Abstract
In order to better understand the solar genesis of interplanetary magnetic clouds (MCs), we model the magnetic and topological properties of four large eruptive solar flares and relate them to observations. We use the three-dimensional Minimum Current Corona model (Longcope, 1996, Solar Phys. 169, 91) and observations of pre-flare photospheric magnetic field and flare ribbons to derive values of reconnected magnetic flux, flare energy, flux rope helicity, and orientation of the flux-rope poloidal field. We compare model predictions of those quantities to flare and MC observations, and within the estimated uncertainties of the methods used find the following: The predicted model reconnection fluxes are equal to or lower than the reconnection fluxes inferred from the observed ribbon motions. Both observed and model reconnection fluxes match the MC poloidal fluxes. The predicted flux-rope helicities match the MC helicities. The predicted free energies lie between the observed energies and the estimated total flare luminosities. The direction of the leading edge of the MC’s poloidal field is aligned with the poloidal field of the flux rope in the AR rather than the global dipole field. These findings compel us to believe that magnetic clouds associated with these four solar flares are formed by low-corona magnetic reconnection during the eruption, rather than eruption of pre-existing structures in the corona or formation in the upper corona with participation of the global magnetic field. We also note that since all four flares occurred in active regions without significant pre-flare flux emergence and cancelation, the energy and helicity that we find are stored by shearing and rotating motions, which are sufficient to account for the observed radiative flare energy and MC helicity.
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Abbett, W.P., Fisher, G.H.: 2003, A coupled model for the emergence of active region magnetic flux into the solar corona. Astrophys. J. Lett. 582, L475 – L485. doi: 10.1086/344613 .
Antiochos, S.K., Devore, C.R., Klimchuk, J.A.: 1999, A model for solar coronal mass ejections. Astrophys. J. Lett. 510, L485 – L493.
Aschwanden, M.J., Wuelser, J.P., Nitta, N.V.: 2009, Solar flares, coronal mass ejections, EUV, stereoscopy. Solar Phys. 256, 3 – 40.
Barnes, G., Longcope, D.W., Leka, K.D.: 2005, Implementing a magnetic charge topology model for solar active regions. Astrophys. J. 629, 561 – 571. doi: 10.1086/431175 .
Berger, M.A.: 1999, Magnetic helicity in space physics. In: Brown, M.R., Canfield, R.C., Pevtsov, A.A. (eds.) Magnetic Helicity in Space and Laboratory Plasmas, Geophysical Monograph 111, AGU Press, Washington, 1 – 9.
Berger, M.A., Field, G.B.: 1984, The topological properties of magnetic helicity. J. Fluid Mech. 147, 133 – 148. doi: 10.1017/S0022112084002019 .
Beveridge, C., Longcope, D.W.: 2006, A hierarchical application of the minimum current corona. Astrophys. J. Lett. 636, L453 – L461.
Bothmer, V., Schwenn, R.: 1998, The structure and origin of magnetic clouds in the solar wind. Ann. Geophys. 16, 1 – 24.
Bradshaw, S.J., Cargill, P.J.: 2010, The cooling of coronal plasmas. III. Enthalpy transfer as a mechanism for energy loss. Astrophys. J. 717, 163 – 174. doi: 10.1088/0004-637X/717/1/163 .
Burlaga, L., Sittler, E., Mariani, F., Schwenn, R.: 1981, Magnetic loop behind an interplanetary shock – voyager, Helios, and imp 8 observations. J. Geophys. Res. 86, 6673 – 6684.
Carmichael, H.: 1964, A process for flares. In: Hess, W.N. (ed.) AAS-NASA Symposium on the Physics of Solar Flares, NASA, Washington, 451.
Chae, J.: 2001, Observational determination of the rate of magnetic helicity transport through the solar surface via the horizontal motion of field line footpoints. Astrophys. J. Lett. 560, L95 – L98. doi: 10.1086/324173 .
Chae, J.: 2007, Measurements of magnetic helicity injected through the solar photosphere. Adv. Space Res. 39, 1700 – 1705. doi: 10.1016/j.asr.2007.01.035 .
Chen, J.: 1989, Effects of toroidal forces in current loops embedded in a background plasma. Astrophys. J. Lett. 338, L453 – L470.
Crooker, N.U.: 2000, Solar and heliospheric geoeffective disturbances. J. Atmos. Solar-Terr. Phys. 62, 1071 – 1085.
Dasso, S., Mandrini, C.H., Démoulin, P., Farrugia, C.J.: 2003, Magnetic helicity analysis of an interplanetary twisted flux tube. J. Geophys. Res. 108, 3 – 1. doi: 10.1029/2003JA009942 .
Dasso, S., Mandrini, C.H., Démoulin, P., Luoni, M.L.: 2006, A new model-independent method to compute magnetic helicity in magnetic clouds. Astron. Astrophys. 455, 349 – 359. doi: 10.1051/0004-6361:20064806 .
Démoulin, P.: 2008, A review of the quantitative links between CMEs and magnetic clouds. Ann. Geophys. 26, 3113 – 3125.
Démoulin, P., Pariat, E.: 2007, Computing magnetic energy and helicity fluxes from series of magnetograms. Mem. Soc. Astron. Italiana 78, 136.
Démoulin, P., Mandrini, C.H., van Driel-Gesztelyi, L., Thompson, B.J., Plunkett, S., Kovári, Z., Aulanier, G., Young, A.: 2002, What is the source of the magnetic helicity shed by CMEs? The long-term helicity budget of AR 7978. Astron. Astrophys. 382, 650 – 665. doi: 10.1051/0004-6361:20011634 .
DeVore, C.R.: 2000, Magnetic helicity generation by solar differential rotation. Astrophys. J. Lett. 539, L944 – L953.
Fan, Y., Gibson, S.E.: 2004, Numerical simulations of three-dimensional coronal magnetic fields resulting from the emergence of twisted magnetic flux tubes. Astrophys. J. Lett. 609, L1123 – L1133. doi: 10.1086/421238 .
Fletcher, L., Hudson, H.: 2001, The magnetic structure and generation of EuV flare ribbons. Solar Phys. 204, 69 – 89.
Forbes, T.G., Priest, E.R.: 1995, Photospheric magnetic field evolution and eruptive flares. Astrophys. J. 446, 377. doi: 10.1086/175797 .
Gibson, S.E., Fan, Y.: 2008, Partially ejected flux ropes: implications for interplanetary coronal mass ejections. J. Geophys. Res. 113, 9103. doi: 10.1029/2008JA013151 .
Gopalswamy, N., Yashiro, S., Kaiser, M.L., Howard, R.A., Bougeret, J.: 2001, Radio signatures of coronal mass ejection interaction: coronal mass ejection cannibalism? Astrophys. J. Lett. 548, L91 – L94. doi: 10.1086/318939 .
Gopalswamy, N., Akiyama, S., Yashiro, S., Mäkelä, P.: 2010, Coronal mass ejections from sunspot and non-sunspot regions. In: Hasan, S.S. and Rutten, R.J. (eds.) Magnetic Coupling Between the Interior and Atmosphere of the Sun, Astrophys. Space Science Proc., Springer, Berlin, 289 – 307. doi: 10.1007/978 .
Gosling, J.T.: 1990, Coronal mass ejections and magnetic flux ropes in interplanetary space. In: Russel, C.T., Priest, E.R., Lee, L.C. (eds.) Physics of Magnetic Flux Ropes, Geophys. Monographs 58, AGU, Washington, 343 – 364.
Green, L.M., López Fuentes, M.C., Mandrini, C.H., Démoulin, P., Van Driel-Gesztelyi, L., Culhane, J.L.: 2002, The magnetic helicity budget of a CME-prolific active region. Solar Phys. 208, 43 – 68.
Gulisano, A.M., Dasso, S., Mandrini, C.H., Démoulin, P.: 2005, Magnetic clouds: a statistical study of magnetic helicity. J. Atmos. Solar-Terr. Phys. 67, 1761 – 1766. doi: 10.1016/j.jastp.2005.02.026 .
Hirayama, T.: 1974, Theoretical model of flares and prominences. i: Evaporating flare model. Solar Phys. 34, 323 – 338.
Hu, Q., Sonnerup, B.U.Ö.: 2001, Reconstruction of magnetic flux ropes in the solar wind. Geophys. Res. Lett. 28, 467 – 470.
Jing, J., Lee, J., Liu, C., Gary, D.E., Wang, H.: 2007, Hard X-ray intensity distribution along Hα ribbons. Astrophys. J. Lett. 664, L127 – L130. doi: 10.1086/520812 .
Kazachenko, M.D., Canfield, R.C., Longcope, D.W., Qiu, J., Des Jardins, A., Nightingale, R.W.: 2009, Sunspot rotation, flare energetics, and flux rope helicity: the eruptive flare on 2005 May 13. Astrophys. J. 704, 1146 – 1158. doi: 10.1088/0004-637X/704/2/1146 .
Kazachenko, M.D., Canfield, R.C., Longcope, D.W., Qiu, J.: 2010, Sunspot rotation, flare energetics, and flux rope helicity: the Halloween flare on 2003 28 October. Astrophys. J. 722, 1539 – 1546. doi: 10.1088/0004-637X/722/2/1539 .
Kopp, R.A., Pneuman, G.W.: 1976, Magnetic reconnection in the corona and the loop prominence phenomenon. Solar Phys. 50, 85 – 98.
Larson, D.E., Lin, R.P., McTiernan, J.M., McFadden, J.P., Ergun, R.E., McCarthy, M., Rème, H., Sanderson, T.R., Kaiser, M., Lepping, R.P., Mazur, J.: 1997, Tracing the topology of the October 18 – 20, 1995, magnetic cloud with 0.1−102 keV electrons. Geophys. Res. Lett. 24, 1911 – 1914.
Leamon, R.J., Canfield, R.C., Pevtsov, A.A.: 2002, Properties of magnetic clouds and geomagnetic storms associated eruption of coronal sigmoids. J. Geophys. Res. 107, 1234.
Leamon, R.J., Canfield, R.C., Jones, S.L., Lambkin, K., Lundberg, B.J., Pevtsov, A.A.: 2004, Helicity of magnetic clouds and their associated active regions. J. Geophys. Res. 109, 5106. doi: 10.1029/2003JA010324 .
Leka, K.D., Canfield, R.C., McClymont, A.N., Van Driel Gesztelyi, L.: 1996, Evidence for current-carrying emerging flux. Astrophys. J. Lett. 462, L547 – L560.
Lepping, R.P., Berdichevsky, D.B., Burlaga, L.F., Lazarus, A.J., Kasper, J., Desch, M.D., Wu, C., Reames, D.V., Singer, H.J., Smith, C.W., Ackerson, K.L.: 2001, The Bastille day magnetic clouds and upstream shocks: near-earth interplanetary observations. Solar Phys. 204, 285 – 303. doi: 10.1023/A:1014264327855 .
Li, Y., Luhman, J.G., Lynch, B.J., Kilpua, E.: 2011, Cyclic reversal of magnetic cloud poloidal field. Solar Phys. 269, 32 – 47. doi: 10.1007/s11207-011-9722-9 .
Lin, J., Raymond, J.C., van Ballegooijen, A.A.: 2004, The role of magnetic reconnection in the observable features of solar eruptions. Astrophys. J. 602, 422 – 435. doi: 10.1086/380900 .
Liu, C., Lee, J., Yurchyshyn, V., Deng, N., Cho, K.s., Karlický, M., Wang, H.: 2007, The eruption from a sigmoidal solar active region on 2005 May 13. Astrophys. J. 669, 1372 – 1381. doi: 10.1086/521644 .
Liu, J., Zhang, Y., Zhang, H.: 2008, Relationship between powerful flares and dynamic evolution of the magnetic field at the solar surface. Solar Phys. 248, 67 – 84. doi: 10.1007/s11207-008-9149-0 .
Longcope, D.W.: 1996, Topology and current ribbons: a model for current, reconnection and flaring in a complex, evolving corona. Solar Phys. 169, 91 – 121. doi: 10.1007/BF00153836 .
Longcope, D.W.: 2001, Separator current sheets: generic features in minimum-energy magnetic fields subject to flux constraints. Phys. Plasmas 8, 5277 – 5290. doi: 10.1063/1.1418431 .
Longcope, D.W., Magara, T.: 2004, A comparison of the minimum current corona to a magnetohydrodynamic simulation of quasi-static coronal evolution. Astrophys. J. 608, 1106 – 1123. doi: 10.1086/420780 .
Longcope, D.W., DesJardins, A.C., Carranza-Fulmer, T., Qiu, J.: 2010, A quantitative model of energy release and heating by time-dependent, localized reconnection in a flare with a thermal loop-top X-ray source. Solar Phys. 267, 107 – 139. doi: 10.1007/s11207-010-9635 .
Longcope, D.W., Beveridge, C., Qiu, J., Ravindra, B., Barnes, G., Dasso, S.: 2007, Modeling and measuring the flux reconnected and ejected by the two-ribbon flare/CME event on 7 November 2004. Solar Phys. 244, 45 – 73. doi: 10.1007/s11207-007-0330-7 .
Longcope, D.W., Barnes, G., Beveridge, C.: 2009, Effects of partitioning and extrapolation on the connectivity of potential magnetic fields. Astrophys. J. 693, 97 – 111. doi: 10.1088/0004-637X/693/1/97 .
Low, B.C.: 1994, Magnetohydrodynamic processes in the solar corona: flares, coronal mass ejections, and magnetic helicity. Phys. Plasmas 1, 1684 – 1690.
Luoni, M.L., Mandrini, C.H., Dasso, S., van Driel-Gesztelyi, L., Démoulin, P.: 2005, Tracing magnetic helicity from the solar corona to the interplanetary space. J. Atmos. Solar-Terr. Phys. 67, 1734 – 1743. doi: 10.1016/j.jastp.2005.07.003 .
Lynch, B.J., Gruesbeck, J.R., Zurbuchen, T.H., Antiochos, S.K.: 2005, Solar cycle-dependent helicity transport by magnetic clouds. J. Geophys. Res. 110, 8107. doi: 10.1029/2005JA011137 .
Mackay, D.H., van Ballegooijen, A.A.: 2006, Models of the large-scale corona. I. Formation, evolution, and liftoff of magnetic flux ropes. Astrophys. J. 641, 577 – 589. doi: 10.1086/500425 .
Mandrini, C.H., Pohjolainen, S., Dasso, S., Green, L.M., Démoulin, P., van Driel-Gesztelyi, L., Copperwheat, C., Foley, C.: 2005, Interplanetary flux rope ejected from an X-ray bright point. The smallest magnetic cloud source-region ever observed. Astron. Astrophys. 434, 725 – 740. doi: 10.1051/0004-6361:20041079 .
Mandrini, C.H., Demoulin, P., Schmieder, B., Deluca, E.E., Pariat, E., Uddin, W.: 2006, Companion event and precursor of the X17 flare on 28 October 2003. Solar Phys. 238, 293 – 312. doi: 10.1007/s11207-006-0205-3 .
Marubashi, K.: 1986, Structure of the interplanetary magnetic clouds and their solar origins. Adv. Space Res. 6, 335 – 338. doi: 10.1016/0273-1177(86)90172-9 .
Masuda, S., Kosugi, T., Hudson, H.S.: 2001, A hard X-ray two-ribbon flare observed with Yohkoh/HXT. Solar Phys. 204, 55 – 67. doi: 10.1023/A:1014230629731 .
Mewe, R., Gronenschild, E.H.B.M., van den Oord, G.H.J.: 1985, Calculated X-radiation from optically thin plasmas. V. Astron. Astrophys. Suppl. Ser. 62, 197 – 254.
Mulligan, T., Russell, C.T., Luhmann, J.G.: 1998, Solar cycle evolution of the structure of magnetic clouds in the inner heliosphere. Geophys. Res. Lett. 25, 2959 – 2962. doi: 10.1029/98GL01302 .
Nindos, A., Zhang, J., Zhang, H.: 2003, The magnetic helicity budget of solar active regions and coronal mass ejections. Astrophys. J. Lett. 594, 1033 – 1048. doi: 10.1086/377126 .
November, L.J., Simon, G.W.: 1988, Precise proper-motion measurement of solar granulation. Astrophys. J. 333, 427 – 442. doi: 10.1086/166758 .
Pariat, E., Démoulin, P., Berger, M.A.: 2005, Photospheric flux density of magnetic helicity. Astron. Astrophys. 439, 1191 – 1203.
Pevtsov, A.A., Balasubramaniam, K.S.: 2003, Helicity patterns on the sun. Adv. Space Res. 32, 1867 – 1874. doi: 10.1016/S0273-1177(03)90620-X .
Poletto, G., Kopp, R.A.: 1986, Macroscopic electric fields during two-ribbon flares. In: Neidig, D.F. (ed.) The Lower Atmospheres of Solar Flares, National Solar Observatory, Sunspot, 453 – 465.
Qiu, J., Gary, D.E.: 2003, Flare-related magnetic anomaly with a sign reversal. Astrophys. J. 599, 615 – 625. doi: 10.1086/379146 .
Qiu, J., Hu, Q., Howard, T.A., Yurchyshyn, V.B.: 2007, On the magnetic flux budget in low-corona magnetic reconnection and interplanetary coronal mass ejections. Astrophys. J. 659, 758 – 772. doi: 10.1086/512060 .
Ravindra, B., Howard, T.A.: 2010, Comparison of energies between eruptive phenomena and magnetic field in AR 10930. Bull. Astron. Soc. India 38, 147 – 163. http://cdsads.u-strasbg.fr/abs/2010BASI...38..147R .
Régnier, S., Priest, E.R.: 2007, Free magnetic energy in solar active regions above the minimum-energy relaxed state. Astrophys. J. Lett. 669, L53 – L56. doi: 10.1086/523269 .
Rosner, R., Tucker, W.H., Vaiana, G.S.: 1978, Dynamics of the quiescent corona. Astrophys. J. Lett. 220, 643 – 655.
Scherrer, P.H., Bogart, R.S., Bush, R.I., Hoeksema, J.T., Kosovichev, A.G., Schou, J., Rosenberg, W., Springer, L., Tarbell, T.D., Title, A., Wolfson, C.J., Zayer, I., MDI Engineering Team: 1995, The solar oscillations investigation – Michelson Doppler imager. Solar Phys. 162, 129 – 188. doi: 10.1007/BF00733429 .
Schrijver, C.J., Derosa, M.L., Metcalf, T.R., Liu, Y., McTiernan, J., Régnier, S., Valori, G., Wheatland, M.S., Wiegelmann, T.: 2006, Nonlinear force-free modeling of coronal magnetic fields Part I: A quantitative comparison of methods. Solar Phys. 235, 161 – 190. doi: 10.1007/s11207-006-0068-7 .
Sturrock, P.A.: 1968, A model of solar flares. In: Kiepenheuer, K.O. (ed.) IAU Symp. 35: Structure and Development of Solar Active Regions, IAU Symp. 35, Reidel, Dordrecht, 471 – 479.
Su, Y., Golub, L., Van Ballegooijen, A.A.: 2007, A statistical study of shear motion of the footpoints in two-ribbon flares. Astrophys. J. 655, 606 – 614. doi: 10.1086/510065 .
Vesecky, J.F., Antiochos, S.K., Underwood, J.H.: 1979, Numerical modeling of quasi-static loops. I. Uniform energy input. Astrophys. J. Lett. 233, L987 – L997.
Webb, D.F., Lepping, R.P., Burlaga, L.F., Deforest, C.E., Larson, D.E., Martin, S.F., Plunkett, S.P., Rust, D.M.: 2000, The origin and development of the May 1997 magnetic cloud. J. Geophys. Res. 105, 27251 – 27260.
Welsch, B.T., Abbett, W.P., DeRosa, M.L., Fisher, G.H., Georgoulis, M.K., Kusano, K., Longcope, D.W., Ravindra, B., Schuck, P.W.: 2007, Tests and comparisons of velocity inversion techniques. Astrophys. J. Lett. 670, L1434 – L1452.
Woods, T.N., Kopp, G., Chamberlin, P.C.: 2006, Contributions of the solar ultraviolet irradiance to the total solar irradiance during large flares. J. Geophys. Res. 111, 10. doi: 10.1029/2005JA011507 .
Yurchyshyn, V., Abramenko, V., Tripathi, D.: 2009, Rotation of white-light coronal mass ejection structures as inferred from LASCO coronagraph. Astrophys. J. 705, 426 – 435. doi: 10.1088/0004-637X/705/1/426 .
Yurchyshyn, V., Hu, Q., Abramenko, V.: 2005, Structure of magnetic fields in NOAA active regions 0486 and 0501 and in the associated interplanetary ejecta. Space Weather 3, 8. doi: 10.1029/2004SW000124 .
Yurchyshyn, V.B., Wang, H., Goode, P.R., Deng, Y.: 2001, Orientation of the magnetic fields in interplanetary flux ropes and solar filaments. Astrophys. J. 563, 381 – 388. doi: 10.1086/323778 .
Yurchyshyn, V., Liu, C., Abramenko, V., Krall, J.: 2006, The May 13, 2005 eruption: observations, data analysis and interpretation. Solar Phys. 239, 317 – 335. doi: 10.1007/s11207-006-0177-3 .
Yurchyshyn, V., Hu, Q., Lepping, R.P., Lynch, B.J., Krall, J.: 2007, Orientations of LASCO Halo CMEs and their connection to the flux rope structure of interplanetary CMEs. Adv. Space Res. 40, 1821 – 1826. doi: 10.1016/j.asr.2007.01.059 .
Zhang, Y., Liu, J., Zhang, H.: 2008, Relationship between rotating sunspots and flares. Solar Phys. 247, 39 – 52. doi: 10.1007/s11207-007-9089-0 .
Zhao, X.P., Hoeksema, J.T.: 1998, Central axial field direction in magnetic clouds and its relation to southward interplanetary magnetic field events and dependence on disappearing solar filaments. J. Geophys. Res. 103, 2077 – 2083. doi: 10.1029/97JA03234 .
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Solar Flare Magnetic Fields and Plasmas
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Kazachenko, M.D., Canfield, R.C., Longcope, D.W. et al. Predictions of Energy and Helicity in Four Major Eruptive Solar Flares. Sol Phys 277, 165–183 (2012). https://doi.org/10.1007/s11207-011-9786-6
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DOI: https://doi.org/10.1007/s11207-011-9786-6