Skip to main content
SpringerLink
Log in

The Alpha Effect and the Observed Twist and Current Helicity of Solar Magnetic Fields

  • Published:
Solar Physics Aims and scope Submit manuscript

Abstract

We present a straightforward comparison of model calculations for the α-effect, helicities, and magnetic field line twist in the solar convection zone with magnetic field observations at atmospheric levels. The model calculations are carried out in a mixing-length approximation for the turbulence with a profile of the solar internal rotation rate obtained from helioseismic inversions. The magnetic field data consist of photospheric vector magnetograms of 422 active regions for which spatially-averaged values of the force-free twist parameter and of the current helicity density are calculated, which are then used to determine latitudinal profiles of these quantities. The comparison of the model calculations with the observations suggests that the observed twist and helicity are generated in the bulk of the convection zone, rather than in a layer close to the bottom. This supports two-layer dynamo models where the large-scale toroidal field is generated by differential rotation in a thin layer at the bottom while the α-effect is operating in the bulk of the convection zone. Our previous observational finding was that the moduli of the twist factor and of the current helicity density increase rather steeply from zero at the equator towards higher latitudes and attain a certain saturation at about 12 – 15∘. In our dynamo model with algebraic nonlinearity, the increase continues, however, to higher latitudes and is more gradual. This could be due to the neglect of the coupling between small-scale and large-scale current and magnetic helicities and of the latitudinal drift of the activity belts in the model.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abramenko, V.I., Wang, T., and Yurchishin, V.B.: 1996, Solar Phys. 168, 75.

    ADS  Google Scholar 

  • Bao, S. and Zhang, H.: 1998, Astrophys. J. 496, L43.

    Article  ADS  Google Scholar 

  • Belvedere, G., Kuzanyan, K.M., and Sokoloff, D.: 2000, Mon. Not. R. Astron. Soc. 315, 778.

    Article  ADS  Google Scholar 

  • Berger, M.A. and Ruzmaikin, A.A.: 2000, J. Geophys. Res. 105, 10481.

    ADS  Google Scholar 

  • Boström, R.: 1973, Astrophys. Space Sci. 22, 353.

    Article  ADS  Google Scholar 

  • Bothmer, V. and Schwenn, R.: 1998, Ann. Geophys. 16, 1.

    ADS  Google Scholar 

  • Canfield, R.C., Hudson, H.S., and McKenzie, D.E.: 1999, Geophys. Res. Lett. 26, 627.

    Article  ADS  Google Scholar 

  • Dasso, S., Mandrini, C.H., Démoulin, P., and Farrugia, C.J.: 2003, J. Geophys. Res. 108, 1362, doi: 10.1029/2003JA009942.

  • Démoulin, P., Mandrini, C.H., van Driel-Gesztelyi, L., López Fuentes, M.C., and Aulanier, G.: 2002, Solar Phys. 207, 87.

    Article  ADS  Google Scholar 

  • DeVore, C.R.: 2000, Astrophys. J. 539, 944.

    ADS  Google Scholar 

  • Ding, Y.J., Hong, Q.F., and Wang, H.Z.: 1987, Solar Phys. 107, 221.

    Article  ADS  Google Scholar 

  • Durney, B.R. and Spruit, H.C.: 1979, Astrophys. J. 234, 1067.

    Article  ADS  Google Scholar 

  • Duvall, Jr., T.L. and Gizon, L.: 2000, Solar Phys. 192, 177.

    ADS  Google Scholar 

  • Frisch, U., Pouquet, A., Léorat, J., and Mazure, A.: 1975, J. Fluid Mech. 68, 769.

    ADS  Google Scholar 

  • Hagino, M. and Sakurai, T.: 2004, Publ. Astron. Soc. Japan 56, 831.

    ADS  Google Scholar 

  • Hale, G.E.: 1927, Nature 119, 708.

    ADS  Google Scholar 

  • Keinigs, R.K.: 1983, Phys. Fluids 26, 2558.

    Article  ADS  MATH  Google Scholar 

  • Kichatinov, L.L.: 1987, Geophys. Astrophys. Fluid Dyn. 38, 273.

    MATH  Google Scholar 

  • Kichatinov, L.L.: 1991, Astron. Astrophys. 243, 483.

    ADS  MATH  Google Scholar 

  • Kichatinov, L.L. and Rüdiger, G.: 1992, Astron. Astrophys. 260, 494.

    ADS  Google Scholar 

  • Kitchatinov, L.L. and Rüdiger, G.: 1999, Astron. Astrophys. 344, 911.

    ADS  Google Scholar 

  • Kleeorin, N.I. and Ruzmaikin, A.A.: 1982, Magnetohydrodynamics 18, 116.

    Google Scholar 

  • Kleeorin, N., Kuzanyan, K., Moss, D., Rogachevskii, I., Sokoloff, D., and Zhang, H.: 2003, Astron. Astrophys. 409, 1097.

    Article  ADS  Google Scholar 

  • Krause, F. and Rädler, K.-H.: 1980, Mean-Field Magnetohydrodynamics and Dynamo Theory, Akademie-Verlag, Berlin.

    Google Scholar 

  • Kuzanyan, K., Bao, S., and Zhang, H.: 2000, Solar Phys. 191, 231.

    Article  ADS  Google Scholar 

  • Leamon, R.J., Canfield, R.C., and Pevtsov, A.A.: 2004, J. Geophys. Res. 109, A05106, doi: 10.1029/2003JA010324.

  • Longcope, D.W. and Pevtsov, A.A.: 2003, Adv. Space Res. 32, 1845.

    ADS  Google Scholar 

  • Longcope, D.W., Fisher, G.H., and Pevtsov, A.A.: 1998, Astrophys. J. 507, 417.

    ADS  Google Scholar 

  • Longcope, D., Linton, M., Pevtsov, A., Fisher, G., and Klapper, I.: 1999, in M.R. Brown, R.C. Canfield, and A.A. Pevtsov (eds.), Magnetic Helicity in Space and Laboratory Plasmas. Vol. 111: Geophysical Monographs, Am. Geophys. U., Washington, DC, p. 93.

  • López Fuentes, M.C., Démoulin, P., Mandrini, C.H., Pevtsov, A.A., and van Driel-Gesztelyi, L.: 2003, Astron. Astrophys. 397, 305.

    Article  ADS  Google Scholar 

  • Low, B.C.: 2001, J. Geophys. Res. 106, 25141.

    Article  ADS  Google Scholar 

  • Martin, S.F.: 1998, in D. Webb, D. Rust, and B. Schmieder (eds.), New Perspectives on Solar Prominences. Vol. 150: ASP Conf. Ser., Astronomical Society of the Pacific, San Francisco, p. 419.

  • Martin, S.F., Bilimoria, R., and Tracadas, P.W.: 1994, in R.J. Rutten and C.J. Schrijver (eds.), Solar Surface Magnetism, Kluwer, Dordrecht, p. 303.

  • Matthaeus, W.H., Goldstein, M.L., and Lantz, S.R.: 1986, Phys. Fluids 29, 1504.

    ADS  MathSciNet  Google Scholar 

  • Moffatt, H.K.: 1978, Magnetic Field Generation in Electrically Conducting Fluids, Cambridge University Press, Cambridge, England.

    Google Scholar 

  • Ossendrijver, M.: 2003, Astron. Astrophys. Rev. 11, 287.

    ADS  Google Scholar 

  • Parker, E.N.: 1979, Cosmical Magnetic Fields, Clarendon Press, Oxford.

    Google Scholar 

  • Pevtsov, A.A.: 2002, in P.C.H. Martens and D.P. Cauffman (eds.), Multi-Wavelength Observations of Coronal Structure and Dynamics. Vol. 13: COSPAR Colloq., Pergamon, Dordrecht, p. 125.

  • Pevtsov, A.A. and Canfield, R.C.: 1999, in M.R. Brown, R.C. Canfield, and A.A. Pevtsov (eds.), Magnetic Helicity in Space and Laboratory Plasmas. Vol. 111: Geophysical Monographs, Am. Geophys. U., Washington, DC, p. 103.

  • Pevtsov, A.A. and Latushko, S.M.: 2000, Astrophys. J. 528, 999.

    Article  ADS  Google Scholar 

  • Pevtsov, A.A., Canfield, R.C., and Latushko, S.M.: 2001, Astrophys. J. 549, L261.

    Article  ADS  Google Scholar 

  • Pevtsov, A.A., Canfield, R.C., and Metcalf, T.R.: 1995, Astrophys. J. 440, L109.

    Article  ADS  Google Scholar 

  • Pipin, V.V.: 2003, Geophys. Astrophys. Fluid Dyn. 97, 25.

    ADS  MathSciNet  Google Scholar 

  • Pipin, V.V., Seehafer, N., and Kuzanyan, K.M.: 2006, Astron. Astrophys. (in preparation).

  • Pouquet, A., Frisch, U., and Léorat, J.: 1976, J. Fluid Mech. 77, 321.

    ADS  Google Scholar 

  • Raadu, M.A.: 1972, Solar Phys. 22, 443.

    ADS  Google Scholar 

  • Rädler, K.-H. and Seehafer, N.: 1990, in H.K. Moffatt and A. Tsinober (eds.), Topological Fluid Mechanics, Cambridge University Press, Cambridge, England, p. 157.

  • Richardson, R.: 1941, Astrophys. J. 93, 24.

    Article  ADS  Google Scholar 

  • Roberts, P.H. and Soward, A.M.: 1992, Ann. Rev. Fluid Mech. 24, 459.

    Article  ADS  MathSciNet  Google Scholar 

  • Rüdiger, G. and Arlt, R.: 2003, in A. Ferriz-Mas and M. Núñez (eds.), Advances in Nonlinear Dynamos, Taylor and Francis, London, p. 147.

    Google Scholar 

  • Rüdiger, G. and Brandenburg, A.: 1995, Astron. Astrophys. 296, 557.

    ADS  Google Scholar 

  • Rüdiger, G. and Kichatinov, L.L.: 1993, Astron. Astrophys. 269, 581.

    ADS  Google Scholar 

  • Rüdiger, G. and Pipin, V.V.: 2000, Astron. Astrophys. 362, 756.

    ADS  Google Scholar 

  • Rüdiger, G., Brandenburg, A., and Pipin, V.V.: 1999, Astron. Nachr. 320, 135.

    Article  ADS  Google Scholar 

  • Rüdiger, G., Pipin, V.V., and Belvedere, G.: 2001, Solar Phys. 198, 241.

    Article  ADS  Google Scholar 

  • Rust, D.M.: 1994, Geophys. Res. Lett. 21, 241.

    Article  ADS  Google Scholar 

  • Rust, D.M.: 2001, J. Geophys. Res. 106, 25075.

    Article  ADS  Google Scholar 

  • Rust, D.M. and Kumar, A.: 1994, Solar Phys. 155, 69.

    Article  ADS  Google Scholar 

  • Rust, D.M. and Kumar, A.: 1996, Astrophys. J. 464, L199.

    Article  ADS  Google Scholar 

  • Ruzmaikin, A.A., Martin, S., and Hu, Q.: 2003, J. Geophys. Res. 108, 1096, doi: 10.1029/2002JA009588.

  • Schou, J., Antia, H.M., Basu, S., Bogart, R.S., Bush, R.I., Chitre, S.M., Christensen-Dalsgaard, J., Di Mauro, M.P., Dziembowski, W.A., Eff-Darwich, A., Gough, D.O., Haber, D.A., Hoeksema, J.T., Howe, R., Korzennik, S.G., Kosovichev, A.G., Larsen, R.M., Pijpers, F.P., Scherrer, P.H., Sekii, T., Tarbell, T.D., Title, A.M., Thompson, M.J., and Toomre, J.: 1998, Astrophys. J. 505, 390.

    Article  ADS  Google Scholar 

  • Seehafer, N.: 1990, Solar Phys. 125, 219.

    Article  ADS  Google Scholar 

  • Seehafer, N.: 1994, Europhys. Lett. 27, 353.

    Google Scholar 

  • Seehafer, N.: 1996, Phys. Rev. E 53, 1283.

    Article  ADS  Google Scholar 

  • Seehafer, N., Gellert, M., Kuzanyan, K.M., and Pipin, V.V.: 2003, Adv. Space Res. 32, 1819.

    ADS  Google Scholar 

  • Steenbeck, M., Krause, F., and Rädler, K.-H.: 1966, Z. Naturforsch. 21a, 369.

    ADS  Google Scholar 

  • Stix, M.: 2002, The Sun. An Introduction, 2nd edn., Springer, Berlin.

    Google Scholar 

  • van Ballegooijen, A.A. and Martens, P.C.H.: 1990, Astrophys. J. 361, 283.

    Article  ADS  Google Scholar 

  • van Ballegooijen, A.A., Cartledge, N.P., and Priest, E.R.: 1998, Astrophys. J. 501, 866.

    Article  ADS  Google Scholar 

  • Zeldovich, Y., Ruzmaikin, A.A., and Sokoloff, D.D.: 1983, Magnetic Fields in Astrophysics, Gordon and Breach, New York.

    Google Scholar 

  • Zhang, H. and Bao, S.: 1998, Astron. Astrophys. 339, 880.

    ADS  Google Scholar 

  • Zhang, H.Q., Bao, S.D., and Kuzanyan, K.M.: 2002, Astron. Rep. 46, 424.

    Article  ADS  Google Scholar 

  • Zirker, J.B., Martin, S.F., Harvey, K., and Gaizauskas, V.: 1997, Solar Phys. 175, 27.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China

    K. M. Kuzanyan

  2. Institute for Terrestrial Magnetism, Ionosphere and Radiowave Propagation (IZMIRAN), Troitsk, Moscow Region, Russia

    K. M. Kuzanyan

  3. Department of Applied Mathematics, University of Leeds, Leeds, U.K.

    K. M. Kuzanyan

  4. Institute for Solar-Terrestrial Physics, Irkutsk, Russia

    V. V. Pipin

  5. Institut für Physik, Universitäat Potsdam, Potsdam, Germany

    N. Seehafer

Authors
  1. K. M. Kuzanyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Pipin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Seehafer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. M. Kuzanyan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuzanyan, K.M., Pipin, V.V. & Seehafer, N. The Alpha Effect and the Observed Twist and Current Helicity of Solar Magnetic Fields. Sol Phys 233, 185–204 (2006). https://doi.org/10.1007/s11207-006-1636-6

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11207-006-1636-6

Keywords

Search

Navigation