Abstract
This paper presents a new class of exact solutions describing the non-linear force-free field above a spatially localized photospheric bipolar magnetic region. An essential feature is the variation in all three Cartesian directions and this could not be modelled adequately with previously known symmetric force-free fields. Sequences of force-free fields are constructed and analyzed to simulate the slow growth of a pair of spots on the photosphere. The axis connecting the spots executes rotational motion, distorting the photospheric neutral line separating fluxes of opposite signs. We show directly from the analytic solutions that the resulting reversal of the positions of the spots relative to the background field is associated with (i) the creation of magnetic free energy, (ii) the severe shearing of localized low-lying loops in the vicinity where the photospheric transverse field aligns with the photospheric neutral line, and (iii) the emergence and disappearance of flux from the photosphere at these highly stressed regions. The model relates theoretically for the first time these different magnetic field features that have been suggested by observation and theoretical considerations to be flare precursors. A general formula, based on the virial theorem, is also given for the free energy of a force-free field, strictly in terms of the field value at the photosphere. This formula has obvious practical application.
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References
Barnes, C. W. and Sturrock, P. A.: 1972, Astrophys. J. 174, 659.
Birn, J., Goldstein, H., and Schindler, K.: 1978, Solar Phys. 57, 81.
Beckers, J. M.: 1971, in R. Howard (ed.), ‘Solar Magnetic Fields’, IAU Symp. 43, 3.
Canfield, R. C., Priest, E. R., and Rust, D. M.: 1974, in Flare Related Magnetic Field Dynamics, NCAR, p. 361.
Chandrasekhar, S.: 1961, Hydrodynamic and Hydromagnetic Stability, Oxford Univ. Press.
Chandrasekhar, S. and Kendall, P. C.: 1957, Astrophys. J. 126, 457.
Cheng, C. C.: 1977, Solar Phys. 55, 413.
Cohen, R. H., Coppi, B., and Treves, A.: 1973, Astrophys. J. 179, 269.
Gold, T.: 1964, in W. N. Hess (ed.), AAS-NASA Symp. Physics of Solar Flares, NASA, p. 389.
Hagyard, M. J., Cumings, N. P., and West, E. A.: 1981, Rev. Scientific Instruments, (submitted).
Harvey, J. W.: 1977, Highlights of Astronomy 4, 223.
Heyvaerts, J., Priest, E. R., and Rust, D. M.: 1977, Astrophys. J. 216, 123.
Jackson, J. D.: 1962, Classical Electrodynamics, Wiley, New York.
Jockers, K.: 1978, Solar Phys. 56, 37.
Kahler, S. W., Krieger, A. S., and Vaiana, C. S.: 1975, Astrophys. J. Letters 199, L57.
Kahler, S. W., Spicer, D., Uchida, Y., and Zirin, H.: 1980, in P. A. Sturrock (ed.), Solar Flares, Colorado Associated Univ. Press, p. 83.
Levine, R. H.: 1975, Solar Phys. 44, 365.
Livingston, W. C.: 1974, in Flare Related Magnetic Field Dynamics, NCAR, p. 269.
Low, B. C.: 1977a, Astrophys. J. 212, 234.
Low, B. C.: 1977b, Astrophys. J. 217, 988.
Low, B. C.: 1980a, Astrophys. J. 239, 377.
Low, B. C.: 1980b, MSFC/NASA Preprint.
Low, B. C.: 1982, Rev. Geophys. Space Phys., (in press).
Low, B. C. and Chalmers, J.: 1981, in preparation.
Lüst, R. and Schlüter, A.: 1954, Z. Astrophys. 34, 263, 365.
Martin, S. F.: 1973, Solar Phys. 31, 3.
Martin, S. F. and Ramsey, H. E.: 1972, in P. McIntosh and M. Dryer (eds.), Solar Activity Observations and Predictions, MIT Press, p. 371.
Milsom, F. and Wright, G. A. E.: 1976, Monthly Notices Roy. Astron. Soc. 174, 307.
Molodensky, M. M.: 1974, Solar Phys. 39, 393.
Morikawa, G. K.: 1969, Phys. Fluid 12, 1648.
Nakagawa, Y. and Raadu, M. A.: 1972, Solar Phys. 25, 127.
Petrasso, R. D., Kahler, S. W., Krieger, A. S., Silk, J. K., and Vaiana, G. S.: 1975, Astrophys. J. Letters 199, L127.
Prata, S. W.: 1972, Solar Phys. 25, 36.
Priest, E. R. and Milne, A. M.: 1980, Solar Phys. 65, 315.
Ribes, E.: 1969, Astron. Astrophys. 2, 316.
Roy, T.-R. and Tang, F.: 1975, Solar Phys. 42, 425.
Rust, D. M.: 1968, in K. O. Kiepenheuer (ed.), ‘Structure and Development of Solar Active Regions’, IAU Symp. 35, 77.
Rust, D. M.: 1972, Solar Phys. 25, 141.
Rust, D. M.: 1973, Solar Phys. 33, 205.
Rust, D. M.: 1976, Solar Phys. 47, 21.
Rust, D. M., Nakagawa, Y., and Neupert, W. M.: 1975, Solar Phys. 41, 397.
Sakurai, T.: 1979, Publ. Astron. Soc. Japan, 31, 209.
Sakurai, T.: 1981a, Solar Phys. 69, 343.
Sakurai, T.: 1981b, preprint.
Schmidt, H.: 1964, in W. N. Hess (ed.), AAS-NASA Symp. Physics of Solar Flares, NASA, p. 107.
Schmidt, H.: 1968, in K. O. Kiepenheuer (ed.), ‘Structure and Development of Solar Active Regions’, IAU Symp. 35, 95.
Smith Jr., J. B., Hagyard, M. J., and Krall, K.: 1981, preprint.
Stenflo, J. O.: 1978, Rep. Prog. Phys. 41, 865.
Sturrock, P. A.: 1967, in P. A. Sturrock (ed.), Plasma Astrophysics, Academic Press, p. 168.
Sturrock, P. A. (ed.): 1980, Solar Flares, Colorado Assoc. Univ. Press.
Sturrock, P. A. and Woodbury, E. T.: 1967, in P. A. Sturrock (ed.), Plasma Astrophysics, Academic Press, p. 155.
Su, Q.-R.: 1980, Acta Astron. Sinica 21, 152.
Švestka, Z.: 1976, Solar Flares, D. Reidel Publ. Co., Dordrecht, Holland.
Tanaka, K.: 1976, Solar Phys. 47, 247.
Tandberg-Hanssen, E.: 1974, Solar Prominences, D. Reidel Publ. Co., Dordrecht, Holland.
Vorpahl, J. A.: 1973, Solar Phys. 28, 115.
Vorpahl, J. A.: 1976, Astrophys. J. 205, 868.
Vorpahl, J. A., Gibson, E. G., Landecker, P. B., McKenzie, D. L., and Underwood, J. H.: 1975, Solar Phys. 45, 199.
Zirin, H.: 1970a, Solar Phys. 14, 428.
Zirin, H.: 1970b, Solar Phys. 14, 342.
Zirin, H.: 1972, Solar Phys. 22, 34.
Zirin, H.: 1974, Vistas Astron. 16, 1.
Zirin, H. and Lazareff, B.: 1975, Solar Phys. 41, 425.
Zirin, H. and Tanaka, K.: 1973, Solar Phys. 32, 173.
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The National Center for Atmospheric Research is sponsored by the National Science Foundation.
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Low, B.C. Magnetic field configurations associated with polarity intrusion in a solar active region. Sol Phys 77, 43–61 (1982). https://doi.org/10.1007/BF00156094
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DOI: https://doi.org/10.1007/BF00156094