Astrophysics and Space Science

, Volume 4, Issue 3, pp 255–274 | Cite as

The equilibrium and stability of magnetopolytropes

  • S. P. S. Anand


The theory of the oscillations of axisymmetric gaseous configurations with a prevalent magnetic field is presented. The virial tensor method is used to obtain the nine second harmonic modes of oscillations of the system. It is found that out of the nine modes, three are neutral, four are non-radial, and two are coupled. For the Prendergast spherical model it is found that one of the coupled modes is radial and the other non-radial. Both the radial and the non-radial modes obtained in this case agree with the corresponding formulae obtained byChandrasekhar andLimber (1954) andWoltjer (1962).

The equilibrium structure of gaseous polytropes with toroidal magnetic fields is also investigated in detail for values of the polytropic indexn=1, 1.5, 2, 3 and 3.5. For this model the components of the moment of intertia and potential energy tensors together with the non-zero components of the supermatrix potential are obtained. The final results in terms of the effect of weak toroidal magnetic fields on the characteristic frequencies of distorted polytropes are presented in the form of tables.


Magnetic Field Potential Energy Characteristic Frequency Couple Mode Spherical Model 
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  1. Anand, S. P. S. andKushwaha, R. S.: 1962,Ann. Astrophys. 25, 310.Google Scholar
  2. Chandrasekhar, S.: 1961a,Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford, Chapter 13.Google Scholar
  3. Chandrasekhar, S.: 1961b,Astrophys. J. 134, 662.Google Scholar
  4. Chandrasekhar, S.: 1962a,Astrophys. J. 136, 248.Google Scholar
  5. Chandrasekhar, S.: 1962b,Astrophys. J. 136, 1082.Google Scholar
  6. Chandrasekhar, S. andLebovitz, N. R.: 1962,Astrophys. J. 135, 238.Google Scholar
  7. Chandrasekhar, S. andLimber, D. N.: 1954,Astrophys. J.:119, 7.Google Scholar
  8. Clement, M. J.: 1965,Astrophys. J. 141, 210.Google Scholar
  9. Monaghan, J. J.: 1965,Monthly Notices Roy. Astron. Soc. 131, 105.Google Scholar
  10. Monaghan, J. J.: 1966a,Monthly Notices Roy. Astron. Soc. 132, 1.Google Scholar
  11. Monaghan, J. J.: 1966b,Monthly Notices Roy. Astron. Soc. 134, 275.Google Scholar
  12. Prendergast, K. H.: 1956,Astrophys. J. 123, 498.Google Scholar
  13. Roxburgh, I. W.: 1962, inProceedings Enrico Fermi Summer School in Star Evolution, Varrena, Academic Press, New York, p. 446.Google Scholar
  14. Roxburgh, I. W.: 1963a,Monthly Notices Roy. Astron. Soc. 126, 67.Google Scholar
  15. Roxburgh, I. W.: 1963b, inProceedings I.A.U. Symposium No. 22 on Stellar and Solar Magnetic Fields, North-Holland Publishing Company, Amsterdam, p. 103.Google Scholar
  16. Roxburgh, I. W.: 1966,Monthly Notices Roy. Astron. Soc. 132, 347.Google Scholar
  17. Roxburgh, I. W.: 1967,Monthly Notices Roy. Astron. Soc. 135, 329.Google Scholar
  18. Roxburgh, I. W. andDurney, B. R.: 1967,Monthly Notices Roy. Astron. Soc. 135, 329.Google Scholar
  19. Sinha, N. K.: 1968,Australian J. Phys. 21, 283.Google Scholar
  20. Wentzel, D. G.: 1960,Astrophys. J., Supp. 5, 187.Google Scholar
  21. Wentzel, D. G.: 1961,Astrophys. J. 133, 170.Google Scholar
  22. Woltjer, L.: 1962,Astrophys. J. 135, 235.Google Scholar

Copyright information

© D. Reidel Publishing Company 1969

Authors and Affiliations

  • S. P. S. Anand
    • 1
  1. 1.David Dunlap ObservatoryUniversity of TorontoCanada

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