Abstract
An X-ray or EUV image of the corona or chromosphere is a 2D representation of an extended 3D complex for which a general inversion process is impossible. A specific model must be incorporated in order to understand the full 3D structure. We approach this problem by modeling a set of optically-thin 3D plasma flux tubes which we render these as synthetic images. The resulting images allow the interpretation of the X-ray/EUV observations to obtain information on (1) the 3D structure of X-ray images, i.e., the geometric structure of the flux tubes, and on (2) the internal structure using specific plasma characteristics, i.e., the physical structure of the flux tubes. The data-analysis technique uses magnetograms to characterize photospheric magnetic fields and extrapolation techniques to form the field lines. Using a new set of software tools, we have generated 3D flux tube structures around these field lines and integrated the plasma emission along the line of sight to obtain a rendered image. A set of individual flux-tube images is selected by a non-negative least-squares technique to provide a match with an observed X-ray image. The scheme minimizes the squares of the differences between the synthesized image and the observed image with a non-negative constraint on the coefficients of the brightness of the individual flux-tube loops. The derived images are used to determine the specific photospheric foot points and physical data, i.e., scaling laws for densities and loop lengths. The development has led to computer efficient integration and display software that is compatible for comparison with observations (e.g., Yohkoh SXT data, NIXT, or EIT). This analysis is important in determining directly the magnetic field configuration, which provides the structure of coronal loops, and indirectly the electric currents or waves, which provide the energy for the heating of the plasma. We have used very simple assumptions (i.e., potential magnetic fields and isothermal corona) to provide an initial test of the techniques before complex models are introduced. We have separated the physical and geometric contributions of the emission for a set of flux tubes and concentrated, in this initial study, on the geometric contributions by making approximations to the physical contributions. The initial results are consistent with the scaling laws derived from the Yohkoh SXT data.
Similar content being viewed by others
References
Airapetian, V. S. and Smartt, R. N.: 1995, Astrophys. J. 445, 489.
Alexander, D. and Katsev, S.: 1996, Solar Phys. 167, 153.
Bray, R. J., Cram, L. E., Durrant, C. J., and Loughhead, R. E.: 1991, Plasma Loops in the Solar Corona, Cambridge University Press, Cambridge.
Ciaravella, A., Peres, G., Maggio, A., and Serio, S.: 1996, Astron. Astrohys. 306, 553.
Culhane, J. L.: 1969, Monthly Notices Roy. Astron. Soc. 144, 379.
Davis, H. F.: 1963, Fourier Series and Orthogonal Functions, Allyn and Bacon, Boston, Ch. 2, p. 52.
Démoulin, P., van Driel-Geszfelyi, Schmiedder, B., Hénoux, J. C., Csepura, G., and Hagyard, M. J.: 1993, Astron. Astrophys. 271, 292.
Démoulin, P., Mandrini, C. H., Rovira, M. G., Hénoux, J. C., and Machado, M. E.: 1994, Solar Phys. 150, 221.
Drebin, R. A., Carpenter, L., and Hanrahan, P.: 1988, Computer Graphics 22, 65.
Elwert, G.: 1961, J. Geophys Res. 66, 391.
Fox, P.: 1908, Astrophys J. 28, 253.
Gary, G. A.: 1992, Mem. Soc. Astron. It. 61, 457.
Gibson, E. G.: 1973, The Quiet Sun, NASA SP-303, p. 295.
Godovnikov, N. V. and Smirnova, E. P.: 1965, Izv. Krymsk. Astrofiz. Obs. 33, 86.
Hagyard, M. J.: 1988, Solar Phys. 115, 167.
Hagyard, M. J.: 1990, Mem. Soc. Astron. It. 61, 337.
Harvey, J. W.: 1966, Evaluation of Solar Magnetograms, Astro-Geophysical Memorandum No. 2, High Altitude Observatory, Boulder, Colorado.
Harvey, J. W.: 1969, Ph.D. thesis, University Colorado.
Hilderbrand, F. B.: 1952, Methods of Applied Mathematics, Prentice-Hall, Englewood, p. 25.
Hoyng, P. and 23 co-authors: 1981, Astrophys. J. 244, L153.
Kano, R. and Tsuneta, S.: 1995, Astrophys. J. 454, 934.
Kaufman, A.: 1987, Computer Graphics 21, 191.
Klimchuk, J. D.: 1995, Bull. Am. Astron. Soc. 27, 996.
Klimchuk, J., Lemen, J., Feldman, U., Tsuneta, S., and Uchida, Y.: 1992, Publ. Astron. Soc. Japan 44, L181.
Lang, K. R.: 1980, Astrophysical Formulae, Springer-Verlag, New York, p. 46 and p. 456.
Lawson, C. L. and Hanson, R. J.: 1974, Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, p. 58.
Levine, R. H.: 1975, Solar Phys. 44, 365.
Levine, R. H.: 1976, Solar Phys. 46, 159.
Levine, R. H.: 1982, Solar Phys. 79, 203.
Levine, R. H. and Altschuler, M: 1977, Solar Phys. 36, 345.
Maggio, A. and Peres, G.: 1996, Astron. Astrophys. 306, 563.
McClymont, A. N. and Mikic, Z.: 1994, Astrophys. J. 422, 899.
Mewe, R., Gronenschild, E. H. B. M., and van der Oord, G. H. J.: 1985, Astron. Astrophys. Suppl. Ser. 63, 195.
Mewe, R., Lemen, J. R., and van der Oord, G. H. J.: 1986, Astron. Astrophys. Suppl. Ser. 65, 511.
Mikic, Z. and McClymont, A. N.: 1994, in K. S. Balasubramaniam and G. Simon (eds.), Solar Active Region Evolution, ASP Conf. Ser. 68, p. 240.
Mikic, Z., Barnes, D. C., and Schnack, D. D.: 1988, Astrophys. J. 328, 830.
Mikic, Z., Schnack, D. D., and Van Hoven, G.: 1989, Astrophys. J. 338, 1148.
Mikic, Z., Schnack, D. D., and Van Hoven, G.: 1990, Astrophys. J. 361, 690.
Moore, R. L., Hagyard, M. J., and Davis, J. M.: 1987, Solar Phys. 113, 347.
Nakagawa, Y.: 1973, Astron. Astrophys. 27, 95.
Nakagawa, Y. and Raadu, M. A.: 1972, Solar Phys. 25, 127.
Nakagawa, Y., Raadu, M. A., Billings, D. E., and McNamara, D.: 1971, Solar Phys. 19, 72.
Parker, E. N.: 1979, Cosmical Magnetic Fields, Clarendon Press, Oxford, p. 123.
Priest, E. R.: 1982, Solar Magnetohydrodynamics, D. Reidel Publ. Co., Dordrecht, Holland, p. 108.
Poletto, G. and Kopp, R. A.: 1988, Solar Phys. 116, 163.
Poletto, G., Vaiana, G. S., Zombeck, M. V., Krieger, A. S., and Timothy, A. F.: 1975, Solar Phys. 44, 83.
Raadu, M. A. and Nakagawa, Y.: 1971, Solar Phys. 20, 64.
Reale, F. and Peres, G.: 1995, Astron. Astrophys. 299, 225.
Rosner, R., Tucker, W. H., and Vaiana, G. S.: 1978, Astrophys. J. 220, 643.
Roumeliotis, G.: 1994, in K. S. Balasubramaniam and G. Simon (eds.), Solar Active Region Evolution, ASP Conf. Ser. 68, p. 240.
Rust, D. M.: 1966, Thesis, University of Colorado.
Rust, D. M.: 1970, AIAA Observations and Predictions of Solar Activity Conf., Huntsville, AL.
Rust, D. M. and Roy, J.-R.: 1971, in R. Howard (ed.), ‘Solar Magnetic Fields’, IAU Symp. 43, 569.
Sakurai, T.: 1981, Solar Phys. 69, 343.
Sakurai, T.: 1982, Solar Phys. 76, 301.
Schmidt, H. U.: 1964, in W. N. Ness (ed.), Solar Flares, AAS-NASA Symp., NASA SP-50, p. 107.
Schmidt, H. U.: 1965, Mitt. Astron. Ges., Sept, 89.
Serio, S., Peres, G., Vaiana, G. S., Golub, L., and Rosner, R.: 1981, Astrophys. J. 243, 288.
Semel, M.: 1967, Ann. Astrophys. 30, 513.
Sheeley, N. R., Jr., Bohlin, J. D., Brueckner, G. E., Purcell, J. D., Scherrer, V., and Tousey, K.: 1975, Solar Phys. 40, 103.
Shimizu, T.: 1994, in S. Enome and T. Hirayarna (eds.), New Look at the Sun with Emphasis on Advance Observations of Coronal Dynamics and Flares, Nobeyama Radio Observatory, Nagano, p. 61.
Shimizu, T., Tsuneta, S., Action, L., Lemen, J., Ogawara, Y., and Uchida, Y.: 1994, Astrophys. J. 422, 906.
Smartt, R., Zhang, Z., and Smotko, M. F.: 1993, Solar Phys. 148, 139.
Somov, B. V.: 1992, Physical Processes in Solar Flares, Kluwer Academic Publishers, Dordrecht, Holland, p. 15.
Tsuneta, S.: 1996, Astrophys. J. 456, L63.
Wang, H.: 1992, Solar Phys. 140, 85.
Webb, D. F.: 1981, in F. Q. Orrall (ed.), Solar Active Regions, Skylab Solar Workshop III, Colorado Associated Press, Boulder, p. 165.
Wellck, R. E. and Nakagawa, Y.: 1973, NCAR Tech. Note TN/STR-87, NCAR, Boulder, CO.
Wu, S. T, Chang, H. M., and Hagyard, M. J.: 1985, in M. J. Hagyard (ed.), Measurements of Solar Vector Magnetic Fields, NASA CP-2374, p. 17.
Wu, S. T. and Sakurai, T.: 1990, Mem. Soc. Astron. It. 62, 477.
Wu, S. T., Sun, M. T., Chang, H. M., Hagyard, M. J., and Gary, G. A.: 1990, Astrophys. J. 362, 698.
Yoshida, T. and Ogama, Y.: 1995, Publ. Astron. Soc. Japan 47, L15.
Yoshida, T. and Tsuneta, S.: 1996, Astrophys. J. 495, 342.
Yoshida, T., Tsuneta, S., Golub, L., Strong, K., and Ogawara, Y.: 1995, Publ. Astron. Soc. Japan 47, L15.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gary, G.A. RENDERING THREE-DIMENSIONAL SOLAR CORONAL STRUCTURES. Solar Physics 174, 241–263 (1997). https://doi.org/10.1023/A:1004978630098
Issue Date:
DOI: https://doi.org/10.1023/A:1004978630098