Solar Physics

, Volume 229, Issue 2, pp 255–271 | Cite as

MAG Waves in Sunspots Umbrae: Slow Waves Leaking to the Corona

  • Lotfi Yelles ChaoucheEmail author
  • Toufik E. Abdelatif


The linear oscillations of a stratified atmosphere embedded in a uniform vertical magnetic field are studied here. We use a simple theoretical model, formed by the superposition of two isothermal layers, representing, respectively, i) the photosphere and the chromosphere, and ii) the corona. The bottom layer behaves, for some modes, as a resonant cavity where MAG waves are semi-trapped. We find the existence of two types of modes: 1) Fast modes which are trapped below the transition layer, 2) Mixed modes which are resonant modes in the first layer and leak part of the energy to the corona. These mixed modes have been found to be damped in the horizontal direction and can explain the observed slow modes in the corona.


Magnetic Field Horizontal Direction Bottom Layer Slow Wave Transition Layer 
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  1. Abdelatif, T. E.: 1990, Solar Phys. 129, 201.CrossRefADSGoogle Scholar
  2. Banerjee, D., Hasan, S. S., and Christensen-Dalsgaard, J.: 1995, Astrophys. J. 451, 825.CrossRefADSGoogle Scholar
  3. Banerjee, D., Hasan, S. S., and Christensen-Dalsgaard, J.: 1996, Bull. Astronom. Soc. India 24, 325.ADSGoogle Scholar
  4. Banerjee, D., Hasan, S. S., and Christensen-Dalsgaard, J.: 1997, Solar Phys. 172, 53.CrossRefADSGoogle Scholar
  5. Banerjee, D., O'Shea, E., Goossens, M., Doyle, J. G., and Poedts, S.: 2002, Astron. Astrophys. 395, 263.ADSGoogle Scholar
  6. Birch, A. C., Kosovichev, A. G., Spiegel, E. A., and Tao, L.: 2001, Solar Phys. 199, 291.CrossRefADSGoogle Scholar
  7. Bogdan, J. T.: 2000, Solar Phys. 192, 373.CrossRefADSGoogle Scholar
  8. Bray, R. J. and Loughhead, R. E.: 1974, The Solar Chromosphere, Intern. Astrophys. Ser. London Chapman and Hall.Google Scholar
  9. Brynildsen, N., Kjeldseth-Moe, O., Maltby, P., and Wilhelm, K.: 1999a, Astrophys. J. 517, 159.CrossRefADSGoogle Scholar
  10. Brynildsen, N., Maltby, P., Brekke, P., Haugan, S. V. H., and Kjeldseth-Moe, O.: 1999b, Solar Phys. 186, 141.CrossRefADSGoogle Scholar
  11. Brynildsen, N., Maltby, P., Leifsen, T., Kjeldseth-Moe, O., and Wilhelm, K.: 2000, Solar Phys. 191, 129.CrossRefADSGoogle Scholar
  12. Brynildsen, N., Maltby, P., Fredvik, T., and Kjeldseth-Moe, O.: 2002, Solar Phys. 207, 259.CrossRefADSGoogle Scholar
  13. Brynildsen, N., Maltby, P., Kjeldseth-Moe, O., and Wilhelm, K.: 2003, Astron. Astrophys. 398, L15.CrossRefADSGoogle Scholar
  14. Brynildsen, N., Maltby, P., Foley, C. R., Fredvik, T., and Kjeldseth-Moe, O.: 2004, Solar Phys. 221, 237.CrossRefADSGoogle Scholar
  15. Cally, P. S.: 2001, Astrophys. J. 548, 473.CrossRefADSGoogle Scholar
  16. Cally, P. S. and Bogdan, T. J.: 1993, Astrophys. J. 402, 721.CrossRefADSGoogle Scholar
  17. Cally, P. S., Bogdan, T. J., and Zweibel, E. G. : 1994, Astrophys. J. 437, 505.CrossRefADSGoogle Scholar
  18. Ferraro, V. C. A. and Plumpton, C.: 1958, Astrophys. J. 127, 459.CrossRefADSMathSciNetGoogle Scholar
  19. Hasan, S. S. and Christensen-Dalsgaard, J.: 1992, Astrophys. J. 396, 311.CrossRefADSGoogle Scholar
  20. Heyvaerts, J.: 1980, Ann. Physique 5, 309.Google Scholar
  21. King, D. B., Nakariakov, V. M., Deluca, E. E., Golub, L., and McClements, K. G.: 2003, Astron. Astrophys. 404, L1.CrossRefADSGoogle Scholar
  22. Leroy, B. and Schwartz, S. J.: 1982, Astron. Astrophys. 112, 84.ADSGoogle Scholar
  23. Lites, B. W.: 1992, in J. H. Thomas and N. O. Weiss (ed.), Sunspots: Theory and Observations, Kluwer Academic Publishers, Drodrecht, p. 261.Google Scholar
  24. Lites, B. W., Thomas, J. H., Bogdan, T. J., and Cally, P. S.: 1998, Astrophys. J. 497, 464.CrossRefADSGoogle Scholar
  25. Maltby, P., Brynildsen, N., Fredvik, T., Kjeldseth-Moe, O., and Wilhelm, K.: 1999, Solar Phys. 190, 437.CrossRefADSGoogle Scholar
  26. Maltby, P., Brynildsen, N., Kjeldseth-Moe, O., and Wilhelm, K.: 2001, Astron. Astrophys. 373, L1.CrossRefADSGoogle Scholar
  27. Nakariakov, V. M., King, D. B., and Tsiklauri, D.: 2002, in A. Wilson (ed.), Solar Variability: From Core to Outer Frontiers, ESA Publications Division, Noordwijk, Prague, Czech Republic, p. 705.Google Scholar
  28. O'Shea, E., Muglach, K., and Fleck, B.: 2002, Astron. Astrophys. 387, 642.CrossRefADSGoogle Scholar
  29. Rendtel, J., Staude, J., and Curdt, W.: 2003, Astron. Astrophys. 410, 315.CrossRefADSGoogle Scholar
  30. Rüedi, I. and Cally, P. S.: 2003, Astron. Astrophys. 410, 1023.ADSGoogle Scholar
  31. Scheuer, M. A. and Thomas, J. H.: 1981, Solar Phys. 71, 21.CrossRefADSGoogle Scholar
  32. Settele, A., Staude, J., and Zhugzhda, Y. D.: 2001, Solar Phys. 202, 281.CrossRefADSGoogle Scholar
  33. Settele, A., Zhugzhda, Y. D., and Staude, J.: 1999, Astron. Nachr. 320, 147.CrossRefADSGoogle Scholar
  34. Staude, J.: 1999, in B. Schmieder, A. Hofmann, J. Staude (eds.), Third Advances in Solar Physics Euroconference: Magnetic Fields and Oscillations, ASP Conference Series, 113.Google Scholar
  35. Thomas, J. H.: 1983, Ann. Rev. Fluid Mech. 15, 321.CrossRefADSzbMATHGoogle Scholar
  36. Wood, W. P.: 1990, Solar Phys. 128, 353.CrossRefADSGoogle Scholar
  37. Zhugzhda, Iu. D. and Dzhalilov, N. S.: 1982, Astron. Astrophys. 112, 16.ADSGoogle Scholar
  38. Zhugzhda, Y. D. and Dzhalilov, N. S.: 1984, Astron. Astrophys. 132, 45.ADSGoogle Scholar
  39. Zhugzhda, Y. D., Locans, V., and Staude, J.: 1983, Solar Phys. 82, 369.ADSGoogle Scholar
  40. Zhugzhda, Y. D., Locans, V., and Staude, J.: 1987, Astron. Nachr. 308, 257.ADSGoogle Scholar
  41. Zhugzhda, Y. D., Staude, J., and Locans, V.: 1984, Solar Phys. 91, 219.ADSGoogle Scholar

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© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Département d'Astronomie et Astrophysique(CRAAG)AlgiersAlgeria

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