Solar Physics

, 294:155 | Cite as

Mapping Magnetic Field Lines for an Accelerating Solar Wind

  • S. TasnimEmail author
  • Iver H. Cairns
  • B. Li
  • M. S. Wheatland


Mapping of magnetic field lines is important for studies of the solar wind and the sources and propagation of energetic particles between the Sun and observers. A recently developed mapping approach is generalized to use a more advanced solar wind model that includes the effects of solar wind acceleration, non-radial intrinsic magnetic fields and flows at the source surface/inner boundary, and conservation of angular momentum. The field lines are mapped by stepping along \(\mathbf{B}\) and via a Runge–Kutta algorithm, leading to essentially identical maps. The new model’s maps for Carrington rotation CR 1895 near solar minimum (19 April to 15 May 1995) and a solar rotation between CR 2145 and CR 2146 near solar maximum (14 January to 9 February 2014) are compared with the published maps for a constant solar wind model. The two maps are very similar on a large scale near both solar minimum and solar maximum, meaning that the field-line orientations, winding angles, and connectivity generally agree very well. However, close inspection shows that the field lines have notable small-scale structural differences. An interpretation is that inclusion of the acceleration and intrinsic azimuthal velocity has significant effects on the local structure of the magnetic field lines. Interestingly, the field lines are more azimuthal for the accelerating solar wind model for both intervals. In addition, predictions for the pitch angle distributions (PADs) for suprathermal electrons agree at the 90 – 95% level with observations for both solar wind models for both intervals.


Mapping Magnetic field lines Accelerating solar wind 


Disclosure of Potential Conflict of Interest

The authors declare that they have no conflicts of interest.


  1. Borovsky, J.E.: 2010, On the variations of the solar wind magnetic field about the Parker spiral direction. J. Geophys. Res.115, A09101. DOI. ADSCrossRefGoogle Scholar
  2. Bruno, R., Bavassano, B.: 1997, On the winding of the IMF spiral for slow and fast wind within the inner heliosphere. Geophys. Res. Lett.24, 2267. DOI. ADSCrossRefGoogle Scholar
  3. Burlaga, L.F., Lepping, R.P., Behannon, K.W.: 1982, Large-scale variations of the interplanetary magnetic field: Voyager 1 and 2 observations between 1 – 5 AU. J. Geophys. Res.87, 4345. DOI. ADSCrossRefGoogle Scholar
  4. Crooker, N.U., Huang, C.-L., Lamassa, S.M., Larson, D.E., Kahler, S.W., Spence, H.E.: 2004a, Heliospheric plasma sheets. J. Geophys. Res.109, A03107. DOI. ADSCrossRefGoogle Scholar
  5. Crooker, N.U., Kahler, S.W., Larson, D.E., Lin, R.P.: 2004b, Large-scalemagnetic field inversions at sector boundaries. J. Geophys. Res.109, A03108. DOI. ADSCrossRefGoogle Scholar
  6. Crooker, N.U., Huang, C.-L., Lamassa, S.M., Larson, D.E., Kahler, S.W., Spence, H.E.: 2010, Intermittent release of transients in the slow solar wind: 2. In situ evidence. J. Geophys. Res.115, A04104. DOI. CrossRefGoogle Scholar
  7. Dósa, M., Erdős, G.: 2017, Long-term longitudinal recurrences of the open magnetic flux density in the Heliosphere. Astrophys. J.834, 104. DOI. ADSCrossRefGoogle Scholar
  8. Feldman, W.C., Asbridge, J.R., Bame, S.J., Montgomery, M.D., Gary, S.P.: 1975, Solar wind electrons. J. Geophys. Res.80, 4181. DOI. ADSCrossRefGoogle Scholar
  9. Fisk, L.A.: 1996, Motion of the footpoint of the heliospheric magnetic field lines at the Sun: Implications for recurrent energetic particle events at high heliographic latitude. J. Geophys. Res.101, 547. DOI. CrossRefGoogle Scholar
  10. Forsyth, R.J., Balogh, A., Horbury, T.S., Erdos, G., Smith, E.J., Burton, M.E.: 1996, The heliospheric magnetic field at solar minimum: Ulysses observations from pole to pole. Astron. Astrophys.316, 287. ADS. ADSGoogle Scholar
  11. Gosling, J.T., Roelof, E.C.: 1974, A comment on the detection of closedmagnetic structures in the solar wind. Solar Phys.39, 405. DOI. ADSCrossRefGoogle Scholar
  12. Gosling, J.T., Skoug, R.M.: 2002, On the origin of radial magnetic fields in the heliosphere. J. Geophys. Res.107(A10), 1327. DOI. CrossRefGoogle Scholar
  13. Gosling, J.T., Baker, D.N., Bame, S.J., Feldman, W.C., Zwickl, R.D., Smith, E.J.: 1987, Bidirectional solar wind electron heat flux events. J. Geophys. Res.92, 8519. DOI. ADSCrossRefGoogle Scholar
  14. Hu, Y.Q.: 1993, Evolution of corotating stream structures in the heliospheric equatorial plane. J. Geophys. Res.98, 13,201. ADSCrossRefGoogle Scholar
  15. Hu, Y.Q., Habbal, S.R.: 1992, Double shock pairs in the solar wind. J. Geophys. Res.98, 3551. ADSCrossRefGoogle Scholar
  16. Jian, L.: 2010, Interplanetary coronal mass ejections (ICMEs) from Wind and ACE data during 1995 – 2009. Updated November 18, 2014.
  17. Kutchko, F.J., Briggs, P.R., Armstrong, T.P.: 1982, The bidirectional particle event of October 12, 1977, possibly associated with a magnetic loop. J. Geophys. Res.82, 1419. DOI. ADSCrossRefGoogle Scholar
  18. Li, B., Cairns, I.H., Gosling, J.T., Malaspina, D.M., Neudegg, D., Steward, G., Lobzin, V.V.: 2016a, Comparisons of mapped magnetic field lines with the source path of the 7 April 1995 type III solar radio burst. J. Geophys. Res.121, 6141. DOI. CrossRefGoogle Scholar
  19. Li, B., Cairns, I.H., Gosling, J.T., Steward, G., Francis, M., Neudegg, D., in den Bäumen, H.S., Player, P.R., Milne, A.R.: 2016b, Mapping magnetic field lines between the Sun and Earth. J. Geophys. Res.121, 925. DOI. CrossRefGoogle Scholar
  20. Li, B., Cairns, I.H., Owens, M.J., Neudegg, D., Lobzin, V.V., Steward, G.: 2016c, Magnetic field inversions at 1 AU: Comparisons between mapping predictions and observations. J. Geophys. Res.121, 10728. DOI. CrossRefGoogle Scholar
  21. McComas, D.J., et al.: 1989, Electron heat flux dropouts in the solar wind – Evidence for interplanetarymagnetic field reconnection? J. Geophys. Res.94, 6907. DOI. ADSCrossRefGoogle Scholar
  22. Nolte, J.T., Roelof, E.C.: 1973a, Large-scale structure of the interplanetary medium I: High coronal source longitude of the quite-time solar wind. Solar Phys.33, 241. DOI. ADSCrossRefGoogle Scholar
  23. Nolte, J.T., Roelof, E.C.: 1973b, Large-scale structure of the interplanetary medium II: Evolving magnetic configurations deduced from multi-spacecraft observations. Solar Phys.33, 483. DOI. ADSCrossRefGoogle Scholar
  24. Odstřcil, D.: 1994, Interactions of solar wind streams and related small structures. J. Geophys. Res.99, 17,653. ADSCrossRefGoogle Scholar
  25. Owens, M.J., Forsyth, R.J.: 2013, The heliospheric magnetic field. Living Rev. Solar Phys.10, 5. DOI. ADSCrossRefGoogle Scholar
  26. Parker, E.N.: 1958, Dynamics of the interplanetary gas and magnetic fields. Z. Astrophys.29, 274. DOI. CrossRefGoogle Scholar
  27. Reiner, M.J., Fainberg, J., Stone, R.G.: 1995, Large-scale interplanetary magnetic field configuration revealed by solar radio bursts. Science270, 461. DOI. ADSCrossRefGoogle Scholar
  28. Richardson, I.G.: 2018, Solar wind stream interaction regions through out the heliosphere. Living Rev. Solar Phys.15, 104. DOI. CrossRefGoogle Scholar
  29. Richardson, I.G., Cane, H.V., von Rosenvinge, T.T.: 1991, Prompt arrival of solar energetic particles from far eastern events – The role of large-scale interplanetary magnetic field structure. J. Geophys. Res.96, 7853. DOI. ADSCrossRefGoogle Scholar
  30. Richardson, J.D., Belcher, J.W., Lazarus, A.J., Paularena, K.I., Steinberg, J.T., Gazis, P.R.: 1996, Non-radial flows in the solar wind. AIP Conf. Proc.382, 479. ADSCrossRefGoogle Scholar
  31. Rosenbauer, H., Schwenn, R., Marsch, E., Meyer, B., Miggenrieder, H., Montgomery, M.D., Muehlhaeuser, K.H., Pilipp, W., Voges, W., Zink, S.M.: 1977, A survey on initial results of the HELIOS plasma experiment. J. Geophys.42, 561. Google Scholar
  32. Ruffolo, D., et al.: 2006, Relativistic solar protons on 1989 October 22: Injection and transport along both legs of a closed interplanetary magnetic loop. Astrophys. J.639, 1186. DOI. ADSCrossRefGoogle Scholar
  33. Schatten, K.H., Ness, N.F., Wilcox, J.M.: 1968, Influence of a solar active region on the interplanetary magnetic field. Solar Phys.5, 240. DOI. ADSCrossRefGoogle Scholar
  34. Schulte in den Bäumen, H., Cairns, I.H., Robinson, P.A.: 2011, Modeling 1 AU solar wind observations to estimate azimuthal magnetic fields at the solar source surface. Geophys. Res. Lett.38, L24101. DOI. ADSCrossRefGoogle Scholar
  35. Schulte in den Bäumen, H., Cairns, I.H., Robinson, P.A.: 2012, Nonzero azimuthal magnetic fields at the solar source surface: Extraction, model, and implications. J. Geophys. Res.117, 104. DOI. CrossRefGoogle Scholar
  36. Schwadron, N.A., Connick, D.E., Smith, C.W.: 2010, Magnetic flux balance in the heliosphere. Astrophys. J. Lett.722, L132. DOI. ADSCrossRefGoogle Scholar
  37. Smith, E.J.: 1979, Interplanetary magnetic fields. Rev. Geophys.17, 610. DOI. ADSCrossRefGoogle Scholar
  38. Suzuki, S., Dulk, G.A.: 1985, Bursts of type III and type V. In: Solar Radiophysics, Cambridge University Press, Cambridge. Google Scholar
  39. Tasnim, S., Cairns, I.H.: 2016, An equatorial solar wind model with angular momentum conservation and non-radial magnetic fields and flow velocities at an inner boundary. J. Geophys. Res.121, 4966. DOI. CrossRefGoogle Scholar
  40. Tasnim, S., Cairns, I.H., Wheatland, M.S.: 2018, A generalized equatorial model for the accelerating solar wind. J. Geophys. Res.123, 1061. DOI. CrossRefGoogle Scholar
  41. Thomas, B.T., Smith, E.J.: 1980, The parker spiral configuration of the interplanetary magnetic field between 1 and 8.5 AU. J. Geophys. Res.85, 6861. DOI. ADSCrossRefGoogle Scholar
  42. Veselovsky, I.S., Persiantsev, I.G., Shugai, Y.S.: 2006, Forecast of the solar wind velocity and the interplanetary magnetic field radial component polarity at the phase of decay of solar cycle 23. Geomagn. Aeron.46, 701. DOI. ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.The Center for Space Plasma and Aeronomic ResearchThe University of Alabama in HuntsvilleHuntsvilleUSA
  2. 2.School of PhysicsThe University of SydneyCamperdownAustralia

Personalised recommendations