Abstract
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, B02∼zn+1 , where n is the polytropic index. Using numerical and asymptotic methods, we deduce an explicit dispersion relation for fast pressure-driven waves: Ω2∼K2m+n[1+1/MA2(4−2γ + cos2θ−3cos4θ)/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.
Published Version
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