1. Magnetohydrodynamic simulations of the ejection of a
magnetic flux rope
Akinsanmi A. Babatunde
Department of Astronomy
University of Porto
Paper by Pagano et al (2013)
AST 4005, January 2016
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 1 / 27

2. Outline
1 INTRODUCTION
2 MOTIVATION
3 BACKGROUND
4 MODEL
5 DISCUSSION AND SUMMARY
6 CONCLUSION
7 REFERENCES
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 2 / 27

3. INTRODUCTION
Introduction
Coronal mass ejections (CMEs) are one of the most violent
phenomena found on the Sun. One model to explain their occurrence
is the flux rope ejection model.
CMEs are huge clouds of plasma and magnetic fileds occasionally
thrown off from the sun which pose threats to earth and space based
technology.
Within each CME is a kernel of tightly wound group of magnetic field
lines called flux ropes that can contain and transport solar materials.
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 3 / 27

4. INTRODUCTION
Flux Rope Formation
Credit: NASA / GSFC
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 4 / 27

5. MOTIVATION
Motivation
Flux rope ejections are believed to be one of the main progenitors of
CMEs.
Investigate whether magnetic flux ropes during its evolution, can
erupt to produce a CME.
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 5 / 27

6. BACKGROUND
Categories
The flux rope ejection model may itself be split into two categories:
Flux ropes formed quasi-statically from perturbations of already
existing coronal arcades.
Flux ropes formed dynamically during the emergence of magnetic flux.
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 6 / 27

7. BACKGROUND
Quasi-statically formed Flux ropes
Undergoes three separate stages of evolution: the formation, equilibrium
and eruption phases.
FORMATION: flux rope forms over time periods of days to weeks as
a coronal arcade is perturbed by photospheric motions and flux
cancellation at a Polarity Inversion Line (PIL).
EQUILIBRIUM: period during which the flux rope lies in near
equilibrium with its surroundings.
ERUPTION: where the flux rope loses equilibrium and is ejected out
of the solar corona over a few hours due to magnetic forces.
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 7 / 27

8. MODEL
Model
The wide variety of time scales involved, in the formation of the flux
rope and then its eruption, poses a considerable challenge to
theoretical models.
The Model is to simulate the whole life span of a flux rope from slow
formation to rapid ejection and investigate if it leads to fast ejection
of plasma.
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 8 / 27

9. MODEL
Models Employed
Global Non-Linear Force-Free Field (GNLFFF) model ( Mackay & van
Ballegooijen, 2006a)
Full MHD approach using ARMVAC code (KU Leuven)
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 9 / 27

10. MODEL
GNLFFF
GNLFFF model produces flux ropes by means of the relative motion
and interaction of two magnetic bipoles (one more tilted than the
other with respect to the equator).
As a result of flux cancellation, a flux rope forms above the PIL of the
more tilted bipole after 19 days of evolution as shown in fig 1
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 10 / 27

11. MODEL
flux rope formed from GNLFFF
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 11 / 27

12. MODEL
ARMVAC CODE
We adopt the stressed non-potential magnetic field that exists on this
day as the initial magnetic field condition for numerical MHD
simulations using ARMVAC that follows the dynamics of the eruption.
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 12 / 27

13. MODEL
Coupling the Models
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 13 / 27

14. MODEL
Equations
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 14 / 27

15. MODEL
Initial configuration for MHD Simulation
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 15 / 27

16. MODEL
Simulating erupting flux rope
Alfven time τAlf = 120s
At t = 0τAlf , the positive Lorentz force present underneath the flux rope
pushes the flux rope and the plasma contained within it upwards and it
immediately starts to rise.
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 16 / 27

17. MODEL
Simulating erupting flux rope
As the flux rope moves up, a horizontal Lorentz force acts below the flux
rope to push oppositely oriented magnetic field lines on either side of the
PIL towards the PIL
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 17 / 27

18. MODEL
Simulating erupting flux rope
Shows plasma being ejected outwards with velocity greater than 8x106 due
to radial Lorentz force and reconnection of MF lines below the flux rope
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 18 / 27

19. MODEL
Between t = 0 & t = 17.40τAlf
Arcades above bipole remain largely unchanged
Dense plasma is ejected outwards by motion of flux rope and tied to
magnetic configuration
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 19 / 27

20. MODEL
After t = 17.40τAlf to end of simulation t = 70τAlf
The ejected flux rope starts to interact/reconnect with the overlying
magnetic field
Magnetic field configuration becomes significantly more complex and
coherence of plasma decreases
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 20 / 27

21. MODEL
flux rope ejection
At t = 70τAlf , the ejection reaches the upper boundary and the dynamics
of the simulation are no longer followed.
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 21 / 27

22. MODEL
ejection of plasma
As flux rope moves up, plasma is displaced.
The front starts from a height of 1.3R and is accelerated by the ejecting
magnetic flux rope. The average speed of the front is about 100 kms1
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 22 / 27

23. DISCUSSION AND SUMMARY
Discussion and Summary
We have modeled the slow formation of flux rope through quasi-static
approximation and its rapid ejection through a full MHD simulation
no additional shearing or stress of the magnetic field is carried out in
the MHD simulation, where the resulting dynamics are solely a result
of the stress built up between the two bipoles during the slow
evolution
Flux rope rises and coronal plasma follow magnetic field evolution and
is expelled out at 2.5R
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 23 / 27

24. DISCUSSION AND SUMMARY
Additional Considerations
Effect of gravity
Implementing only the MHD model for the entire flux rope evolution
Feasibility of a post-eruption MHD state
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 24 / 27

25. CONCLUSION
conclusion
The simulation of evolution of the flux rope shows that plasma
expelled during the flux rope ejection travels outward at a speed of
100 kms-1, which is consistent with the observed speed of CMEs in
the low corona.
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 25 / 27

26. REFERENCES
Reference
Mackay, D. H., & van Ballegooijen, A. A. 2006a, ApJ, 641, 577
Keppens, R., Meliani, Z., van Marle, A. J., et al. 2012, J. Comput.
Phys., 231, 718
Liu, R., Liu, C., Wang, S., Deng, N., Wang, H. 2010, ApJ, 725, L84
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 26 / 27

27. REFERENCES
...............THANK YOU...............
Akinsanmi A. Babatunde (University of Porto)Magnetohydrodynamic simulations of the ejection of a magnetic flux ropeAST 4005, January 2016 27 / 27