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On Fields and Mass Constraints for the Uniform Propagation of Magnetic-Flux Ropes Undergoing Isotropic Expansion

  • FLUX-ROPE STRUCTURE OF CORONAL MASS EJECTIONS
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A Correction to this article was published on 28 November 2019

Abstract

An analytical 3-D magnetohydrodynamic (MHD) solution of a magnetic-flux rope (FR) is presented. This FR solution may explain the uniform propagation, beyond ∼ 0.05 AU, of coronal mass ejections (CMEs) commonly observed by today’s missions like The Solar Mass Ejection Imager (SMEI), Solar and Heliospheric Observatory (SOHO) and Solar Terrestrial Relations Observatory (STEREO), tracked to tens of times the radius of the Sun, and in some cases up to 1 AU, and/or beyond. Once a CME occurs, we present arguments regarding its evolution based on its mass and linear momentum conservation. Here, we require that the gravitational and magnetic forces balance each other in the framework of the MHD theory for a simple model of the evolution of a CME, assuming it interacts weakly with the steady solar wind. When satisfying these ansätze we identify a relation between the transported mechanical mass of the interplanetary CME with its geometrical parameters and the intensity of the magnetic field carried by the structure. In this way we are able to estimate the mass of the interplanetary CME (ICME) for a list of cases, from the Wind mission records of ICME encountered near Earth, at 1 AU. We obtain a range for masses of ∼ 109 to 1013 kg, or assuming a uniform distribution, of ∼ 0.5 to 500 cm−3 for the hadron density of these structures, a result that appears to be consistent with observations.

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References

  • Abramowitz, M., Stegun, I.A.: 1972, Handbook of Mathematical Functions, 9th edn. Dover, New York.

    MATH  Google Scholar 

  • Albertson, V.D., Thorson, J.M., Clayton, R.E., Tripathy, R.E.: 1973, Solar induced currents in power systems: cause and effects. IEEE Trans. Power Appar. Syst. PAS-92, 471.

    Article  Google Scholar 

  • Bartels, J.: 1962, Collection of Geomagnetic Planetary Indices KP and Derived Daily Indices, AP and CP for the Years 1932 to 1961, AGU, Washington. QC811.B28.

    Google Scholar 

  • Berdichevsky, D.B., Lepping, R.P., Farrugia, C.J.: 2003, Geometric considerations of the evolution of magnetic flux ropes. Phys. Rev. E 67, 036405. doi: 10.1103/PhysRevE.036405 .

    Article  ADS  Google Scholar 

  • Berdichevsky, D.B., Stenborg, G., Vourlidas, A.: 2011, Deriving the physical parameters of a solar ejection with an isotropic magnetohydrodynamic evolutionary model. Astrophys. J. 741, 47. doi: 10.1088/0004-637X/741/1/47 .

    Article  ADS  Google Scholar 

  • Berdichevsky, D.B., Farrugia, C.J., Thompson, B.J., Lepping, R.P., Reames, V.V., Kaiser, M.L., Steinberg, J.T., Plunkett, S.P., Michels, D.J.: 2002, Halo-coronal mass ejections near the 23rd solar minimum: lift-off, inner heliosphere, and in situ (1 AU) signatures. Ann. Geophys. 20, 891.

    Article  ADS  Google Scholar 

  • Berdichevsky, D.B., Richardson, I., Lepping, R.P., Martin, S., 2005, On the origin and configuration of the 20 March 2003 interplanetary shock and magnetic cloud at 1 AU. J. Geophys. Res. 110, A09105. doi: 10.1029/2004JA010662 .

    Article  ADS  Google Scholar 

  • Bothmer,V., Schwenn, R.: 1998, The structure of magnetic clouds in the solar wind. Ann. Geophys. 16, 1.

    Article  ADS  Google Scholar 

  • Burlaga, L.F.: 1988, Magnetic clouds and force-free fields with constant alpha. J. Geophys. Res. 93, 7217.

    Article  ADS  Google Scholar 

  • Carrington, R.C.: 1859, Description of a singular appearance seen in the Sun on September 1, 1859. Mon. Not. Roy. Astron. Soc. 20, 13.

    ADS  Google Scholar 

  • Chamberlain, J.W.: 1960, Interplanetary gas II. Expansion of a model solar corona. Astrophys. J. 131, 47.

    Article  ADS  Google Scholar 

  • Chamberlain, J.W.: 1961, Interplanetary gas III. A hydrodynamical model of the corona. Astrophys. J. 133, 675.

    Article  MathSciNet  ADS  Google Scholar 

  • Chapman, S.: 1957, Notes on the solar corona and the terrestrial ionosphere. Smithson. Contrib. Astrophys. 2, 1.

    Article  ADS  Google Scholar 

  • Czech, P., Chano, S., Huynh, H., Dutil, A.: 1992, The hydro-Quebec system blackout of 13 March 1989: system response to geomagnetic disturbance. In: Proc. EPRI Conf. Geomagnetically Induced Currents EPRI TR-100450, Burlingame, CA. 19-1.

    Google Scholar 

  • Farrugia, C.J., Berdichevsky, D.B.: 2004, Evolutionary signatures in complex ejecta and their driven shocks. Ann. Geophys. 22, 3679.

    Article  ADS  Google Scholar 

  • Goldstein, H.: 1956, Classical Mechanics, 4th edn. Addison Wesley, Cambridge.

    Google Scholar 

  • Garrett, H.B.: 1981, The charging of spacecraft surfaces. Rev. Geophys. 19, 577.

    Article  ADS  Google Scholar 

  • Hidalgo, M.A., Nieves-Chinchilla, T., Cid, C.: 2002, Elliptical cross-section model for the magnetic topology of magnetic clouds. Geophys. Res. Lett. 29, 1637. doi: 10.1029/2001GL013875 .

    Article  ADS  Google Scholar 

  • Hirshberg, J., Bame, S.J., Robbins, D.E.: 1972, Solar flares and solar wind helium enrichments: July 1965. Solar Phys. 23, 467.

    Article  ADS  Google Scholar 

  • Holzer, T.E.: 1979. In: Parker, E.N., Kennel, C.F., Lanzerotti, L.J. (eds.): Solar and Solar Wind Plasma Physics. 1, North-Holland, Amsterdam, 101.

    Google Scholar 

  • Hu, Q., Sonnerup, U.O.: 2001, Reconstruction of magnetic flux-ropes in the solar wind. Geophys. Res. Lett. 28, 467.

    Article  ADS  Google Scholar 

  • Huttunen, K.E.J., Schwenn, R., Bothmer, V., Koskinen, H.E.J.: 2005, Properties and geoffectiveness of magnetic clouds in the rising, maximum and early declining phases of solar cycle 23. Ann. Geophys. 23, 625.

    Article  ADS  Google Scholar 

  • Jackson, J.D.: 1966, Electrodinámica Clásica, 1st Spanish edn. Alhambra, Madrid.

    Google Scholar 

  • Landau, L., Lifchitz, E.: 1966, Physique Théorique, Tome i, Mécanique, 2me edn. MIR, Moscow.

    Google Scholar 

  • Lanzerotti, L.J., Breglia, C., Maurer, D.W., Maclennan, C.G.: 1998, Studies of spacecraft charging on a geosynchronous telecommunications satellite. Adv. Space Res. 22, 79.

    Article  ADS  Google Scholar 

  • Le, G., Gosling, J.T., Russell, C.T., Elphic, R.C., Thomsen, M.F., Newbury, J.A.: 1999, The magnetic and plasma of flux transfer events. J. Geophys. Res. 104, 233.

    Article  ADS  Google Scholar 

  • Le, G., Zheng, Y., Russell, C.T., Pfaff, R.F., Slavin, J.A., Lin, N., Mozer, F., Parks, G., Wilber, M., Petrinec, S.M., Lucek, E.A., Réme, H.: 2008, Flux transfer events simultaneously observed by Polar and Cluster: flux rope in the subsolar region and flux tube addition to the polar cusp. J. Geophys. Res. 113, A01205.

    Article  ADS  Google Scholar 

  • Lepping, R.P., Jones, J.E., Burlaga, L.F.: 1990, Magnetic field structure of interplanetary magnetic clouds at 1 AU. J. Geophys. Res. 108, 11957.

    Article  ADS  Google Scholar 

  • Lepping, R.P., Berdichevsky, D.B., Burlaga, L.F., Lazarus, A.J., Kasper, J., Desch, M.D., Wu, C.C., Reames, D.-V., Singer, H.J., Smith, C.W., Ackerson, K.L.: 2001a, The Bastille day magnetic clouds and upstream shocks: near earth interplanetary observations. Solar Phys. 204, 287.

    Article  ADS  Google Scholar 

  • Lepping, R.P., Berdichevsky, D.B., Szabo, A., Lazarus, A.J., Thompson, B.J.: 2001b, Upstream shocks and interplanetary magnetic cloud speed and expansion: Sun, Wind, and Earth observations. In: Chao, K. (ed.) COSPAR 2000. Adv. Space Res., 26, 87.

    Google Scholar 

  • Lepping, R.P, Berdichevsky, D.B., Szabo, A., Arqueros, C., Lazarus, A.J.: 2003, Profile of an average magnetic cloud at 1 AU for the quiet solar phase: Wind observations. Solar Phys. 212, 425.

    Article  ADS  Google Scholar 

  • Lepping, R.P., Berdichevsky, D.B., Wu, C.-C., Szabo, A., Narock, T., Mariani, F., Lazarus, A.J., Quivers, A.J.: 2006, A summary of Wind magnetic clouds for years 1995 – 2003: model-fitted parameters, associated errors and classifications. Ann. Geophys. 24, 215.

    Article  ADS  Google Scholar 

  • Lepping, R.P., Wu, C.-C., Berdichevsky, D.B., Szabo, A: 2011, Magnetic clouds at/near the 2007 – 2009 solar minimum: frequency of occurrence and some unusual properties. Solar Phys. 274, 345.

    Article  ADS  Google Scholar 

  • Lundquist, S.: 1951, Magnetohydrostatic fields. Ark. Fys. 2, 61.

    MathSciNet  Google Scholar 

  • Osherovich, V.A., Fainberg, J., Stone, R.G., MacDowall, R.J., Berdichevsky, D.B.: 1997 In: Proc. 31st. ESLAB Symp., Correlated Phenomena at the Sun, in the Heliosphere and in Geospace, SA SP-415, ESA, Noordwijk, 771.

    Google Scholar 

  • Parker, E.N.: 1958, Dynamics of the interplanetary gas and magnetic fields. Astrophys. J. 124, 664.

    Article  ADS  Google Scholar 

  • Pirjola, R., Lehtinen, M.: 1985, Currents produced in the Finnish natural gas pipeline by geomagnetically induced electric fields. Ann. Geophys. 3, 485.

    Google Scholar 

  • Richardson, I.J., Cane, H.V.: 2004, Identification of interplanetary coronal mass ejections at 1 AU using multiple solar wind plasma composition anomalies. J. Geophys. Res. 109, A09104.

    Article  ADS  Google Scholar 

  • Richardson, D.J., Kasper, C., Wang, C., Belcher, J.W., Lazarus, A.J.: 2008, Cool heliosheath plasma and deceleration of the upstream solar wind at the termination shock. Nature 454(3), 63.

    Article  ADS  Google Scholar 

  • Rouillard, A.P., Davies, J.A., Forsyth, R.J., Savani, N., Sheeley, R., Thernisien, A., Burlaga, L.F., Zhang, T.-L., Vourlidas, A., Howard, R.A., Wang, Y.-M., Rees, A., Anderson, B., Krimiges, T., Slavin, J., Carr, C.M., Tsang, S., Lockwood, M., Davis, C.J., Harrison, R.A., Bewsher, D., Crothers, S.R, Eyles, C.J., Brown, D.S., Habgood, M., Perry, C.H., Whittaker, I., Jones, G.H., Coates, A.J., Reande, M., Frahm, R.A., Winningan, J.D.: 2009, A solar storm observed from the Sun to Venus using the STEREO Venus-Express, and MESSENGER spacecraft. J. Geophys. Res. 114, 07106. doi: 10.1029/2008JA014034 .

    Article  Google Scholar 

  • Sittler, E.C. Jr., Burlaga, L.F.: 1998, Electron temperatures within magnetic clouds between 2 and 4 AU: Voyager 2 observations. J. Geophys. Res. 103, 17447.

    Article  ADS  Google Scholar 

  • Shimazu, H., Vandas, M.: 2002, A self-similar solution of expanding cylindrical flux ropes for any polytropic index value. Earth Planet Sci. J. 54, 783.

    ADS  Google Scholar 

  • Slavin, J.A., Fairfield, D.H., Lepping, R.P., Hesse, M., Ieda, A., Tanskanen, E., Østgaard, N., Mukai, T., Nagai, T., Singer, H.J., Sutcliffe, P.R.: 2002, Simultaneous observations of earthward flow bursts and plasmoid ejection during magnetospheric substorms. J. Geophys. Res. 107, A7. doi: 10.1029/2000JA003501 .

    Article  Google Scholar 

  • Thernisien, A., Vourlidas, A., Howard, R.A.: 2009, A catalog of white light coronal mass ejections observed by the STEREO/SECCHI data. Solar Phys. 256, 111.

    Article  ADS  Google Scholar 

  • WIND MFI Science Team: 1995, (– start date), Page (–Table 2, ‘a living document’) at http://wind.gsfc.nasa.gov/mfi/mag_cloud_S1.html .

  • Wood, B.E., Howard, R.A.: 2009, An empirical reconstruction of the 2008 april 26 coronal mass ejection. Astrophys. J. 702, 901. doi: 10.1088/0004-637X/702/2/901 .

    Article  ADS  Google Scholar 

  • Wood, B.E., Wu, C.-C., Howard, R.A., Socker, D.G., Rouillard, A.P.: 2011, Empirical reconstruction and numerical modeling of the first geoeffective coronal mass ejection of solar cycle 24. Astrophys. J. 729, 70. doi: 10.1088/0004-637X/729/1/70 .

    Article  ADS  Google Scholar 

  • Yashiro, S., Gopalswamy, N., Michalek, G., St. Cyr, O.-C., Plunkett, S.P., Rich, N.B., Howard, R.A.: 2004, A catalog of white light coronal mass ejections observed by the SOHO spacecraft. J. Geophys. Res. 109, A07105. doi: 101029/2003JA010282 .

    Article  ADS  Google Scholar 

  • Zirin, H.: 1966, The Solar Atmosphere, Blaisdell, Waltham.

    Google Scholar 

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Acknowledgements

I acknowledge my father Carlos David, for his unconditional support of a whole life. Also I acknowledge the professional support of Santiago Berdichevsky, who helped to put this text in better English, making it more understandable.

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  1. College Park, MD, 20740-4111, USA

    Daniel Benjamín Berdichevsky

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  1. Daniel Benjamín Berdichevsky
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Correspondence to Daniel Benjamín Berdichevsky.

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Flux-Rope Structure of Coronal Mass Ejections

Guest Editors: N. Gopalswamy, T. Nieves-Chinchilla, M. Hidalgo, J. Zhang, and P. Riley

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Berdichevsky, D.B. On Fields and Mass Constraints for the Uniform Propagation of Magnetic-Flux Ropes Undergoing Isotropic Expansion. Sol Phys 284, 245–259 (2013). https://doi.org/10.1007/s11207-012-0176-5

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