Abstract
Doing numerical calculations of axially symmetric force-free fields, Milsom and Wright (1976) have noticed that there seem to be no solutions if the toroidal component of the field exceeds a certain limit. In the present paper this problem is reexamined in the approximation of a plane stellar surface using a very simple analytic approximation. The results of Milsom and Wright (1976) are confirmed but, in contrast to their interpretation, it is shown that these limitations do not indicate the possibility of sudden changes of the topology of the magnetic field. This is because in a stellar atmosphere the toroidal component of the surface magnetic field is no independent quantity but is produced by shearing motions in the star which will prevent the toroidal magnetic field from exceeding its maximum value. To study the possibility of sudden changes in the magnetic field, which could cause stellar flares, the calculations are re-done prescribing the motion of the magnetic footpoints (shear in the stellar surface) instead of the toroidal component of the surface field. Using the same mathematical formalism it is found that no sudden changes can occur for configurations where all field lines connect to the stellar surface but that sudden changes may be possible for a more complicated field topology.
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References
Anzer, U. and Tandberg-Hanssen, E.: 1970, Solar Phys. 11, 61.
Barnes, C. W. and Sturrock, P. A.: 1972, Astrophys. J. 174, 659.
Bruzek, A.: 1963, in W. N. Hess (ed.), AAS-NASA Symposium on the Physics of Solar Flares, NASA SP-50, p. 301.
Courant, R. and Hilbert, D.: 1962, Methods of Mathematical Physics, Vol. II by R. Courant, Interscience, New York, London.
Gold, T.: 1963, in W. N. Hess (ed.), AAS-NASA Symposium on the Physics of Solar Flares, NASA SP-50, p. 389.
Grad, H. and Rubin, H.: 1958, Proc. 2nd UN International Conference on Peaceful Uses of Atomic Energy, 31, 190.
Harvey, J. W.: 1969, NCAR-University of Colorado Cooperative Thesis No. 17.
Kadomzev, B. B., 1963, English translation in M. A. Leontovich (ed.), Reviews of Plasma Physics, Vol. 2, New York, 1966, p. 153.
Krieger, A. S., de Feiter, L. D., and Vaiana, G. S.: 1976, Solar Phys. 47, 117.
Low, B. C. and Nakagawa, Y.: 1975, Astrophys. J. 199, 237.
Martres, M. J., Rayrole, J., Ribes, E., Semel, M., and Soru-Escaut, I.: 1974, in Y. Nakagawa and D. M. Rust (eds.), Flare-Related Magnetic Field Dynamics, HAO-NCAR, p. 334.
Milsom, F. and Wright, G. A. E.: 1976, Monthly Notices Roy. Astron. Soc. 174, 307.
Raadu, M. A.: 1971, Astrophys. Space Sci. 14, 464.
Rust, D. M. and Bar, V.: 1973, Solar Phys. 33, 445.
Rust, D. M., Nakagawa, Y., and Neupert, W. M.: 1975, Solar Phys. 41, 397.
Shavranov, V. D.: 1963, English translation in M. A. Leontovich (ed.), Reviews of Plasma Physics, Vol. 2, New York, 1966, p. 103.
Sheeley, N. R., Jr., Bohlin, J. D., Brueckner, G. E., Purcell, J. D., Scherrer, V. E., Tousey, R., Smith, J. B., Jr., Speich, D. M., Tandberg-Hanssen, E., Wilson, R. M., de Loach, A. C., Hoover, R. B., and McGuire, J. P.: 1975, Solar Phys. 45, 377.
Tanaka, K.: 1976, Solar Phys. 47, 247.
Vrabec, D.: 1974, in R. G. Athay (ed.), ‘Chromospheric Fine Structure’, IAU Symp. 56, 201.
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Jockers, K. Upper limits in the toroidal component of force-free magnetic fields in stellar atmospheres in the context of solar and stellar flares. Sol Phys 50, 405–427 (1976). https://doi.org/10.1007/BF00155303
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DOI: https://doi.org/10.1007/BF00155303