.

4. [GYRE MESA file format version 1.01](https://gyre.readthedocs.io/en/stable/ref-guide/stellar-models/mesa-file-format-v1.01.html)

   Exact header/column definitions and CGS units of the complete licensed structural members.

5. [Lindsay et al. 2025, Precise Asteroseismic Ages for the Helmi Streams](https://arxiv.org/html/2507.01091v1)

   Pinned arXiv2507.01091v1; sections II.2/III/V.3/V.4, Figures 3/5, Tables 3/4/6 and Appendix A. Published as ApJ 989, 189; full optimization and its age errors are external results.

6. [Lindsay et al., Zenodo15102877 v1 model/observed-mode archive](https://zenodo.org/records/15102877)

   CC-BY4 dataset metadata; complete selected HD128279 observations, history/index, eight GYRE structures and published mode tables. One fixed-physics track, not the 840-track optimizer ensemble.

7. [Li, Deheuvels & Ballot 2024, Core and envelope rotation rates for 2006 red giants](https://arxiv.org/html/2405.12116v1)

   Pinned 2405.12116v1; sections 2.2–2.5, near-degeneracy mock Figure 6 and Appendix E. Published as A&A 688, A184. Keep angular/cyclic units and g-phase convention explicit.

8. [Li, Deheuvels & Ballot, Zenodo13207485 v2](https://zenodo.org/records/13207485)

   CC-BY4 rotation catalog and selected KIC3860179 mode files. Dipole bin\_points are approximate seeds; fitted l0/l2 tables have separate uncertainties. Ambiguous auxiliary fields remain excluded.

9. [MAST public data use and acknowledgment](https://stdatu.stsci.edu/publishing/data-use)

   Original mission PUBLIC products downloaded using the supplied MAST product URI; preserve NASA/Kepler/TESS/SPOC/STScI attributions and frozen data releases.

10. [Ball & Gizon 2014, A new correction of stellar oscillation frequencies for near-surface effects](https://arxiv.org/abs/1408.0986)

    Inverse/cubic inertia-weighted surface terms; Lindsay2025 Appendix A supplies the concrete application. The original paper has a corrigendum DOI10.1051/0004-6361/201424325e; this course does not claim a full independent reproduction.