Oscillations of a Polytrope with a Toroidal Magnetic Field

Details Oscillations of a Polytrope with a Toroidal Magnetic Field Oscillations of a Polytrope with a Toroidal Magnetic Field

Jun 1972

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972ap%26ss..16..451s&link_type=abstract

Astrophysics and Space Science, Volume 16, Issue 3, pp.451-464

Astronomy and Astrophysics

Astrophysics

17

Scientific paper

The radial and the non-radial (l=2) modes of oscillation of a gaseous polytrope with a toroidal magnetic field are examined using a variational principle. It is found that the frequencies of oscillation of the radial mode and the Kelvin mode (l=2) decrease due to the presence of the magnetic field. The shift in the frequency of the Kelvin mode may be split up into two parts, viz. the shift in frequency due to the magnetic field on the unperturbed sphere [(σ12) m, say] and the shift in frequency due to the distortion of the structure by the magnetic field [(σ12) s, say]. In the first order calculations using one parameter trial function, it is found that (σ12) m is indeed positive but is overweighed by a negative (σ12) s. In the second order calculations using a trial function with two variational parameters, we find that the general behaviour of (σ12) m and (σ12) s is unchanged but that (σ12) m becomes negative for polytropic indicesn≥1.5. In Appendix I we study the effect of a small rotation and toroidal magnetic field on the structure of a polytrope. It is found that the resulting configuration is a prolate spheroid, a sphere or an oblate spheroid according asT gtreqqless q mathfrak{M} respectively. Heremathfrak{M} denotes the magnetic energy andT the kinetic energy due to rotation andq is a constant which depends on the polytropic indexn. The values ofq are given in Table I.

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