AC26
Read the interior of a star
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.
L1
Why stars ring
A star’s changing brightness carries many rhythms. Their frequency pattern reveals how waves travel through its hidden interior.
L1
Standing waves inside a sphere
Derive radial acoustic modes from a regular center and a pressure-release boundary, then calculate frequencies and node positions.
L2
Sound crossing a layered star
Calculate how a sound-speed boundary changes radial modes, verify the numerical solution, and see why one frequency leaves many interiors possible.
L3
From a light curve to stellar modes
Follow a saved stochastic signal through exposure, gaps, spectral estimation and conditional frequency inference, with reproducible coverage checks.
L3
Test a red giant model with TESS data
Fit HD128279 lightcurves and compare the modes with new calculations from eight native structures, testing windows, noise and surface corrections.
L4
Read core rotation from mixed modes
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
Sources and calculation scope
- GYRE v7.1: Boundary conditions
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.
- GYRE7.2.1 official release and source
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.
- MESA School 2026, Lab 3: Asteroseismology
Official classroom treatment of oscillation frequencies, sound-travel integrals and model evolution. The controllable constant-density cavity here is a separate declared teaching model.
- GYRE MESA file format version 1.01
Exact header/column definitions and CGS units of the complete licensed structural members.
- Lindsay et al. 2025, Precise Asteroseismic Ages for the Helmi Streams
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.
- Lindsay et al., Zenodo15102877 v1 model/observed-mode archive
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.
- Li, Deheuvels & Ballot 2024, Core and envelope rotation rates for 2006 red giants
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.
- Li, Deheuvels & Ballot, Zenodo13207485 v2
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.
- MAST public data use and acknowledgment
Original mission PUBLIC products downloaded using the supplied MAST product URI; preserve NASA/Kepler/TESS/SPOC/STScI attributions and frozen data releases.
- Ball & Gizon 2014, A new correction of stellar oscillation frequencies for near-surface effects
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.