Solar Physics

, Volume 289, Issue 1, pp 167–182 | Cite as

Effects of Stratification and Flows on P1/P2 Ratios and Anti-node Shifts Within Closed Loop Structures

Article

Abstract

The solar atmosphere is a dynamic environment, constantly evolving to form a wide range of magnetically dominated structures (coronal loops, spicules, prominences, etc.) which cover a significant percentage of the surface at any one time. Oscillations and waves in many of these structures are now widely observed and have led to the new analytic technique of solar magneto-seismology, where inferences of the background conditions of the plasma can be deduced by studying magneto-hydrodynamic (MHD) waves. Here, we generalise a novel magneto-seismological method designed to infer the density distribution of a bounded plasma structure from the relationship of its fundamental and subsequent harmonics. Observations of the solar atmosphere have emphatically shown that stratification, leading to complex density profiles within plasma structures, is common thereby rendering this work instantly accessible to solar physics. We show, in a dynamic waveguide, how the period ratio differs from the idealised harmonic ratios prevalent in homogeneous structures. These ratios show strong agreement with recent observational work. Next, anti-node shifts are also analysed. Using typical scaling parameters for bulk flows within atmospheric waveguides, e.g., coronal loops, it is found that significant anti-node shifts can be predicted, even to the order of 10 Mm. It would be highly encouraged to design specific observations to confirm the predicted anti-node shifts and apply the developed theory of solar magneto-seismology to gain more accurate waveguide diagnostics of the solar atmosphere.

Keywords

Oscillations, solar Waves, magnetohydrodynamic Waves, propagation 

References

  1. Andries, J., Arregui, I., Goossens, M.: 2005, Determination of the coronal density stratification from the observation of harmonic coronal loop oscillations. Astrophys. J. Lett. 624, L57. ADSCrossRefGoogle Scholar
  2. Andries, J., van Doorsselaere, T., Roberts, B., Verth, G., Verwichte, E., Erdélyi, R.: 2009, Coronal seismology by means of kink oscillation overtones. Space Sci. Rev. 149, 3. ADSCrossRefGoogle Scholar
  3. Aschwanden, M.J., Fletcher, L., Schrijver, C.J., Alexander, D.: 1999, Coronal loop oscillations observed with the Transition Region and Coronal Explorer. Astrophys. J. 520, 880. ADSCrossRefGoogle Scholar
  4. Bender, C.M., Orszag, S.A.: 1978, Advanced Mathematical Methods for Scientists and Engineers, McGraw Hill, New York, 484. MATHGoogle Scholar
  5. Berghmans, D., Clette, F.: 1999, Active region EUV transient brightenings – First results by EIT of SOHO JOP80. Solar Phys. 186, 207. ADSCrossRefGoogle Scholar
  6. Campos, L.M.B.C.: 1986, On umbral oscillations as a sunspot diagnostic. In: Gough, D.O., (ed.), Seismology of the Sun and the Distant, Stars, NATO ASI Series C 169, 293. CrossRefGoogle Scholar
  7. Campos, L.M.B.C.: 1987, On waves in gases. Part II: Interaction of sound with magnetic and internal modes. Rev. Mod. Phys. 59, 363. MathSciNetADSCrossRefGoogle Scholar
  8. De Moortel, I.: 2009, Longitudinal waves in coronal loops. Space Sci. Rev. 149, 65. ADSCrossRefGoogle Scholar
  9. De Moortel, I., Brady, C.S.: 2007, Observation of higher harmonic coronal loop oscillations. Astrophys. J. 664, 1210. ADSCrossRefGoogle Scholar
  10. Deforest, C.E., Gurman, J.B.: 1998, Observation of quasi-periodic compressive waves in solar polar plumes. Astrophys. J. Lett. 501, L217. ADSCrossRefGoogle Scholar
  11. Díaz, A.J., Oliver, R., Ballester, J.L.: 2010, Prominence thread seismology using the P1/2P2 ratio. Astrophys. J. 725, 1742. ADSCrossRefGoogle Scholar
  12. Dymova, M.V., Ruderman, M.S.: 2005, Non-axisymmetric oscillations of thin prominence fibrils. Solar Phys. 229, 79. ADSCrossRefGoogle Scholar
  13. Edwin, P.M., Roberts, B.: 1983, Wave propagation in a magnetic cylinder. Solar Phys. 88, 179. ADSCrossRefGoogle Scholar
  14. Erdélyi, R.: 2006, In: Fletcher, K., Thompson, M., (eds.) Proceedings of SOHO 18/GONG 2006/HELAS I, Beyond the Spherical Sun SP-624, ESA, Noordwijk, 15.1. (on CDROM). Google Scholar
  15. Erdélyi, R., Taroyan, Y.: 2008, Hinode EUV spectroscopic observations of coronal oscillations. Astron. Astrophys. 489, L49. ADSCrossRefGoogle Scholar
  16. Erdélyi, R., Verth, G.: 2007, The effect of density stratification on the amplitude profile of transversal coronal loop oscillations. Astron. Astrophys. 462, 743. ADSCrossRefGoogle Scholar
  17. Ferraro, C.A., Plumpton, C.: 1958, Hydromagnetic waves in a horizontally stratified atmosphere. V. Astrophys. J. 127, 459. MathSciNetADSCrossRefGoogle Scholar
  18. Jess, D.B., Mathioudakis, M., Erdélyi, R., Verth, G., McAteer, R.T.J., Keenan, F.P.: 2008, Discovery of spatial periodicities in a coronal loop using automated edge-tracking algorithms. Astrophys. J. 680, 1523. ADSCrossRefGoogle Scholar
  19. Jess, D.B., Mathioudakis, M., Erdélyi, R., Crockett, P.J., Keenan, F.P., Christian, D.J.: 2009, Alfvén waves in the lower solar atmosphere. Science 323, 1582. ADSCrossRefGoogle Scholar
  20. Kopp, R.A., Poletto, G., Noci, G., Bruner, M.: 1985, Analysis of loop flows observed on 27 March, 1980 by the UVSP instrument during the Solar Maximum Mission. Solar Phys. 98, 91. ADSCrossRefGoogle Scholar
  21. Leroy, B., Bel, N.: 1979, Propagation of waves in an atmosphere in the presence of a magnetic field. I – The method. Astron. Astrophys. 78, 129. MathSciNetADSGoogle Scholar
  22. Mathioudakis, M., Jess, D.B., Erdélyi, R.: 2012, Alfvén waves in the solar atmosphere. Space Sci. Rev., 94. doi:10.1007/s11214-012-9944-7.
  23. Morton, R.J., Erdélyi, R.: 2009, Transverse oscillations of a cooling coronal loop. Astrophys. J. 707, 750. ADSCrossRefGoogle Scholar
  24. Nakariakov, V.M., Ofman, L.: 2001, Determination of the coronal magnetic field by coronal loop oscillations. Astron. Astrophys. 372, L53. ADSCrossRefGoogle Scholar
  25. Ofman, L., Wang, T.J.: 2008, Hinode observations of transverse waves with flows in coronal loops. Astron. Astrophys. 482, L9. ADSCrossRefGoogle Scholar
  26. O’Shea, E., Srivastava, A.K., Doyle, J.G., Banerjee, D.: 2007, Evidence for wave harmonics in cool loops. Astron. Astrophys. 473, L13. ADSCrossRefGoogle Scholar
  27. Roberts, B.: 2000, Waves and oscillations in the corona (invited review). Solar Phys. 193, 139. ADSCrossRefGoogle Scholar
  28. Roberts, B., Edwin, P.M., Benz, A.O.: 1984, On coronal oscillations. Astrophys. J. 279, 857. ADSCrossRefGoogle Scholar
  29. Rosenberg, H.: 1970, Evidence for MHD pulsations in the solar corona. Astron. Astrophys. 9, 159. ADSGoogle Scholar
  30. Ruderman, M.S.: 2010, The effect of flows on transverse oscillations of coronal loops. Solar Phys. 267, 377. ADSCrossRefGoogle Scholar
  31. Ruderman, M.S., Erdélyi, R.: 2009, Transverse oscillations of coronal loops. Space Sci. Rev. 149, 199. ADSCrossRefGoogle Scholar
  32. Soler, R., Goossens, M.: 2011, Kink oscillations of flowing threads in solar prominences. Astron. Astrophys. 531, A167. ADSCrossRefGoogle Scholar
  33. Soler, R., Ruderman, M.S., Goossens, M.: 2012, Damped kink oscillations of flowing prominence threads. Astron. Astrophys. 546, A82. ADSCrossRefGoogle Scholar
  34. Srivastava, A.K., Zaqarashvili, T.V., Uddin, W., Dwivedi, B.N., Kumar, P.: 2008, Observation of multiple sausage oscillations in cool post-flare loop. Mon. Not. Roy. Astron. Soc. 388, 1899. ADSCrossRefGoogle Scholar
  35. Taroyan, Y., Erdélyi, R.: 2009, Heating diagnostics with MHD waves. Space Sci. Rev. 149, 229. ADSCrossRefGoogle Scholar
  36. Uchida, Y.: 1970, Diagnosis of coronal magnetic structure by flare-associated hydromagnetic disturbances. Publ. Astron. Soc. Japan 22, 341. ADSGoogle Scholar
  37. Van Doorsselaere, T., Nakariakov, V.M., Verwichte, E.: 2007, Coronal loop seismology using multiple transverse loop oscillation harmonics. Astron. Astrophys. 473, 959. ADSCrossRefGoogle Scholar
  38. Verth, G., Erdélyi, R.: 2008, Effect of longitudinal magnetic and density inhomogeneity on transversal coronal loop oscillations. Astron. Astrophys. 486, 1015. ADSCrossRefMATHGoogle Scholar
  39. Verth, G., Erdélyi, R., Jess, D.B.: 2008, Refined magnetoseismological technique for the solar corona. Astrophys. J. Lett. 687, L45. ADSCrossRefGoogle Scholar
  40. Verth, G., Van Doorsselaere, T., Erdélyi, R., Goossens, M.: 2007, Spatial magneto-seismology: Effect of density stratification on the first harmonic amplitude profile of transversal coronal loop oscillations. Astron. Astrophys. 475, 341. ADSCrossRefGoogle Scholar
  41. Verwichte, E., Nakariakov, V.M., Ofman, L., Deluca, E.E.: 2004, Characteristics of transverse oscillations in a coronal loop arcade. Solar Phys. 223, 77. ADSCrossRefGoogle Scholar
  42. Wang, T.: 2011, Standing slow-mode waves in hot coronal loops: observations, modeling, and coronal seismology. Space Sci. Rev. 158, 397. ADSCrossRefGoogle Scholar
  43. Zhugzhda, Y.D.: 1984, Resonance oscillations in sunspots. Sov. Astron. Lett. 10, 19. ADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Solar Physics and Space Plasma Research CenterUniversity of SheffieldSheffieldUK
  2. 2.Armagh ObservatoryArmaghUK

Personalised recommendations