Magnetic waves in a stratified medium: dispersion relations and exact solutions

Abstract

We solve for waves in an isothermal, stratified medium with a magnetic field that points along a direction perpendicular to that of gravity and varies exponentially in the direction of gravity. For waves propagating along the magnetic field, we calculate approximate dispersion relation as a function of the magnetic field strength. We also find exact solutions for two different cases: (a) waves propagating along the direction of the magnetic field and (b) waves propagating along the direction of gravity. In each of these cases, we find solutions in terms of either confluent hypergeometric functions or Gauss hypergeometric functions depending on whether the ratio of the scale height of the magnetic field over the density scale height is equal to two or not.