Solar Physics

, Volume 283, Issue 2, pp 413–428 | Cite as

Effect of Variable Background on an Oscillating Hot Coronal Loop



We investigate the effect of a variable, i.e. time-dependent, background on the standing acoustic (i.e. longitudinal) modes generated in a hot coronal loop. A theoretical model of 1D geometry describing the coronal loop is applied. The background temperature is allowed to change as a function of time and undergoes an exponential decay with characteristic cooling times typical for coronal loops. The magnetic field is assumed to be uniform. Thermal conduction is assumed to be the dominant mechanism for damping hot coronal oscillations in the presence of a physically unspecified thermodynamic source that maintains the initial equilibrium. The influence of the rapidly cooling background plasma on the behaviour of standing acoustic (longitudinal) waves is investigated analytically. The temporally evolving dispersion relation and wave amplitude are derived by using the Wenzel–Kramers–Brillouin theory. An analytic solution for the time-dependent amplitude that describes the influence of thermal conduction on the standing longitudinal (acoustic) wave is obtained by exploiting the properties of Sturm–Liouville problems. Next, numerical evaluations further illustrate the behaviour of the standing acoustic waves in a system with a variable, time-dependent background. The results are applied to a number of detected loop oscillations. We find a remarkable agreement between the theoretical predictions and the observations. Despite the emergence of the cooling background plasma in the medium, thermal conduction is found to cause a strong damping for the slow standing magneto–acoustic waves in hot coronal loops in general. In addition to this, the increase in the value of thermal conductivity leads to a strong decay in the amplitude of the longitudinal standing slow MHD waves.


Magnetohydrodynamics (MHD) Plasmas Sun: corona Waves 



The authors would like to thank M.S. Ruderman and R.J. Morton for useful discussions. R.E. acknowledges M. Kéray for patient encouragement. The authors are also grateful to NSF, Hungary (OTKA, Ref. No. K83133), Science and Technology Facilities Council (STFC), UK, and Ministry of Higher Education, Oman for the financial support.


  1. Aschwanden, M.J., Terradas, J.: 2008, Astrophys. J. Lett. 686, L127. ADSCrossRefGoogle Scholar
  2. Berghmans, D., Clette, F.: 1999, Solar Phys. 186, 207. ADSCrossRefGoogle Scholar
  3. Bradshaw, S.J., Erdélyi, R.: 2008, Astron. Astrophys. 483, 301. ADSCrossRefGoogle Scholar
  4. De Moortel, I.: 2009, Space Sci. Rev. 149, 65. ADSCrossRefGoogle Scholar
  5. De Moortel, I., Hood, A.W.: 2003, Astron. Astrophys. 408, 755. ADSCrossRefGoogle Scholar
  6. De Moortel, I., Ireland, J., Walsh, R.W.: 2000, Astron. Astrophys. 355, L23. ADSGoogle Scholar
  7. De Pontieu, B., Erdélyi, R., De Moortel, I.: 2005, Astrophys. J. Lett. 624, L61. ADSCrossRefGoogle Scholar
  8. Erdélyi, R., Taroyan, Y.: 2008, Astron. Astrophys. 489, 49. CrossRefGoogle Scholar
  9. Erdélyi, R., Al-Ghafri, K.S., Morton, R.J.: 2011, Solar Phys. 272, 73. ADS:2011SoPh..272...73E, doi: 10.1007/s11207-011-9795-5. ADSCrossRefGoogle Scholar
  10. Erdélyi, R., Luna-Cardozo, M., Mendoza-Briceño, C.A.: 2008, Solar Phys. 252, 305. ADS:2008SoPh..252..305E, doi: 10.1007/s11207-008-9274-9. ADSCrossRefGoogle Scholar
  11. Luna-Cardozo, M., Verth, G., Erdélyi, R.: 2012, Astrophys. J. 748, 110. ADSCrossRefGoogle Scholar
  12. Mariska, J.T.: 2005, Astrophys. J. Lett. 620, L67. ADSCrossRefGoogle Scholar
  13. Mariska, J.T.: 2006, Astrophys. J. 639, 484. ADSCrossRefGoogle Scholar
  14. McEwan, M.P., De Moortel, I.: 2006, Astron. Astrophys. 448, 763. ADSCrossRefGoogle Scholar
  15. McLaughlin, J.A., Hood, A.W., De Moortel, I.: 2011, Space Sci. Rev. 158, 205. ADSCrossRefGoogle Scholar
  16. Mendoza-Briceño, C.A., Erdélyi, R., Sigalotti, L.D.G.: 2002, Astrophys. J. Lett. 579, L49. ADSCrossRefGoogle Scholar
  17. Mendoza-Briceño, C.A., Erdélyi, R., Sigalotti, L.D.G.: 2004, Astrophys. J. 605, 493. ADSCrossRefGoogle Scholar
  18. Morton, R., Erdélyi, R.: 2009, Astrophys. J. 707, 750. ADSCrossRefGoogle Scholar
  19. Morton, R., Erdélyi, R.: 2010, Astrophys. J. 519, A43. Google Scholar
  20. Morton, R., Hood, A.W., Erdélyi, R.: 2010, Astron. Astrophys. 512, A23. ADSCrossRefGoogle Scholar
  21. Nakariakov, V.M., Verwichte, E., Berghmans, D., Robbrecht, E.: 2000, Astron. Astrophys. 362, 1151. ADSGoogle Scholar
  22. Nightingale, R.W., Aschwanden, M.J., Hurlburt, N.E.: 1999, Solar Phys. 190, 249. ADS:1999SoPh..190..249N, doi: 10.1023/A:1005211618498. ADSCrossRefGoogle Scholar
  23. Ofman, L., Wang, T.: 2002, Astrophys. J. Lett. 580, L85. ADSCrossRefGoogle Scholar
  24. Ofman, L., Nakariakov, V.M., DeForest, C.E.: 1999, Astrophys. J. 514, 441. ADSCrossRefGoogle Scholar
  25. Ofman, L., Romoli, M., Poletto, G., Noci, C., Kohl, J.L.: 1997, Astrophys. J. Lett. 491, L111. ADSCrossRefGoogle Scholar
  26. Ofman, L., Romoli, M., Poletto, G., Noci, C., Kohl, J.L.: 2000a, Astrophys. J. 529, 592. ADSCrossRefGoogle Scholar
  27. Priest, E.R.: 2000, Solar Magneto-Hydrodynamics, Kluwer Academic, Dordrecht, 86. Google Scholar
  28. Ruderman, M.S.: 2011, Solar Phys. 271, 41. ADS:2011SoPh..271...41R, doi: 10.1007/s11207-011-9772-z. ADSCrossRefGoogle Scholar
  29. Schrijver, C.J., Title, A.M., Berger, T.E., Fletcher, L., Hurlburt, N.E., Nightingale, R.W., Shine, R.A., Tarbell, T.D., Wolfson, J., Golub, L., Bookbinder, J.A., DeLuca, E.E., McMullen, R.A., Warren, H.P., Kankelborg, C.C., Handy, B.N., De Pontieu, B.: 1999, Solar Phys. 187, 261. ADS:1999SoPh..187..261S, doi: 10.1023/A:1005194519642. ADSCrossRefGoogle Scholar
  30. Sigalotti, L.D.G., Mendoza-Briceño, C.A., Luna-Cardozo, M.: 2007, Solar Phys. 246, 187. ADS:2007SoPh..246..187S, doi: 10.1007/s11207-007-9077-4. ADSCrossRefGoogle Scholar
  31. Soler, R., Oliver, R., Ballester, J.L.: 2008, Astrophys. J. 684, 725. ADSCrossRefGoogle Scholar
  32. Taroyan, Y., Bradshaw, S.: 2008, Astron. Astrophys. 481, 247. ADSCrossRefGoogle Scholar
  33. Taroyan, Y., Erdélyi, R.: 2009, Space Sci. Rev. 149, 229. ADSCrossRefGoogle Scholar
  34. Taroyan, Y., Erdélyi, R., Wang, T.J., Bradshaw, S.J.: 2007, Astrophys. J. Lett. 659, L173. ADSCrossRefGoogle Scholar
  35. Verth, G., Erdélyi, R.: 2008, Astron. Astrophys. 486, 1015. ADSMATHCrossRefGoogle Scholar
  36. Verwichte, E., Haynes, M., Arber, T.D., Brady, C.S.: 2008, Astrophys. J. 685, 1286. ADSCrossRefGoogle Scholar
  37. Wang, T.: 2011, Space Sci. Rev. 158, 397. ADSCrossRefGoogle Scholar
  38. Wang, T.J., Ofman, L., Davila, J.M.: 2009, Astrophys. J. 696, 1448. ADSCrossRefGoogle Scholar
  39. Wang, T.J., Solanki, S.K., Curdt, W., Innes, D.E., Dammasch, I.E.: 2002, Astrophys. J. Lett. 574, L101. ADSCrossRefGoogle Scholar
  40. Wang, T.J., Solanki, S.K., Curdt, W., Innes, D.E., Dammasch, I.E., Kliem, B.: 2003a, Astron. Astrophys. 406, 1105. ADSCrossRefGoogle Scholar
  41. Wang, T.J., Solanki, S.K., Innes, D.E., Curdt, W., Marsch, E.: 2003b, Astron. Astrophys. 402, L17. ADSCrossRefGoogle Scholar
  42. Wang, T.J., Solanki, S.K., Innes, D.E., Curdt, W.: 2005, Astron. Astrophys. 435, 753. ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Solar Physics and Space Plasma Research Centre (SP²RC)University of SheffieldSheffieldUK

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