Oscillations of a polytrope with a toroidal magnetic field |
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| Authors: | N K Sood S K Trehan |
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| Institution: | (1) Dept. of Mathematics, Panjab University, Chandigarh, India;(2) Joint Institute for Laboratory Astrophysics, University of Colorado, Boulder, Colo., USA;(3) Dept. of Mathematics, Panjab University, Chandigarh, India |
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| Abstract: | 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 ( 12)m, say] and the shift in frequency due to the distortion of the structure by the magnetic field (12)s, say]. In the first order calculations using one parameter trial function, it is found that (12)m is indeed positive but is overweighed by a negative (12)s. In the second order calculations using a trial function with two variational parameters, we find that the general behaviour of (12)m and (12)s is unchanged but that (12)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 as
respectively. Here
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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