Anisotropic Magnetized Asteroseismic Waves

Abstract

We solve for waves in a polytropic, stratified plasmas 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 explicit dispersion relation for fast pressure-driven waves: $\hat{I}{\text{c◯}}^2\sim K\left(2m+n\right)\left[1+(1/M_{\mathrm{A}}{)}^2(4-2{\hat{I}}^3+{\cos }^2\hat{I}¸-3{\cos }^4\hat{I}¸)/4\right]$. Here, $\hat{I}\text{c◯}$ is the frequency, $K$ the wavenumber, $\hat{I}¸$ the angle the wave-vector makes with the background magnetic field, $M_{\mathrm{A}}$ the Alfvénic Mach number, and $m$ an integer representing the eigenstate. We discuss roles of such an explicit formula in asteroseismology.

Accepted for publication in ApJ. Comments welcome!