ANGEO Annales Geophysicae ANGEO Ann. Geophys. 1432-0576 Copernicus Publications Göttingen, Germany 10.5194/angeo-28-1229-2010 On arc-polarized structures in the solar wind Sonnerup B. U. Ö. 1 Haaland S. E. 2 3 Paschmann G. 4 Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire, USA Max Planck Institut für Sonnensystemforschung, Katlenburg-Lindau, Germany Department of Physics and Technology, University of Bergen, Bergen, Norway Max Planck Institut für extraterrestrische Physik, Garching, Germany 08 06 2010 28 6 1229 1248 Copyright: © 2010 B. U. Ö. Sonnerup et al. 2010 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://angeo.copernicus.org/articles/28/1229/2010/angeo-28-1229-2010.html The full text article is available as a PDF file from https://angeo.copernicus.org/articles/28/1229/2010/angeo-28-1229-2010.pdf

A theoretical model is proposed to account for some of the behavior of arc-polarized magnetic structures seen in the solar wind. To this end, an exact analytical solution is developed that describes infinite plane wave trains of arbitrary amplitude in a plasma governed by ideal Hall MHD. The main focus is on intermediate-mode wave trains, which display double-branched magnetic hodogram signatures similar to those seen in the solar wind. The theoretically derived hodograms have field rotation in the ion-polarized sense at a slightly depressed field magnitude on one branch and an electron-polarized rotation at a slightly enhanced field magnitude on the other branch. The two branches are joined at the two "turning points", at which the normal flow is exactly Alfvénic. The behavior is accounted for in terms of the opposite dispersive properties of ion and electron whistlers. The hodograms derived from the theory are shown to compare favorably with those of one event, observed by the Cluster spacecraft near the ecliptic plane, and one event at high heliographic latitude observed by the Ulysses spacecraft. However, these two observed structures comprise only a single full wave period, approximately from one turning point to the other and then back again. The theory can be used to predict propagation direction (away from, or towards, the sun) from magnetic data alone, provided the sign of the magnetic field component along the wave normal can be reliably determined. Under the same condition, it also predicts whether the ion-polarized branch should precede or follow the electron-polarized branch. Both behaviors are seen in the solar wind. The major shortcoming of the theory is that it fails to reproduce the observed saw-tooth like time series for the magnetic field, in which the field rotation is rapid in the ion sense and slow in the electron sense. Instead, the theory gives about the same rotation rates. Possible explanations for this discrepancy are discussed. Also discussed is the fact that the magnetic field measurements by Cluster, while giving high quality determinations of normal direction and normal field component for each of the four spacecraft, indicate a reversal of the normal field component and the predicted propagation sense during the event, as well as a wide spread in the four normal vector orientations.

 References Haaland, S. E., Sonnerup, B. U. Ö., Dunlop, M. W., Balogh, A., Georgescu, E., Hasegawa, H., Klecker, B., Paschmann, G., Puhl-Quinn, P., Rème, H., Vaith, H., and Vaivads, A.: Four-spacecraft determination of magnetopause orientation, motion and thickness: comparison with results from single-spacecraft methods, Ann. Geophys., 22, 1347–1365, 2004. Hau, L.-N. and Sonnerup, B. U. Ö.: On the structure of resistive intermediate shocks, J. Geophys. Res., 94, 6539–6551, 1989. Hau, L.-N. and Sonnerup, B. U. Ö.: The structure of resistive-dispersive intermediate shocks, J. Geophys. Res., 95, 18791–18808, 1990. Horbury, T. and Tsurutani, B. T.: Ulysses measurements of waves, turbulence and discontinuities, Chapter 4, pp 167–227, in: The Heliosphere Near Solar Minimum, edited by: Balogh, A., Marsden, R. G., and Smith, E. J., Springer Verlag, Berlin, ISBN 1-85233-204-2, 2001. Khrabrov, A. V. and Sonnerup, B. U. Ö.: DeHoffmann-Teller Analysis, Ch. 9, pp 221–248, in: Analysis Methods for Multi-Spacecraft Data, edited by: Paschmann, G. and Daly, P. W., ISSI SR-001, ESA Publ. Div. Noordwijk, 1998. Lichtenstein, B. R. and Sonett, C. P.: Dynamic magnetic structure of large amplitude Alfvénic variations in the solar wind, Geophys. Res. Lett., 7, 189–192, 1980. Riley, P., Sonett, C. P., Tsurutani, B. T., Balogh, A., Forsyth, R. J., and Hoogeveen, G. W.: Properties of arc-polarized Alfvén waves in the ecliptic plane: Ulysses observations, J. Geophys. Res., 101, 19987–19993, 1996. Sonnerup, B. U. Ö. and Scheible, M.: Minimum and maximum variance analysis, Ch. 8, pp 185–220, in: Analysis Methods for Multi-Spacecraft Data, edited by: Paschmann, G. and Daly, P. W., ISSI SR-001, ESA Publ. Div. Noordwijk, 1998. Spangler, S. R., Sheerin, J. P., and Payne, G. L.: A numerical study of nonlinear Alfvén waves and solitons, Phys. Fluids, 28, 104–109, 1985. Tsurutani, B. T., Ho, C. M., Smith, E. J., Neugebauer, M., Goldstein, B. E., Mok, J. S., Arballo, J. K., Balogh, A., Southwood, D. J., and Feldman, W. C.: The relationship between interplanetary discontinuities and Alfvén waves: Ulysses observations, Geophys Res. Lett., 21, 2267–2270, 1994. Tsurutani, B. T., Ho, C. M., Arballo, J. K., Smith, E. J., Goldstein, B. E., Neugebauer, M., Balogh, A., and Feldman, W. C.: Interplanetary discontinuities and Alfvén waves at high heliographic latitudes: Ulysses, J. Geophys. Res., 101, 11027–11038, 1996. Tsurutani, B. T., Ho, C. M., Arballo, J. K., Lakhina, G. S., Glassmeier, K.-H., and Neubauer, F. M.: Nonlinear electromagnetic waves and spherical arc-polarized waves in space plasmas, Plasma Phys. Contr. Fusion, 39(A5), A237–A250, 1997. Tsurutani, B. T. and Ho, C. M.: A review of discontinuities and Alfvén waves in interplanetary space: Ulysses results, Rev. Geophys., 37(4), 517–541, 1999. Vasquez, B. J. and Hollweg, J. V.: Formation of arc-shaped Alfvén waves and rotational discontinuities from oblique linearly polarized wave trains, J. Geophys. Res., 101, 13527–13540, 1996. Vasquez, B. J. and Hollweg, J. V.: Formation of spherically polarized Alfvén waves and embedded rotational discontinuities from a small number of entirely oblique waves, J. Geophys. Res., 103, 335–347, 1998a. Vasquez, B. J. and Hollweg, J. V.: Formation of embedded rotational discontinuities with nearly field-aligned normals, J. Geophys. Res., 103, 349–365, 1998b.