Astrophysics > Solar and Stellar Astrophysics
[Submitted on 3 May 2024]
Title:Anisotropic Magnetized Asteroseismic Waves
View PDF HTML (experimental)Abstract:We solve for waves in a polytropic, stratified medium with a spatially varying background magnetic field that points along a horizontal $x$-direction, and with gravity that is directed along the vertical $z$-direction. Force balance determines the magnitude of the background magnetic field, $B_0^2 \sim z^{n+1}$, where $n$ is the polytropic index. Using numerical and asymptotic methods, we deduce an accurate and explicit dispersion relation for fast pressure-driven waves: $\Omega^2 \sim K\left(2m+n\right) \left[1 + (1/M_\mathrm{A})^2 (4-2\gamma+\cos^2\theta-3\cos^4\theta)/4 \right]$. Here, $\Omega$ is the frequency, $K$ the wavenumber, $\theta$ the angle the wave-vector makes with the background magnetic field, $M_\mathrm{A}$ the Alfvénic Mach number, and $m$ an integer representing the eigen state. Applications of our result are in magnetoseismology and nonlinear asteroseismology.
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