Asteroseismology Simulator

What is Asteroseismology?

Asteroseismology is the study of the internal structure of stars by interpreting their frequency spectra. Stars act as giant resonant cavities where sound waves (p-modes) and gravity waves (g-modes) become trapped. By observing how these waves warp the surface and change the star's brightness, astronomers can precisely determine a star's mass, age, internal rotation, and evolutionary state.

Spherical Harmonics

The macroscopic oscillation patterns on the stellar surface are described mathematically by Spherical Harmonics, denoted as \( Y_l^m(\theta, \phi) \).

\( Y_l^m(\theta, \phi) = \sqrt{\frac{2l+1}{4\pi} \frac{(l-m)!}{(l+m)!}} P_l^m(\cos\theta) e^{im\phi} \)

• Degree (\(l\)): The total number of node lines on the stellar surface. Higher \(l\) values correspond to more localized, higher-frequency surface patches.
• Order (\(m\)): The number of longitudinal node lines passing through the poles. \(m\) ranges from \(-l\) to \(+l\). When a star rotates, modes with different \(m\) values split in frequency, revealing the internal rotation rate!

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