Waves And Instabilities Of A Toroidal Magnetic-Flux Tube In A Rotating Star

The oscillation modes and instabilities of a toroidal flux tube lying in the equatorial plane of a differentially rotating star are investigated using the thin flux-tube approximation. The behavior of the frequencies as functions of the magnetic field strength and of the superadiabaticity is explored for both axisymmetric and nonaxisymmetric modes. In limiting cases, the modes can be identified with known normal modes of simple configurations (e.g., a plane-parallel atmosphere with constant gravity or a magnetic flux tube embedded in a homogeneous medium). The axisymmetric modes are essentially radial modes oscillating with a magnetically modified Brunt-Vaisala frequency. As to the nonaxisymmetric modes in the limit of rapid rotation (or of weak magnetic field) there is one pair of stable inertial waves, which are due to the Coriolis force, and one pair of magnetostrophic modes, which are longitudinal slow modes modified by rotation. In the general case (intermediate rotation rates), the modes do not have a definite character, but their properties can be investigated analytically. The corresponding bifurcation diagrams are discussed.