Anisotropic Magnetized Asteroseismic Waves

TL;DR

This paper derives an explicit dispersion relation for anisotropic magnetized waves in stratified plasmas with a background magnetic field, providing insights relevant for asteroseismology.

Contribution

It presents a new explicit dispersion relation for magnetized waves in stratified plasmas with spatially varying magnetic fields, combining numerical and asymptotic methods.

Findings

Derived an explicit wave dispersion relation involving magnetic field and stratification parameters.

Identified the dependence of wave frequency on magnetic field orientation and strength.

Discussed implications of the dispersion relation for asteroseismic observations.

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: $\Omega^2 \sim K\left(2m+n\right) \left[1 + (1/M_\mathrm{A})^2 (4-2\gamma+\cos^2\theta-3\cos^4\theta)/4 \right]$. Here, $\Omega$ is the frequency, $K$ the wavenumber, $\theta$ the angle the wave-vector makes with the background magnetic field, $M_\mathrm{A}$ the Alfv\'enic Mach number, and $m$ an integer representing the eigenstate. We discuss roles of such an explicit formula in asteroseismology.