Nonlinear force-free modeling of the solar coronal magnetic field

Journal of Geophysical Research: Space Physics

Volumn 113, Issue 3, 2008, Pages

  Wiegelmann, T ^a  

^a MAX PLANCK INSTITUT FÜR SONNENSYSTEMFORSCHUNG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 44349109465     PISSN: None     EISSN: 21699402     Source Type: Journal    
DOI: 10.1029/2007JA012432     Document Type: Conference Paper

References (112)

1. Alissandrakis, C. E. (1981), On the computation of constant alpha forcefree magnetic field, Astron. Astrophys., 100, 197-200.
2. Aly, J. J. (1984), On some properties of force-free magnetic fields in infinite regions of space, Astrophys. J., 283, 349-362, doi:10.1086/162313.
3. Aly, J. J. (1989), On the reconstruction of the nonlinear force-free coronal magnetic field from boundary data, Sol. Phys., 120, 19-48.
4. Aly, J. J. (2005), A uniqueness result for a simple force-free magnetic field submitted to a topological constraint, Astron. Astrophys., 429, 15-18, doi:10.1051/0004-6361:20041547.
5. Amari, T., J. J. Aly, J. F. Luciani, T. Z. Boulmezaoud, and Z. Mikic (1997), Reconstructing the solar coronal magnetic field as a force-free magnetic field, Sol. Phys., 174, 129-149.
6. Amari, T., T. Z. Boulmezaoud, and Z. Mikic (1999), An iterative method for the reconstructionbreak of the solar coronal magnetic field. I. Method for regular solutions, Astron. Astrophys., 350, 1051-1059.
7. Amari, T., T. Z. Boulmezaoud, and J. J. Aly (2006), Well posed reconstruction of the solar coronal magnetic field, Astron, Astrophys., 446, 691-705, doi:10.1051/0004-6361:20054076.
8. Aschwanden, M. J. (2001a), Revisiting the determination of the coronal heating function from Yohkoh data, Astrophys. J., 559, L171-L174, doi:10.1086/323788.
9. Aschwanden, M. J. (2001b), An evaluation of coronal heating models for active regions based on Yohkoh, SOHO, and TRACE observations, Astrophys. J., 560, 1035-1044, doi10.1086/323064.
10. Aschwanden, M. J. (2005), Physics of the Solar Corona: An Introduction with Problems and Solutions, 2nd ed., Springer, New York.
11. 6 K, Astrophys. J., 515, 842-867, doi:10.1086/307036.
12. Bineau, M. (1972), Existence of force-free magnetic-fields, Commun. Pure Appl. Math., 25, 77-84.
13. Bleybel, A., T. Amari, L. van Driel-Gesztelyi, and K. D. Leka (2002), Global budget for an eruptive active region. I. Equilibrium reconstruction approach, Astron. Astrophys., 395, 685-695, doi:10.1051/0004-6361: 20021332.
14. Borrero, J. M., S. Tomczyk, A. Norton, T. Darnell, J. Schou, P. Scherrer, R. Bush, and Y. Lui (2006), Magnetic field vector retrieval with HMI, in Solar Polarization 4, ASP Conf Ser., vol. 358, edited by R. Casini and B. W. Lites, p. 144, Astron. Soc. of the Pac., San Francisco, Calif. (Available at http.//arxiv.org/abs/astro-ph/0602130)
15. Bossavit, A. (1988), Mixed finite elements and the complex of Whitney forms, in The Mathemetics of Finite Elements and Applications VI, edited by J. Whiteman, pp. 137-144, Academic Press, London.
16. Boulmezaoud, T. Z., and T. Amari (2000), On the existence of non-linear force-free fields in three-dimensional domains, ZAMP, 51, 942-967.
17. Carcedo, L., D. S. Brown, A. W. Hood, T. Neukirch, and T. Wiegelmann (2003), A quantitative method to optimise magnetic field line fitting of observed coronal loops, Sol. Phys., 218, 29-40.
18. Chiu, Y. T., and H. H. Hilton (1977), Exact Green's function method of solar force-free magnetic-field computations with constant alpha. I. Theory and basic test cases, Astrophys. J., 212, 873-885.
19. Chodura, R., and A. Schlueter (1981), A 3D code for MHD equilibrium and stability, J. Comput Phys., 41, 68-88.
20. Cuperman, S., L. Ofman, and M. Semel (1990), Extrapolation of photospheric potential magnetic fields using oblique boundary values - A simplified approach, Astron. Astrophys., 227, 583-590.
21. Cuperman, S., P. Demoulin, and M. Semel (1991), Removal of singularities in the Cauchy problem for the extrapolation of solar force-free magnetic fields, Astron. Astrophys., 245, 285-288.
22. Dedner, A., F. Kemm, D. Kröner, C.-D. Munz, T. Schnitzer, and M. Wesenberg (2002), Hyperbolic divergence cleaning for the MHD equations, J. Comput Phys., 175, 645-673.
23. Demoulin, P., and E. R. Priest (1992), The properties of sources and sinks of a linear force-free field, Astron. Astrophys., 258, 535-541.
24. Gary, G. A. (2001), Plasma Beta above a solar active region: Rethinking the paradigm, Sol. Phys., 203, 71-86.
25. Gary, G. A., and M. J. Hagyard (1990), Transformation of vector magnetograms and the problems associated with the effects of perspective and the azimuthal ambiguity, Sol. Phys., 126, 21-36.
26. Grad, H., and H. Rubin (1958), Hydromagnetic equilibria and force-free fields, paper presented at 2nd International Conference on Peaceful Uses of Atomic Energy, Int. At. Energy Agency, Geneva.
27. He, H., and H. Wang (2006), The validity of the boundary integral equation for magnetic field extrapolation in open space above a spherical surface, Mon. Not. R. Astron. Soc., 369, 207-215, doi.10.1111/j.1365- 2966.2006.10288.x.
28. Henney, C. J., C. U. Keller, and J. W. Harvey (2006), SOLIS-VSM solar vector magnetograms, in Solar Polarization 4, ASP Conf. Ser., vol. 358, edited by R. Casini and B. W. Lites, p. 92, Astron, Soc. of the Pac., San Francisco, Calif. (Available at http.//arxiv.org/abs/astro-ph/0701122)
29. Inhester, B., and T. Wiegelmann (2006), Nonlinear force-free magnetic field extrapolations: Comparison of the Grad Rubin and Wheatland Sturrock Roumefiotis algorithm, Sol. Phys., 235, 201-221, doi:10.1007/s11207-006- 0065-x.
30. Jiao, L., A. N. McClymont, and Z. Mikic (1997), Reconstruction of the three-dimensional coronal magnetic field, Sol. Phys., 174, 311-327.
31. Judge, P. G. (1998), Spectral lines for polarization measurements of the coronal magnetic field. I. Theoretical intensities, Astrophys. J., 500, 1009-1022.
32. Kageyama, A., and T. Sato (2004), "Yin-Yang grid": An overset grid in spherical geometry, Geochem. Geophys. Geosyst., 5, Q09005, doi:10.1029/2004GC000734.
33. Keppens, R., M. Nool, G. Tóth, and J. P. Goedbloed (2003), Adaptive mesh refinement for conservative systems: Multi-dimensional efficiency evaluation, Comput. Phys. Commun., 153, 317-339.
34. Klimchuk, J. A., and P. A. Sturrock (1992), Three-dimensional force-free magnetic fields and flare energy buildup, Astrophys. J., 385, 344-353, doi:10.1086/170943.
35. Kramar, M., and B. Inhester (2006), Inversion of coronal Zeeman and Hanle observations to reconstruct the coronal magnetic field, Mem. Soc. Astron. Ital., 78, 120. (Available at http://arxiv.org/abs/astro-ph/0612639)
36. Kramar, M., B. Inhester, and S. K. Solanki (2006), Vector tomography for the coronal magnetic field. I. Longitudinal Zeeman effect measurements, Astron. Astrophys., 456, 665-673, doi:10.1051/0004-6361:20064865.
37. LaBonte, B. J., D. L. Mickey, and K. D. Leka (1999), The imaging vector magnetograph at Haleakalamacr;: II. Reconstruction of Stokes spectra, Sol. Phys., 189, 1-24.
38. Lagg, A., J. Woch, N. Krupp, and S. K. Solanki (2004), Retrieval of the full magnetic vector with the He I multiplet at 1083 nm: Maps of an emerging flux region, Astron. Astrophys., 414, 1109-1120.
39. Leka, K. D., and A. Skumanich (1999), On the value of 'αAR' from vector magnetograph data: I. Methods and caveats, Sol. Phys., 188, 3-19.
40. Li, Z., Y. Yan, and G. Song (2004), Properties of the boundary integral equation for solar non-constant-α force-free magnetic fields, Mon. Not. R. Astron. Soc., 347, 1255-1265, doi:10.1111/j.1365-2966.2004.07309.x.
41. Lin, H., J. R. Kuhn, and R. Coulter (2004), Coronal magnetic field measurements, Astrophys. J. Lett., 613, L177-L180, doi: 10.1086/425217.
42. Liu, Y., X. P. Zhao, J. T. Hoeksema, P. H. Scherrer, J. Wang, and Y. Yan (2002), On formation of the sigmoidal structure in solar active region NOAA 8100, Sol. Phys., 206, 333-346.
43. Low, B. C., and Y. Q. Lou (1990), Modeling solar force-free magnetic fields, Astrophys. J., 352, 343-352.
44. McClymont, A. N., L. Jiao, and Z. Mikic (1997), Problems and progress in computing three-dimensional coronal active region magnetic fields from boundary data, Sol. Phys., 174, 191-218.
45. Metcalf, T. R. (1994), Resolving the 180-degree ambiguity in vector magnetic field measurements: The 'minimum' energy solution, Sol. Phys., 155, 235-242.
46. Metcalf, T. R., L. Jiao, A. N. McClymont, R. C. Canfield, and H. Uitenbroek (1995), Is the solar chromospheric magnetic field force-free?, Astrophys. J., 439, 474-481, doi:10.1086/175188.
47. Metcalf, T. R., et al. (2006), An overview of existing algorithms for resolving the 180-degree ambiguity in vector magnetic fields: Quantitative tests with synthetic data, Sol. Phys., 237, 267-296, doi:10.1007/S11207-006- 0170-X.
48. Metcalf, T. R., M. L. DeRosa, C. J. Schrijver, G. Barnes, A. VanBallegooijen, T. Wiegelmann, M. S. Wheatland, G. Valori, and J. M. McTiernan (2007), Non-linear force-free modeling of coronal magnetic fields. II. Modeling a filament arcade from simulated chromospheric and photospheric vector fields, Sol. Phys., in press.
49. Mickey, D. L., R. C. Canfield, B. J. Labonte, K. D. Leka, M. F. Waterson, and H. M. Weber (1996), The imaging vector magnetograph at Haleakala, Sol. Phys., 168, 229-250.
50. Mikic, Z., and A. N. McClymont (1994), Deducing coronal magnetic fields nom vector magnetograms, in Solar Active Region Evolution: Comparing Models with Observations, ASP Conf. Ser., vol. 68, edited by K. S. Balasubramaniam and G. W. Simon, pp. 225-232, Astron. Soc. of the Pac., San Francisco, Calif.
51. Mikic, Z., D. C. Barnes, and D. D. Schnack (1988), Dynamical evolution of a solar coronal magnetic field arcade, Astrophys. J., 328, 830-847, doi:10.1086/166341.
52. Molodensky, M. M. (1969), Integral properties of force-free fields, Soviet Astron., Engl. Transl., 12, 585-588.
53. Molodensky, M. M. (1974), Equilibrium and stability of force-free magnetic field, Sol. Phys., 39, 393-404.
54. Nakagawa, Y. (1974), Dynamics of the solar magnetic field. I. Method of examination of force-free magnetic fields, Astrophys. J., 190, 437-440.
55. Nakagawa, Y., and M. A. Raadu (1972), On practical representation of magnetic field, Sol. Phys., 25, 127-135.
56. Pevtsov, A. A., R. C. Canfield, and T. R. Metcalf (1994), Patterns of helicity in solar active regions, Astrophys. J. Lett., 425, L117-L119, doi:10.1086/187324.
57. Press, W. H. (2002), Numerical Recipes in C++: The Art of Scientific Computing, 1002 pp., Cambridge Univ. Press, New York.
58. Priest, E. (1996), Coronal heating by magnetic reconnection, Astrophys. Space Sci., 237, 49-73.
59. Priest, E. R. (1999), Heating the solar corona by magnetic reconnection, Astrophys. Space Sci., 264, 77-100.
60. Priest, E. R., and C. J. Schrijver (1999), Aspects of three-dimensional magnetic reconnection (invited review), Sol. Phys., 190, 1-24, doi:10.1023/A:1005248007615.
61. Priest, E. R., D. W. Longcope, and J. Heyvaerts (2005), Coronal heating at separators and separatrices, Astrophys. J., 624, 1057-1071, doi:10.1086/429312.
62. Régnier, S., and T. Amari (2004), 3D magnetic configuration of the Ha filament and X-ray sigmoid in NOAA AR 8151, Astron. Astrophys., 425, 345-352.
63. Régnier, S., and R. C. Canfield (2006), Evolution of magnetic fields and energetics of flares in active region 8210, Astron. Astrophys., 451, 319 -330, doi:10.1051/0004-6361:20054171.
64. Régnier, S., T. Amari, and E. Kersalé (2002), 3D coronal magnetic field from vector magnetograms: Non-constant-alpha force-free configuration of the active region NOAA 8151, Astron. Astrophys., 392, 1119-1127.
65. Régnier, S., T. Amari, and R. C. Canfield (2005), Self and mutual magnetic helicities in coronal magnetic configurations, Astron. Astrophys., 442, 345-349, doi: 10.1051/0004-6361:20053509.
66. Roumeliotis, G. (1996), The "stress-and-relax" method for reconstructing the coronal magnetic field from vector magnetograph data, Astrophys. J., 473, 1095-1103.
67. Sakurai, T. (1981), Calculation of force-free magnetic field with non constant alpha, Sol. Phys., 69, 343-359.
68. Sakurai, T. (1982), Green's function methods for potential magnetic fields, Sol. Phys., 76, 301-321.
69. Sakurai, T. (1989), Computational modeling of magnetic fields in solar active regions, Space Sci. Rev., 51, 11-48.
70. Sakurai, T., et al. (1995), Solar flare telescope at Mitaka, Publ. Astron. Soc. Jpn., 47, 81-92.
71. Schatten, K. H., J. M. Wilcox, and N. F. Ness (1969), A model of interplanetary and coronal magnetic fields, Sol. Phys., 6, 442-455.
72. Schmidt, H. U. (1964), On the observable effects of magnetic energy storage and release connected with solar flares, in The Physics of Solar Flares, edited by W. N. Hess, pp. 107-114, NASA, Washington, D. C.
73. Schrijver, C. J., and A. A. van Ballegooijen (2005), Is the quiet-sun corona a quasi-steady, force-free environment?, Astrophys. J., 630, 552-560, doi:10.1086/431754.
74. Schrijver, C. J., A. W. Sandman, M. J. Aschwanden, and M. L. DeRosa (2004), The coronal heating mechanism as identified by full-sun visualizations, Astrophys. J., 615, 512-525, doi:10.1086/424028.
75. Schrijver, C. J., M. L. DeRosa, A. M. Title, and T. R. Metcalf (2005), The nonpotentiality of active-region coronae and the dynamics of the photospheric magnetic field, Astrophys. J., 628, 501-513, doi:10.1086/430733.
76. Schrijver, C. J., M. L. Derosa, T. R. Metcalf, Y. Liu, J. McTiernan, S. Régnier, G. Valori, M. S. Wheatland, and T. Wiegelmann (2006), Nonlinear force-free modeling of coronal magnetic fields part i: A quantitative comparison of methods, Sol. Phys., 235, 161-190, doi:10.1007/s11207-006-0068-7.
77. Seehafer, N. (1978), Determination of constant alpha force-free solar magnetic fields from magnetograph data, Sol. Phys., 58, 215-223.
78. Seehafer, N. (1982), A comparison of different solar magnetic field extrapolation procedures, Sol. Phys., 81, 69-80.
79. Semel, M. (1967), Contribution à létude des champs magn\' etiques dans les régions actives solaires, Ann. Astrophys., 30, 513.
80. Semel, M. (1988), Extrapolation functions for constant-alpha force-free fields - Green's method for the oblique boundary value, Astron. Astrophys., 198, 293-299.
81. Shimizu, T. (2004), SolarB Solar Optical Telescope (SOT), in The Solar-B Mission and the Forefront of Solar Physics, ASP Conf. Ser., vol. 325, edited by T. Sakurai and T. Sekii, p. 3, Astron. Soc. of the Pac., San Francisco, Calif.
82. Solanki, S. K., A. Lagg, J. Woch, N. Krupp, and M. Collados (2003), Three-dimensional magnetic field topology in a region of solar coronal heating, Nature, 425, 692-695.
83. Song, M. T., C. Fang, Y. H. Tang, S. T. Wu, and Y. A. Zhang (2006), A new and fast way to reconstruct a nonlinear force-free field in the solar corona, Astrophys. J., 649, 1084-1092, doi:10.1086/506249.
84. Titov, V. S., and P. Démoulin (1999), Basic topology of twisted magnetic configurations in solar flares, Astron. Astrophys., 351, 707-720.
85. Török, T., and B. Kliem (2003), The evolution of twisting coronal magnetic flux tubes, Astron. Astrophys., 406, 1043-1059, doi:10.1051/0004-6361:20030692.
86. Valori, G., B. Kliem, and R. Keppens (2005), Extrapolation of a nonlinear force-free field containing a highly twisted magnetic loop, Astron. Astrophys., 433, 335-347.
87. van Ballegooijen, A. A. (2004), Observations and modeling of a filament on the Sun, Astrophys. J., 612, 519-529, doi:10.1086/422512.
88. van Ballegooijen, A. A., E. E. Deluca, K. Squires, and D. H. Mackay (2007), Modeling magnetic flux ropes in the solar atmosphere, J. Atmos. Terr. Phys., 69, 24-31, doi:10.1016/j.jastp.2006.06.007.
89. Wang, H., Y. Yan, T. Sakurai, and M. Zhang (2000), Topology of magnetic field and coronal heating in solar active regions. II. The role of quasi-separatrix layers, Sol. Phys., 197, 263-273.
90. Wheatland, M. S. (1999), A better linear force-free field, Astrophys. J., 518, 948-953, doi:10.1086/307301.
91. Wheatland, M. S. (2004), Parallel construction of nonlinear force-free fields, Sol. Phys., 222, 247-264.
92. Wheatland, M. S. (2006), A fast current-field iteration method for calculating nonlinear force-free fields, Sol. Phys., 238, 29-39, doi:10.1007/s11207-006-0232-0.
93. Wheatland, M. S., P. A. Sturrock, and G. Roumeliotis (2000), An optimization approach to reconstructing force-free fields, Astrophys. J., 540, 1150-1155.
94. Wiegelmann, T. (2004), Optimization code with weighting function for the reconstruction of coronal magnetic fields, Sol. Phys., 219, 87-108.
95. Wiegelmann, T. (2007), Computing nonlinear force-free coronal magnetic fields in spherical geometry, Sol. Phys., 240, 227-239, doi:10.1007/s11207-006-0266-3.
96. Wiegelmann, T., and B. Inhester (2003), Magnetic modeling and tomography: First steps towards a consistent reconstruction of the solar corona, Sol. Phys., 214, 287-312.
97. Wiegelmann, T., and T. Neukirch (2002), Including stereoscopic information in the reconstruction of coronal magnetic fields, Sol. Phys., 208, 233-251.
98. Wiegelmann, T., and T. Neukirch (2003), Computing nonlinear force free coronal magnetic fields, Nonlinear Processes Geophys., 10, 313-322.
99. Wiegelmann, T., and T. Neukirch (2006), An optimization principle for the computation of MHD equilibria in the solar corona, Astron. Astrophys., 457, 1053-1058, doi:10.1051/0004-6361:20065281.
100. Wiegelmann, T., B. Inhester, A. Lagg, and S. K. Solanki (2005a), How to use magnetic field information for coronal loop identification, Sol. Phys., 228, 67-78, doi:10.1007/s11207-005-2511-6.
101. Wiegelmann, T., A. Lagg, S. K. Solanki, B. Inhester, and J. Woch (2005b), Comparing magnetic field extrapolations with measurements of magnetic loops, Astron. Astrophys., 433, 701-705.
102. Wiegelmann, T., B. Inhester, B. Kliem, G. Valori, and T. Neukirch (2006a), Testing non-linear force-free coronal magnetic field extrapolations with the Titov-Démoulin equilibrium, Astron. Astrophys., 453, 737-741, doi:10.1051/0004-6361:20054751.
103. Wiegelmann, T., B. Inhester, and T. Sakurai (2006b), Preprocessing of vector magnetograph data for a nonlinear force-free magnetic field reconstruction, Sol. Phys., 233, 215-232.
104. Wu, S. T., H. M. Chang, and M. J. Hagyard (1985), On the numerical computation of nonlinear force-free magnetic fields, in Measurements of Solar Vector Magnetic Fields, NASA Conf. Publ., 2374, 17-40.
105. Wu, S. T., M. T. Sun, H. M. Chang, M. J. Hagyard, and G. A. Gary (1990a), On the numerical computation of nonlinear force-free magnetic fields, Astrophys. J., 362, 698-708.
106. Wu, S. T., M. T. Sun, and T. Sakurai (1990b), A comparison between progressive extension method (PEM) and iterative method (IM) for magnetic field extrapolations in the solar atmosphere, Mem. Soc. Astron. Ital., 61, 477-484.
107. Yan, Y., and Z. Li (2006), Direct boundary integral formulation for solar non-constant-α force-free magnetic fields, Astrophys. J., 638, 1162-1168, doi:10.1086/499064.
108. Yan, Y., and T. Sakurai (2000), New boundary integral equation representation for finite energy force-free magnetic fields in open space above the Sun, Sol. Phys., 195, 89-109.
109. Yan, Y., M. J. Aschwanden, S. Wang, and Y. Deng (2001a), Evolution of magnetic flux rope in the active region NOAA 9077 on 14 July 2000, Sol. Phys., 204, 27-40, doi:10.1023/A:1014265123601.
110. Yan, Y., Y. Deng, M. Karlický, Q. Fu, S. Wang, and Y. Liu (2001b), The magnetic rope structure and associated energetic processes in the 2000 July 14 solar flare, Astrophys. J. Lett., 551, L115-L119, doi:10.1086/319829.
111. Yang, W. H., P. A. Sturrock, and S. K. Antiochos (1986), Force-free magnetic fields: The magneto-frictional method, Astrophys. J., 309, 383-391, doi:10.1086/164610.
112. Yee, K. S. (1966), Numerical solition of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas Propag., AP-14(4), 302-307.