The Oscillations and the Stability of Rotating Masses with Toroidal Magnetic Fields. II.
Abstract
The oscillations and the stability of rotating gaseous masses with prevalent toroidal magnetic fields are examined by using the second-order tensor virial equations. It is shown that in the presence of rotation (solid body and differential) and toroidal magnetic field the point of bifurcation, where the Jacobi ellipsoids branch off from the Maclaurin spheroids, is unaffected by the presence of the magnetic field and differential rotation. The presence of the magnetic field increases the critical value of the eccentricity, where the Maclaunn spheroids become unstable, above the value e = 0.9529 that obtains in the absence of a magnetic field. In the equipartition state it is the radial mode which becomes unstable for whereas for it is the Kelvin mode which becomes unstable. The solid-body rotation has a stabilixing influence on both these modes. The frequencies of the transverse shear modes, the toroidal modes, and the pulsation modes are tabulated for (the ratio of the magnetic to the gravitational energies) = 0.05, 0.15, and 0.30 and for = 1.3, 1.4,1.5, 1.6, and 53
- Publication:
-
The Astrophysical Journal
- Pub Date:
- September 1971
- DOI:
- 10.1086/151081
- Bibcode:
- 1971ApJ...168..265K