Skip to main content
Log in

Conditions for Propagation of Torsional Waves in Solar Magnetic Flux Tubes

  • Published:
Solar Physics Aims and scope Submit manuscript

Abstract

Propagation of torsional waves along isothermal and initially-untwisted magnetic-flux tubes embedded in the solar atmosphere is studied analytically. Conditions for wave propagation along thin and wide magnetic-flux tubes are determined, and it is shown that the propagation along thin tubes is cutoff free; however, for wide tubes the propagation is affected by a cutoff frequency. A method to determine the cutoff frequency is presented and applied to a specific model of solar magnetic flux tubes. An interesting result is that the cutoff frequency is a local quantity in the model and that its value at a given height determines the frequency that torsional tube waves must have to propagate at this height.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Defouw, R.J.: 1976, Astrophys. J. 209, 226.

    Article  ADS  Google Scholar 

  • Edwards, C.H., Penney, D.E.: 1989, Elementary Differential Equations with Boundary Value Problems, Prentice-Hall, Englewood Cliffs, 137.

    MATH  Google Scholar 

  • Ferriz-Mas, A., Schüssler, M., Anton, V.: 1989, Astron. Astrophys. 210, 425.

    ADS  Google Scholar 

  • Ferriz-Mas, A., Schüssler, M.: 1994, Astrophys. J. 433, 852.

    Article  ADS  Google Scholar 

  • Hasan, S.S., Kalkofen, W.: 1999, Astrophys. J. 519, 899.

    Article  ADS  Google Scholar 

  • Hasan, S.S., Kalkofen, W., van Ballegooijen, A.A., Ulmschneider, P.: 2003, Astrophys. J. 585, 1138.

    Article  ADS  Google Scholar 

  • Hollweg, J.V.: 1978, Solar Phys. 56, 305.

    Article  ADS  Google Scholar 

  • Hollweg, J.V.: 1981, Solar Phys. 70, 25.

    Article  ADS  Google Scholar 

  • Hollweg, J.V.: 1985, In: Buti, B. (ed.) Adv. Space Plasma Phys., World Scientific, Singapore, 77.

    Google Scholar 

  • Hollweg, J.V.: 1990, In: Russell, C.T., Priest, E.R., Lee, L.C. (eds.) Physics of Magnetic Flux Ropes, Geophys. Monograph 58, American Geophysical Union, Washington, 23.

    Google Scholar 

  • Hollweg, J.V.: 1992, Asroppys. J. 389, 731.

    Article  ADS  Google Scholar 

  • Hollweg, J.V., Jackson, S., Galloway, D.: 1982, Solar Phys. 75, 35.

    Article  ADS  Google Scholar 

  • Kahn, P.B.: 1990, Mathematical Methods for Scientists and Engineers, Wiley, New York.

    MATH  Google Scholar 

  • Kudoh, T., Shibata, K.: 1999, Astrophys. J. 514, 493.

    Article  ADS  Google Scholar 

  • Lamb, H.: 1932, Hydrodynamics, Dover, New York.

    MATH  Google Scholar 

  • Musielak, Z.E., Fontenla, J.M., Moore, R.L.: 1992, Phys. Fluids 4, 13.

    Article  Google Scholar 

  • Musielak, Z.E., Musielak, D.E., Mobashi, H.: 2006, Phys. Rev. E 73, 036612-1.

    Article  ADS  Google Scholar 

  • Musielak, Z.E., Rosner, R., Ulmschneider, P.: 1987, In: Linsky, J.L., Stencel, R.E. (eds.) Cool Stars, Stellar Systems, and the Sun, Lecture Notes in Physics 291, 66.

  • Musielak, Z.E., Routh, S., Hammer, R.: 2007, Astrophys. J. 659, 650.

    Article  ADS  Google Scholar 

  • Musielak, Z.E., Ulmschneider, P.: 2001, Astron. Astrophys. 370, 541.

    Article  ADS  Google Scholar 

  • Musielak, Z.E., Ulmschneider, P.: 2003, Astron. Astrophys. 400, 1057.

    Article  ADS  Google Scholar 

  • Musielak, Z.E., Rosner, R., Gail, H.P., Ulmschneider, P.: 1995, Astrophys. J. 448, 865.

    Article  ADS  Google Scholar 

  • Narain, U., Ulmschneider, P.: 1996, Space Sci. Rev. 75, 453.

    Article  ADS  Google Scholar 

  • Noble, M.W., Musielak, Z.E., Ulmschneider, P.: 2003, Astron. Astrophys. 409, 1085.

    Article  ADS  Google Scholar 

  • Parker, E.N.: 1979, Cosmic Magnetic Fields: Their Origin and Their Activity, Clarendon Press, Oxford.

    Google Scholar 

  • Poedts, S., Hermans, D., Goossens, M.: 1985, Astron. Astrophys. 151, 16.

    MATH  ADS  MathSciNet  Google Scholar 

  • Priest, E.R.: 1982, Solar Magneto-Hydrodynamics, Reidel, Dordrecht.

    Google Scholar 

  • Rae, I.C., Roberts, B.: 1982, Astrophys. J. 256, 761.

    Article  ADS  Google Scholar 

  • Roberts, B.: 1991, Geophys. Astrophys. Fluid Dyn. 62, 83.

    Article  ADS  Google Scholar 

  • Roberts, B., Ulmschneider, P.: 1997, In: Simett, G.M., Alissandrakis, C.E., Vlahos, L. (eds.) Solar and Heliospheric Plasma Physics, Springer, Berlin, 75.

    Google Scholar 

  • Roberts, B., Webb, A.R.: 1979, Solar Phys. 64, 77.

    Article  ADS  Google Scholar 

  • Routh, S., 2006, M.S. thesis, Univ. Texas at Arlington.

  • Saito, T., Kudoh, T., Shibata, K.: 2001, Astrophys. J. 554, 1151.

    Article  ADS  Google Scholar 

  • Solanki, S.K.: 1993, Space Sci. Rev. 63, 1.

    Article  ADS  Google Scholar 

  • Spruit, H.C.: 1981, Astron. Astrophys. 98, 155.

    MATH  ADS  Google Scholar 

  • Spruit, H.C.: 1982, Solar Phys. 75, 3.

    Article  ADS  Google Scholar 

  • Stix, M.: 2004, The Sun: An Introduction, Springer, Berlin.

    MATH  Google Scholar 

  • Ulmschneider, P., Musielak, Z.E.: 2003, In: Pevtsov, A.A., Uitenbroek, H. (eds.) 21st NSO/SP Workshop on Current Theoretical Models and Future High Resolution Solar Observations: Preparation for ATST, ASP Conf. Ser. 286, 363.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. Hammer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Routh, S., Musielak, Z.E. & Hammer, R. Conditions for Propagation of Torsional Waves in Solar Magnetic Flux Tubes. Sol Phys 246, 133–143 (2007). https://doi.org/10.1007/s11207-007-0400-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11207-007-0400-x

Keywords

Navigation