Skip to main content
SpringerLink
Log in

The nature of the sunspot phenomenon

I: Solutions of the heat transport equation

  • Published:
Solar Physics Aims and scope Submit manuscript

Abstract

Heat transport in the Sun is describable by a Fokker-Planck, or diffusion, transfer equation. A study of the general character of the solutions of the transfer equation shows that the inhibition of convective transport beneath the photosphere produces a photospheric dark ring surrounded by a bright ring, or at best, a dark area surrounded by a bright ring. The mean temperature beneath the ‘sunspot’ is unavoidably above normal, so that the enhanced gas pressure would disperse, rather than concentrate, the magnetic field. Hence we conclude that the inhibition of convection cannot be the cause of a sunspot.

We suggest, instead, that a sunspot is a region of enhanced, rather than inhibited, energy transport and emissivity. The magnetic field of the sunspot causes a dynamical overstability in the outer thousand km of the convective zone, generating copious fluxes of hydromagnetic waves, which propagate rapidly out of the region along the magnetic field. We suggest that this heat engine is so efficient as to convert at least three fourths of the heat flux into waves. Solutions of the heat transport equation in the presence of a heat sink automatically resemble the observed sunspot, including a dark interior, a sharp transition at the edge of the umbra, and an extended grey area around the outside, the penumbra. The mean temperature is reduced, causing the observed concentration of the magnetic field.

The enhanced radiation is in the form of hydromagnetic waves, which do not appear in ordinary photographs, but which light up the ‘sky’ over the sunspot in a manner conspicuous in any UV or X-ray picture. In this respect, then, a sunspot is effectively a hole in the Sun, extending down to temperatures of 2 × 104 K or more.

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

  • Biermann, L.: 1941, Vierteljahrsschr. Astron. Gesellsch. 76, 194.

    Google Scholar 

  • Brückner, G.: 1965, in R. Lüst (ed.), ‘Stellar and Solar Magnetic Fields’, IAU Symp. 22, 293.

  • Chandrasekhar, S.: 1943, Rev. Mod. Phys. 15, 1.

    Google Scholar 

  • Chandrasekhar, S.: 1952, Phil. Mag. 43, 501.

    Google Scholar 

  • Chandrasekhar, S.: 1953, Proc. Roy. Soc. (London) A216, 293.

    Google Scholar 

  • Chandrasekhar, S: 1954, Phil. Mag. 45, 1117.

    Google Scholar 

  • Chandrasekhar, S.: 1961, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford.

    Google Scholar 

  • Chitre, S.: 1963, Monthly Notices. Roy. Astron. Soc. 126, 431.

    Google Scholar 

  • Cowling, T. G.: 1953, in G. P. Kuiper (ed.), The Sun, University of Chicago Press, Chicago.

    Google Scholar 

  • Cowling, T. G.: 1957, Magnetohydrodynamics, John Wiley and Sons, New York.

    Google Scholar 

  • Danielson, R. E.: 1961a, Astrophys. J. 134, 275.

    Google Scholar 

  • Danielson, R. E.: 1961b, Astrophys. J. 134, 289.

    Google Scholar 

  • Danielson, R. E.: 1964, Astrophys. J. 139, 45.

    Google Scholar 

  • Danielson, R. E.: 1965, in R. Lüst (ed.), ‘Stellar and Solar Magnetic Fields’, IAU Symp. 22, 315.

  • de Jager, C.: 1959, Handb. Phys. 52, Springer-Verlag, Berlin, p. 151.

    Google Scholar 

  • Dienzer, W.: 1965, Astrophys. J. 141, 548.

    Google Scholar 

  • Elsasser, H. and Fricke, K.: 1965, in R. Lüst (ed.), ‘Stellar and Solar Magnetic Fields’, IAU Symp. 22, 297.

  • Elste, G.: 1963, J. Quant. Spectrosc. Rad. Transf. 3, 185.

    Google Scholar 

  • Fukao, S. and Tsuda, T.: 1973, J. Plasma Phys. 9, 409.

    Google Scholar 

  • Gokhale, M. H. and Zwaan, C.: 1972, Solar Phys. 26, 52.

    Google Scholar 

  • Greenwich Observatory: 1923, Monthly Notices Roy. Astron. Soc. 84, 96.

    Google Scholar 

  • Houtgast, J. and Sluiters, A. van: 1948, Bull. Astron. Inst. Netherlands 10, 325.

    Google Scholar 

  • Howard, R.: 1958, Astrophys. J. 127, 108.

    Google Scholar 

  • Hoyle, F.: 1949, Some Recent Researches in Solar Physics, Cambridge University Press, Cambridge, P. 10.

    Google Scholar 

  • Jahnke, E. and Emde, F.: 1945, Tables of Functions with Formulae and Curves, Dover Publications, New York.

    Google Scholar 

  • Janssen, J.: 1896, Ann. Obs. Paris, Meudon. 1, Pl. 10, reproduced in Kiepenheuer (1953), p. 341.

    Google Scholar 

  • Kiepenheuer, K. O.: 1953, in G. P. Kuiper (ed.), The Sun, University of Chicago Press, Chicago, p. 322.

    Google Scholar 

  • Kiepenheuer, K. O.: 1966, in G. Barbera (ed.), Proceedings of the Sunspot Symposium, Florence, p. 26.

  • Loughhead, R. E. and Bray, R. J.: 1960, Australian J. Phys. 13, 139.

    Google Scholar 

  • Moore, R. L.: 1973, Solar Phys. 30, 403.

    Google Scholar 

  • Morse, P. M. and Feshbach, H.: 1953, Methods of Theoretical Physics, Vol. I, McGraw-Hill, New York, p. 978.

    Google Scholar 

  • Mullan, D. J.: 1973, Solar Phys. 30, 75.

    Google Scholar 

  • Mullan, D. J. and Yun, H. S.: 1973, Solar Phys. 30, 83.

    Google Scholar 

  • Musman, S.: 1967, Astrophys. J. 149, 201.

    Google Scholar 

  • Öpik, E. J.: 1950, Monthly Notices Roy. Astron. Soc. 110, 559.

    Google Scholar 

  • Osterbrock, D. E.: 1961, Astrophys. J. 134, 347.

    Google Scholar 

  • Parker, E. N. 1955, Astrophys. J. 121, 491.

    Google Scholar 

  • Parker, E. N. 1963, Astrophys. J. Suppl. 8, 177.

    Google Scholar 

  • Parker, E. N. 1973, J. Plasma Phys. 9, 49.

    Google Scholar 

  • Parker, E. N. 1974a, Astrophys. J., in press.

  • Parker, E. N. 1974b, Astrophys. J., submitted for publication.

  • Piddington,. J. H.: 1973, Solar Phys. 31, 229.

    Google Scholar 

  • Priest, E. R.: 1972, Monthly Notices Roy. Astron. Soc. 159, 389.

    Google Scholar 

  • Savage, B. D. 1969, Astrophys. J. 156, 707.

    Google Scholar 

  • Schlüter, A. and Temesvary, St.: 1958, in B. Lehnert (ed.), ‘Electromagnetic Phenomena in Cosmical Physics’, IAU Symp. 6, 263.

  • Schröter, E. H.: 1971, in R. Howard (ed.), ‘Solar Magnetic Fields’, IAU Symp. 43, 167.

  • Smith, E. v. P. and Gottlieb, D. M.: 1974, in preparation.

  • Sonnerup, B. U. O.: 1970, J. Plasma Phys. 4, 161.

    Google Scholar 

  • Sweet, P. A.: 1969, Ann. Rev. Astron. Astrophys. 7, 149.

    Google Scholar 

  • Thompson, W. B.: 1951, Phil. Mag. 42, 1417.

    Google Scholar 

  • Vaiana, G. S., Davis, J. M., Giacconi, R., Krieger, A. S., Silk, J. K., Timothy, A. F., and Zombeck, M.: 1973, Astrophys. J. Letters 185, L47.

    Google Scholar 

  • Walen, C.: 1949, On the Vibratory Rotation of the Sun, Henrik Lindstah's Bokhandel, Stockholm.

    Google Scholar 

  • Weymann, R.: 1960, Astrophys. J. 132, 452.

    Google Scholar 

  • Wilson, P. R.: 1972, Solar Phys. 27, 354, 363.

    Google Scholar 

  • Yeh, Y. and Axford, W. I.: 1970, J. Plasma Phys. 4, 207.

    Google Scholar 

  • Zwaan, C.: 1965, Rech. Astron. Obs. Utrecht 17, No. 4, 141.

    Google Scholar 

  • Zwaan, C.: 1968, Ann. Rev. Astron. Astrophys. 6, 135.

    Google Scholar 

  • Zwaan, C.: 1974, private communication.

Download references

Author information

Authors and Affiliations

  1. Dept. of Physics, Dept. of Astronomy and Astrophysics, University of Chicago, 60637, Chicago, Ill., U.S.A.

    E. N. Parker

Authors
  1. E. N. Parker
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Parker, E.N. The nature of the sunspot phenomenon. Sol Phys 36, 249–274 (1974). https://doi.org/10.1007/BF00151194

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00151194

Keywords

Search

Navigation