Solar Physics

, Volume 252, Issue 2, pp 305–319 | Cite as

Dissipation of Longitudinal Oscillations in Stratified Nonisothermal Hot Coronal Loops

  • R. Erdélyi
  • M. Luna-Cardozo
  • C. A. Mendoza-Briceño
Article

Abstract

We investigate the damping of longitudinal (i.e., slow or acoustic) waves in nonisothermal, hot (T≥ 5.0 MK), gravitationally stratified coronal loops. Motivated by SOHO/SUMER and Yohkoh/SXT observations, and by taking into account a range of dissipative mechanisms such as thermal conduction, compressive viscosity, radiative cooling, and heating, the nonlinear governing equations of one-dimensional hydrodynamics are solved numerically for standing-wave oscillations along a magnetic field line. A semicircular shape is chosen to represent the geometry of the coronal loop. It was found that the decay time of standing waves decreases with the increase of the initial temperature, and the periods of oscillations are affected by the different initial footpoint temperatures and loop lengths studied by the numerical experiments. In general, the period of oscillation of standing waves increases and the damping time decreases when the parameter that characterises the temperature at the apex of the loop increases for a fixed footpoint temperature and loop length. A relatively simple second-order scaling polynomial between the damping time and the parameter determining the apex temperature is found. This scaling relation is proposed to be tested observationally. Because of the lack of a larger, statistically relevant number of observational studies of the damping of longitudinal (slow) standing oscillations, it can only be concluded that the numerically predicted decay times are well within the range of values inferred from Doppler shifts observed by SUMER in hot coronal loops.

Keywords

Waves Hydrodynamics Sun: corona Sun: oscillations 

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References

  1. Andries, J., Arregui, I., Goossens, M.: 2005, Astrophys. J. 624, L57. CrossRefADSGoogle Scholar
  2. Andries, J., Goossens, M., Hollweg, J.V., Arregui, I., Van Doorsselaere, T.: 2005, Astron. Astrophys. 430, 1109. CrossRefADSGoogle Scholar
  3. Banerjee, D., Erdélyi, R., Oliver, R., O’Shea, E.: 2007, Solar Phys. 246, 3. CrossRefADSGoogle Scholar
  4. Bradshaw, S.J., Erdélyi, R.: 2008, Astron. Astrophys. 483, 301. CrossRefADSGoogle Scholar
  5. Braginskii, S.I.: 1965, Rev. Plasma Phys. 1, 205. ADSGoogle Scholar
  6. Erdélyi, R.: 2006a, Phil. Trans. Roy. Soc. A 364, 351. CrossRefADSGoogle Scholar
  7. Erdélyi, R.: 2006b, In: Fletcher K., Thompson, M. (eds.): SOHO 18/GONG 2006/HELAS I, Beyond the Spherical Sun, ESA SP-624, 15. Google Scholar
  8. Erdélyi, R., Goossens, M.: 1995, Astron. Astrophys. 294, 575. ADSGoogle Scholar
  9. Erdélyi, R., Mendoza-Briceño, C.A. (eds.): 2008, Proc. IAU Symposium Waves and Oscillations in the Solar Atmosphere: Heating and Magneto-Seismology, IAUS 247, Cambridge University Press, Cambridge. Google Scholar
  10. Haynes, M., Arber, T.D., Verwichte, E.: 2008, Astron. Astrophys. 479, 235. CrossRefADSGoogle Scholar
  11. Hildner, E.: 1974, Solar Phys. 35, 123. CrossRefADSGoogle Scholar
  12. Klimchuk, J.A., Tanner, S.E.M., De Moortel, I.: 2004, Astrophys. J. 616, 1232. CrossRefADSGoogle Scholar
  13. Luna-Cardozo, M., Erdélyi, R., Mendoza-Briceño, C.A.: 2008, In: Erdélyi, R., Mendoza-Briceño, C.A. (eds.) Proc. IAU Symposium Waves and Oscillations in the Solar Atmosphere: Heating and Magneto-Seismology, IAUS 247, Cambridge University Press, Cambridge, 316. Google Scholar
  14. Mendoza-Briceño, C.A., Luna-Cardozo, M.: 2006, In: Bothmer, V., Hady, A.A. (eds.) Proc. IAU Symposium Solar Activity and its Magnetic Origin, IAUS 233, Cambridge University Press, Cambridge, 179. Google Scholar
  15. Mendoza-Briceño, C.A., Erdélyi, R., Sigalotti, L. Di G.: 2004, Astrophys. J. 605, 493. CrossRefADSGoogle Scholar
  16. Nakariakov, V.M., Verwichte, E.: 2005, Living Rev. Solar Phys. 2(3). http://solarphysics.livingreviews.org/Articles/lrsp-2005-3.
  17. Ofman, L., Wang, T.: 2002, Astrophys. J. 580, L85. CrossRefADSGoogle Scholar
  18. Patsourakos, S., Klimchuk, J.A.: 2006, Astrophys. J. 647, 1452. CrossRefADSGoogle Scholar
  19. Patsourakos, S., Klimchuk, J.A.: 2007, Astrophys. J. 667, 591. CrossRefADSGoogle Scholar
  20. Roberts, B.: 2000, Solar Phys. 193, 139. CrossRefADSGoogle Scholar
  21. Roberts, B., Edwin, P.M., Benz, A.O.: 1984, Astrophys. J. 279, 857. CrossRefADSGoogle Scholar
  22. Selwa, M., Murawski, K., Solanki, S.K.: 2005, Astron. Astrophys. 436, 701. CrossRefADSGoogle Scholar
  23. Selwa, M., Ofman, L., Murawski, K.: 2007, Astrophys. J. 668, L83. CrossRefADSGoogle Scholar
  24. Sigalotti, L.D.G., Mendoza-Briceño, C.A.: 2003, Astron. Astrophys. 397, 1083. CrossRefADSGoogle Scholar
  25. Sigalotti, L.D.G., Mendoza-Briceño, C.A., Luna-Cardozo, M.: 2007, Solar Phys. 246, 187. CrossRefADSGoogle Scholar
  26. Taroyan, Y.: 2008, In: Erdélyi, R., Mendoza-Briceño, C.A. (eds.) Proc. IAU Symposium Waves and Oscillations in the Solar Atmosphere: Heating and Magneto-Seismology, IAUS 247, Cambridge University Press, Cambridge, 186. Google Scholar
  27. Taroyan, Y., Bradshaw, S.J.: 2008, Astron. Astrophys. 481, 247. CrossRefADSGoogle Scholar
  28. Taroyan, Y., Erdélyi, R., Doyle, J.G., Bradshaw, S.J.: 2005, Astron. Astrophys. 438, 713. CrossRefADSGoogle Scholar
  29. Taroyan, Y., Erdélyi, R., Doyle, J.G., Bradshaw, S.J.: 2007a, Astron. Astrophys. 462, 331. CrossRefADSGoogle Scholar
  30. Taroyan, Y., Erdélyi, R., Wang, T.J., Bradshaw, S.J.: 2007b, Astrophys. J. 659, L173. CrossRefADSGoogle Scholar
  31. Uchida, Y.: 1970, Pub. Astron. Soc. Japan 22, 341. ADSGoogle Scholar
  32. Wang, T.J., Innes, D.E., Qiu, J.: 2007, Astrophys. J. 656, 598. CrossRefADSGoogle Scholar
  33. Wang, T.J., Solanki, S.K., Curdt, W., Innes, D.E., Dammasch, I.E.: 2002, Astrophys. J. 574, L101. CrossRefADSGoogle Scholar
  34. Wang, T.J., Solanki, S.K., Innes, D.E., Curdt, W., Marsch, E.: 2003, Astron. Astrophys. 402, L17. CrossRefADSGoogle Scholar
  35. Wang, T.J., Solanki, S.K., Innes, D.E., Curdt, W.: 2005, Astron. Astrophys. 435, 753. CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • R. Erdélyi
    • 1
  • M. Luna-Cardozo
    • 1
  • C. A. Mendoza-Briceño
    • 2
  1. 1.SP²RC, Department of Applied MathematicsUniversity of SheffieldSheffieldUK
  2. 2.Centro de Física Fundamental, Facultad de CienciasUniversidad de Los AndesMéridaVenezuela

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