# Three-Dimensional Simulation Study of the Interactions of Three Successive CMEs during 4–5 November 1998

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Observational Properties of the 4–5 November 1998 CMEs

## 3. Numerical Model

## 4. Simulation Results and Discussion

## 5. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Strong, K.T.; Saba, J.L.R.; Haisch, B.M.; Schmelz, J.T. The Many Faces of the Sun: A Summary of the Results from NASA’s Solar Maximum Mission; Springer: Berlin, Germany, 1999; ISBN 978-1-4612-7145-1. [Google Scholar]
- Webb, D.F.; Howard, R.A. The solar cycle variation of coronal mass ejections and the solar wind mass flux. J. Geophys. Res.
**1994**, 99, 4201–4220. [Google Scholar] [CrossRef] - Nitta, N.V.; Hudson, H.S. Recurrent flare/CME events from an emerging flux region. Geophys. Res. Lett.
**2001**, 28, 3801–3804. [Google Scholar] [CrossRef] [Green Version] - Intriligator, D.S. The August 1972 Solar-Terrestrial Events: Solar Wind Plasma Observations. Space Sci. Rev.
**1976**, 19, 629–660. [Google Scholar] [CrossRef] - Burlaga, L.F.; Behannon, K.W.; Klein, L.W. Compound streams, magnetic clouds, and major geomagnetic storms. J. Geophys. Res.
**1987**, 92, 5725–5734. [Google Scholar] [CrossRef] - Brueckner, G.E.; Howard, R.A.; Koomen, M.J.; Korendyke, C.M.; Eyles, C.J. The large angle spectroscopic coronagraph (LASCO). Sol. Phys.
**1995**, 162, 357–402. [Google Scholar] [CrossRef] - Gopalswamy, N.; Yashiro, S.; Kaiser, M.L.; Howard, R.A.; Bougeret, J.-L. Characteristics of coronal mass ejections associated with long-wavelength type II radio bursts. J. Geophys. Res.
**2001**, 106, 29219–29229. [Google Scholar] [CrossRef] [Green Version] - Kaiser, M.L.; Kucera, T.A.; Davila, J.M.; Cyr, O.; Guhathakurta, M.; Christian, E. The STEREO Mission: An Introduction. Space Sci. Rev.
**2008**, 136, 5–16. [Google Scholar] [CrossRef] - Lugaz, N.; Farrugia, C.J.; Davies, J.A.; Mostl, C.; Davis, C.; Roussev, I.I.; Temmer, M. The deflection of the two interaction coronal mass ejections of 2010 May 23–24 as revealed by combined by in situ measurements and heliopheric imaging. Astrophys. J.
**2012**, 759, 68. [Google Scholar] [CrossRef] [Green Version] - Lugaz, N.; Temmer, M.; Wang, Y.; Farrugia, C.J. The Interaction of Successive Coronal Mass Ejections: A Review. Sol. Phys.
**2016**, 292, 64. [Google Scholar] [CrossRef] [Green Version] - Shen, F.; Wang, Y.; Shen, C.; Feng, X. On the Collision Nature of Two Coronal Mass Ejections: A Review. Sol. Phys.
**2017**, 292, 104. [Google Scholar] [CrossRef] [Green Version] - Temmer, M.; Vrsnak, B.; Rollett, T.; Bein, B.; De Koning, C.A.; Liu, Y.; Bosman, E.; Davies, J.A.; Moestl, C.; Zic, T. Characteristics of kinematics of a coronal mass ejection during the 2010 August 1 CME–CME interaction event. Astrophys. J.
**2012**, 749, 57. [Google Scholar] [CrossRef] [Green Version] - Temmer, M.; Veronig, A.M.; Peinhart, V.; Vrsnak, B. Asymmetry in the CME–CME interaction process for the events from 14–15 February 2011. Astrophys. J.
**2014**, 785, 85. [Google Scholar] [CrossRef] [Green Version] - Colaninno, R.C.; Vourlidas, A. Using multiple-viewpoint observations to determine the interaction of three coronal mass ejections observed on 2012 March 5. Astrophys. J.
**2015**, 815, 70. [Google Scholar] [CrossRef] - Manchester, W.; Kilpua, E.K.J.; Liu, Y.D.; Lugaz, N.; Vrnak, B. The Physical Processes of CME/ICME Evolution. Space Sci. Rev.
**2017**, 212, 1159–1219. [Google Scholar] [CrossRef] [Green Version] - Mishra, W.; Wang, Y.; Srivastava, N.; Shen, C. Assessing the Nature of Collisions of Coronal Mass Ejections in the Inner Heliosphere. Astrophys. J. Suppl.
**2017**, 232, 5. [Google Scholar] [CrossRef] [Green Version] - Wang, Y.M.; Ye, P.Z.; Wang, S. Multiple magnetic clouds: Several examples during March–April. J. Geophys. Res.
**2003**, 108, 1370. [Google Scholar] [CrossRef] - Xue, X.H.; Wang, Y.; Ye, P.Z.; Wang, S.; Xiong, M. Analysis on the interplanetary causes of the great magnetic storms in solar maximum (2000–2001). Planet. Space Sci.
**2005**, 53, 443–457. [Google Scholar] [CrossRef] - Zhang, J.; Richardson, I.G.; Webb, D.F.; Gopalswamy, N. Solar and interplanetary sources of major geomagnetic storms (Dst ≤ 100 nT) during 1996–2005. J. Geophys. Res.
**2017**, 112, A10102. [Google Scholar] - Lugaz, N.; Farrugia, C.J.; Smith, C.W.; Paulson, K. Shocks inside CMEs: A survey of properties from 1997 to 2006. J. Geophys. Res. Space Phys.
**2015**, 120, 2409. [Google Scholar] [CrossRef] [Green Version] - Shen, C.; Chi, Y.; Wang, Y.; Xu, M.; Wang, S. Statistical comparison of the ICME’s geoeffectiveness of different types and different solar phases from 1995 to 2014. J. Geophys. Res. Space Phys.
**2017**, 122, 5931–5948. [Google Scholar] [CrossRef] - Wang, Y.; Ye, P.; Wang, S.; Xiong, M. Theoretical analysis on the geoeffectiveness of a shock overtaking a preceding magnetic cloud. Sol. Phys.
**2003**, 216, 295–310. [Google Scholar] [CrossRef] - Shen, C.; Xu, M.; Wang, Y.; Chi, Y.; Luo, B. Why the Shock-ICME Complex Structure Is Important: Learning from the Early 2017 September CMEs. Astrophys. J.
**2018**, 861, 28. [Google Scholar] [CrossRef] [Green Version] - Farrugia, C.; Berdichevsky, D. Evolutionary signatures in complex ejecta and their driven shocks. Ann. Geophys.
**2004**, 22, 3679. [Google Scholar] [CrossRef] [Green Version] - Farrugia, C.J.; Jordanova, V.K.; Thomsen, M.F.; Lu, G.; Cowley, S.W.H.; Ogilvie, K.W.A. Two-ejecta event associated with a two-step geomagnetic storm. J. Geophys. Res.
**2006**, 111, A11104. [Google Scholar] [CrossRef] - Vandas, M.; Fischer, S.; Dryer, M.; Smith, Z.; Detman, T.; Geranios, A. MHD simulation of an interaction of a shock wave with a magnetic cloud. J. Geophys. Res. Space Phys.
**1997**, 102, 22295–22300. [Google Scholar] [CrossRef] - Lugaz, N.; Manchester, W.B.I.V.; Gombosi, T.I. Numerical simulation of the interaction of two coronal mass ejections from Sun to Earth. Astrophys. J.
**2005**, 634, 651–662. [Google Scholar] [CrossRef] - Lugaz, N.; Farrugia, C.J. A new class of complex ejecta resulting fromthe interaction of two CMEs and its expected geoeffectiveness. Geophys. Res. Lett.
**2014**, 41, 769. [Google Scholar] [CrossRef] [Green Version] - Xiong, M.; Zheng, H.; Wang, Y.; Wang, S. Magnetohydrodynamic simulation of the interaction between interplanetary strong shock and magnetic cloud and its consequent geoeffectiveness: 2. Oblique collision. J. Geophys. Res.
**2006**, 111, A11102. [Google Scholar] [CrossRef] [Green Version] - Shen, F.; Feng, X.S.; Wang, Y.; Wu, S.T.; Song, W.B.; Guo, J.P.; Zhou, Y.F. Three-dimensional MHD simulation of two coronal mass ejections’ propagation and interaction using a successive magnetized plasma blobs model. J. Geophys. Res.
**2011**, 116, A09103. [Google Scholar] [CrossRef] [Green Version] - Shen, F.; Shen, C.; Wang, Y.; Feng, X.; Xiang, C. Could the collision of CMEs in the heliosphere be super-elastic? Validation through three-dimensional simulations. Geophys. Res. Lett.
**2013**, 40, 1457. [Google Scholar] [CrossRef] [Green Version] - Shen, F.; Wang, Y.; Shen, C.; Feng, X. Turn on the super-elastic collision nature of coronal mass ejections through low approaching speed. Sci. Rep.
**2016**, 6, 19576. [Google Scholar] [CrossRef] [Green Version] - Scolini, C.; Chane, E.; Temmer, M.; Kilpua, E.K.J.; Poedts, S. CME–CME interactions as sources of CME geoeffectiveness: The formation of the complex ejecta and interse geomagnetic storm in 2017 early September. Astrophys. J.
**2020**, 247, 21. [Google Scholar] [CrossRef] - Burlaga, L.F.; Plunkett, S.P.; St. Cyr, O.C. Successive CMEs and complex ejecta. J. Geophys. Res.
**2002**, 107, 1266. [Google Scholar] [CrossRef] - Shen, C.; Wang, Y.; Wang, S.; Liu, Y.; Liu, R.; Vourlidas, A.; Miao, B.; Ye, P.; Liu, J.; Zhou, Z. Super-elastic collision of large-scale magnetized plasmoids in the heliosphere. Nat. Phys.
**2012**, 8, 923–928. [Google Scholar] [CrossRef] - Pomoell, J.; Poedts, S. EUHFORIA: European heliospheric forecasting information asset. J. Space Weather Space Clim.
**2018**, 8, A35. [Google Scholar] [CrossRef] - Michalek, G.; Gopalswamy, N.; Yashiro, S. A New Method for Estimating Widths, Velocities, and Source Location of Halo Coronal Mass Ejections. Astrophys. J.
**2003**, 584, 472. [Google Scholar] [CrossRef] [Green Version] - Feng, X.; Zhou, Y.; Wu, S.T. A Novel Numerical Implementation for Solar Wind Modeling by the Modified Conservation Element/Solution Element Method. Astrophys. J.
**2007**, 655, 1110–1126. [Google Scholar] [CrossRef] [Green Version] - Zhou, Y.F.; Feng, X.S.; Wu, S.T.; Du, D.; Shen, F.; Xiang, C.Q. Using a 3-D spherical plasmoid to interpret the Sun-to-Earth propagation of the 4 November 1997 coronal mass ejection event. J. Geophys. Res. Space Phys.
**2012**, 117, A01102. [Google Scholar] [CrossRef] [Green Version] - Luhmann, J.G.; Li, Y.; Arge, C.N.; Gazis, P.R.; Ulrich, R. Solar cycle changes in coronal holes and space weather cycles. J. Geophys. Res.
**2002**, 107, SMP 3-1–SMP 3-12. [Google Scholar] [CrossRef] [Green Version] - Zhao, X.P.; Hoeksema, J.T.; Liu, Y.; Scherrer, P.H. Success rate of predicting the heliospheric magnetic field polarity with Michelson Doppler Imager (MDI) synoptic charts. J. Geophys. Res.
**2006**, 111, A10108. [Google Scholar] [CrossRef] [Green Version] - Jacobs, C.; Poedts, S. A polytropic model for the solar wind. Adv. Space Res.
**2011**, 48, 1958–1966. [Google Scholar] [CrossRef] [Green Version] - Parker, E.N. Interplanetary Dynamical Processes; Interscience Publishers: New York, NY, USA, 1963. [Google Scholar]
- Feng, X.S. Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere; Springer: Singapore, 2020; ISBN 978-981-13-9080-7. [Google Scholar]
- Mishra, W.; Srivastava, N.; Singh, T. Kinematics of interacting CMEs of 25 and 28 September 2012. J. Geophys. Res. Space Phys.
**2015**, 120, 10221–10236. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Comparison between the in situ data obtained by the Wind spacecraft and the simulation during the 7–10 November 1998 event. From top to bottom, shown are flow velocity, number density, magnetic field, and three components of magnetic field in geocentric solar ecliptic (GSE) coordinates. The two vertical lines indicates the time of the shocks. The simulated results at Earth are shown by the solid lines. The Wind observations are shown by the dotted lines.

**Figure 2.**(

**a**) Three-dimensional steady state magnetic field structure and (

**b**) steady state current sheet in the solar corona domain.

**Figure 3.**(

**a**) Steady state solution in the solar equatorial plane. The black streamlines denote the magnetic field lines. The black circle represents Earth. (

**b**) Steady state solution in the Sun–Earth meridional plane. The color contours represent the radial speed (km s${}^{-1}$).

**Figure 4.**A 3D representation of the CME is shown at 50 h after the initiation of the first CME. The color code represents the velocity magnitude. Three-dimensional colored isosurfaces of $\overline{\rho}=1.5{\rho}_{wind}$ are drawn. The blue sphere shows the position of the Earth with a radius of 5 ${R}_{s}$.

**Figure 5.**Profiles of velocity, density, magnetic field and south component of magnetic field as function of time at different heliospheric distances: (

**a**) 50 ${R}_{s}$ (

**b**) 100 ${R}_{s}$ and (

**c**) 1 AU for CME1 (dashed line), CME2 (dash-dotted line) and CME12 (solid line).

**Figure 6.**The contour plots of the relative density $(\rho -{\rho}_{wind})/{\rho}_{wind}$ distribution on the solar-terrestrial meridional plane after (

**a**) 25 h (

**b**) 30 h (

**c**) 35 h and (

**d**) 40 h of the first CME of CME23, where $\rho $ is the total density and ${\rho}_{wind}$ is the density of the background solar wind.

**Figure 7.**The height/time map of the relative density distribution obtained along the Sun–Earth direction during 0–70 h expressed in solar radii from 1 to 215 ${R}_{s}$ for CME23.

**Figure 8.**Profiles of velocity, density, magnetic field and south component of magnetic field as function of time at different heliospheric distances: (

**a**) 50 ${R}_{s}$ (

**b**) 100 ${R}_{s}$ and (

**c**) 1 AU for CME2 (dashed line), CME3 (dash-dotted line) and CME23 (solid line).

**Figure 9.**Profiles of velocity, density, magnetic field and south component of magnetic field as function of time at different heliospheric distances: (

**a**) 50 ${R}_{s}$ (

**b**) 100 ${R}_{s}$ and (

**c**) 1 AU for CME1 (red), CME2 (blue), CME3 (green) and CME123 (black).

**Figure 10.**The contour plots of the relative density distribution on the solar-terrestrial meridional plane after (

**a**) 45 h (

**b**) 50 h (

**c**) 55 h and (

**d**) 60 h.

**Figure 11.**The height/time map of the relative density distribution obtained at the Earth-direction during 0–80 h expressed in solar radii from 1 to 215 ${R}_{s}$ for CME123.

**Table 1.**Perturbation parameters (velocity unit: km s${}^{-1}$, density unit: ${10}^{7}$ cm${}^{-3}$, temperature unit: ${10}^{6}$ K) used in simulating the three successive CMEs and their corresponding energies (E represents energy with unit: ${10}^{31}$ ergs).

${\mathit{V}}_{\mathbf{max}}$ | ${\mathit{\rho}}_{\mathbf{max}}$ | ${\mathit{T}}_{\mathbf{max}}$ | ${\mathit{B}}_{0}$ | Magnetic E | Kinetic E | Thermal E | Total E | |
---|---|---|---|---|---|---|---|---|

CME1 | 270 | 0.73 | 2.47 | 3.0 | 2.46 | 0.026 | 0.297 | 2.78 |

CME2 | 380 | 0.73 | 2.44 | 3.0 | 2.42 | 0.050 | 0.297 | 2.77 |

CME3 | 1000 | 1.41 | 2.38 | 6.0 | 9.74 | 0.507 | 1.483 | 11.73 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhou, Y.; Feng, X.
Three-Dimensional Simulation Study of the Interactions of Three Successive CMEs during 4–5 November 1998. *Universe* **2021**, *7*, 431.
https://doi.org/10.3390/universe7110431

**AMA Style**

Zhou Y, Feng X.
Three-Dimensional Simulation Study of the Interactions of Three Successive CMEs during 4–5 November 1998. *Universe*. 2021; 7(11):431.
https://doi.org/10.3390/universe7110431

**Chicago/Turabian Style**

Zhou, Yufen, and Xueshang Feng.
2021. "Three-Dimensional Simulation Study of the Interactions of Three Successive CMEs during 4–5 November 1998" *Universe* 7, no. 11: 431.
https://doi.org/10.3390/universe7110431