Dispersion Equation of Gravito-MHD Waves

We derive the dispersion equation for gravito-MHD waves in an isothermal, gravitationally stratified plasma with a horizontal inhomogeneous magnetic field. In the present model the sound and the Alfven speeds are constant. It is known that in this model analytical solutions can be obtained for linearized perturbations. There are three modes propagating in the considered plasma: the fast, the slow and the Alfven mode, all modified by gravity. In the extreme short wavelength limit, these waves propagate in a locally uniform plasma. The waves with larger wavelengths will be affected by the nonuniformity of the medium resulting from the action of gravitational force rho g. In the case without magnetic field these waves become gravito-acoustic waves.