Compressible magnetohydrodynamic waves in stellar atmospheres with radial magnetic fields .1. Analytic analysis

A theoretical analysis is performed for three-dimensional compressible magnetohydrodynamic (MHD) perturbations in stellar atmospheres in spherical geometry. The background stellar atmosphere permeated with a radial magnetic field is assumed to be spherically symmetric, isothermal and hydrostatic. The incompressible transverse Alfven wave equations, which decouple from the compressible MHD wave equations considered here, were investigated by Lou & Rosner. Asymptotic solutions are derived analytically for compressible MHD waves both at large radii and near the stellar surface. In these limiting parameter regimes, one can clearly distinguish one type of compressible MI-ID perturbations, which are more magnetic in nature (similar to stellar Alfven waves in many respects), from another type of compressible MI-ID perturbations, which behave more like acoustic-gravity waves in the magnetized stellar atmosphere. Therefore the former are referred to as magnetic waves, and the latter as magneto-acoustic-gravity waves. In the low- and high-frequency regimes, magneto-acoustic-gravity waves in an inhomogeneous atmosphere locally manifest as magneto-gravity waves and magneto-acoustic waves, respectively. Since the Brunt-Vaisala buoyancy frequency decreases with increasing height, low-frequency magneto-gravity waves launched near the stellar surface can be effectively trapped in the mid-atmosphere with tiny leakage in the form of outgoing magneto-acoustic waves and magnetic waves far away; this trapping process involves the transformation into different types of MHD waves.