Magnetically distorted polytropes: structure and radial oscillations

The equilibrium structure of a gaseous polytrope with a toroidal and a poloidal magnetic field is examined under the assumption that the magnetic energy is small compared with the gravitational energy of the configuration. It is found that the magnetic field tends to be more centrally condensed with increasing value of the polytropic index n. The resulting configuration is a prolate spheroid, the prolateness being a decreasing function of n. The ratio of the magnetic energy of the toroidal component to that in the poloidal component varies approximately as n3 for the lowest characteristic mode of the magnetic field. The radial oscillations of the configuration are examined by means of a variational principle. The frequencies of oscillation are tabulated for various values of . The shift in the frequency due to the presence of the magnetic field increases with the value of .