Anisotropic Magnetized Asteroseismic Waves.

We solve for waves in a polytropic, stratified plasma with a spatially varying background magnetic field that points along the 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 ∼ 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: Ω 2 ∼ K 2 m + n [ 1 + 1 / M A 2 (4 − 2 γ + cos 2 θ − 3 cos 4 θ) / 4 ] . Here, Ω is the frequency, K is the wavenumber, θ is the angle the wavevector makes with the background magnetic field, M A is the Alfvénic Mach number, and m is an integer representing the eigenstate. We discuss the roles of such an explicit formula in asteroseismology. [ABSTRACT FROM AUTHOR]