Observations Morphology Quantitative properties Underlying Physics Aly-Sturrock limit

1. Observations Morphology Quantitative properties Underlying Physics Aly-Sturrock limit Present Theories/Models Coronal Mass Ejections (CME) S. K. Antiochos, NASA/GSFC

2. Recap of CME Physics • For some reason magnetic shear concentrates at PILs producing filament channels • Exact topology unclear (especially twist) • Filament field held down by overlying non-sheared coronal field • Need some mechanism to disrupt force balance catastrophically • Simply continuing the shearing does not do it! As shown by many simulations • Agrees with Aly-Sturrock limit

3. Demonstration of Non-Eruption - + (from,DeVore et al, 2005; Aulanier et al, 2005) • Bipolar (one polarity inversion line) initial magnetic field • Filament-field formation by shearing and reconnection • See pronounced expansion & kinking – but no eruption

4. Non-Eruption Underlying physics: • Corona has no lid • Magnetic field lines can stretch indefinitely without breaking • Free to open slowly in response to photospheric stress and gas pressure (rather than erupt as CME) • Slow opening (not associated with filament channels) observed to occur continuously in large-scale corona

5. Aly – Sturrock Limit Force-free field in an infinite volume (Aly 1984) • From div·T = 0, derive that: ∫ (Br2 - Bt2) dA= 0, at limiting bdy • Implies that transverse component cannot increase indefinitely • Virial eqtn: ∫ B2 dV= ∫ r ( -2 Br2 + B2) dA • Energy in interior related to field at bdy • Implies upper bound on energy • Aly-Sturrock conjectured lub is fully open field • Agrees with many simulations

6. Test of Aly – Sturrock Limit • Roumeliotis et al, 2.5D sheared dipolar force-free field in spherical geometry • Beyond certain shear, field expands outward exponentially • Energy saturates at open limit • Only certain BC are physical

7. Present Theories for Eruption • Non-ideal evolution – reconnection • Partial opening – ideal instabilities • Non-quasi-static evolution – flux emergence? • All appear to “work” in numerical simulations

8. NUMERICAL SIMULATIONS • Solve 3D or 2.5D ideal/dissipative MHD with variety of numerical schemes • Both explicit and implicit • Both fixed and fully amr grids • Both Cartesian and spherical grids • Initial conditions: • Usually equilibrium with varying degree of complexity • Simple dipole to observed photospheric fields with solar wind • Boundary Conditions: • Open conditions at outer boundaries • Photospheric conditions main discriminator between models • Simple shear to incomprehensible contortions

9. NUMERICAL SIMULATIONS • Term “simulation” is misnomer • Simply method for obtaining approximate solutions to standard equations • Drastic change in theory techniques, but still comes down to physical insight • Hopefully numerical simulation will turn into user-friendly community tools

10. ARMS NUMERICAL SIMULATIONS • Ideal MHD eqtns. (but numerical resistivity) • Use non-conservative energy equation for low-beta systems • Spherical grid with adaptive mesh refinement

11. Reconnection-Driven CME Models • Breakout: • Field erupts to a state that it cannot get to by any ideal evolution • Magnetic reconnection removes overlying field, decreasing downward pull • Need topologically complex field • More than 1 dipole • Generally present on Sun

12. Non-Dipole Coronal Topology • Field of two dipoles – axi-symmetric • Large global at Sun center, weaker near surface • Must have 4-flux system with separatrix bdys, and null

13. Magnetic Reconnection • Frozen-in condition: • B-field lines ~ constants of the motion • Produces topological complexity and all solar activity • Even in corona have finite diffusion, t ~ L2 /η >> 106 years, for L ~ 1 Mm • If L sufficiently small, field lines lose identity and can “reconnect” on short time scales, but only over localized region • Need to develop significant magnetic structure on small scale for reconnection to be effective • Magnetic topology plays critical role

14. Breakout Model • 2D multi-polar initially potential field • Create filament channel by simple footpoint motions • Outward expansion drives breakout reconnection in corona

15. Breakout Model • Breakout reconnection allows for explosive eruption • Flare current sheet, flare reconnection, and twisted flux rope all consequences of ejection • CME with no flare possible for slow eruptions

16. Breakout Model • 3D simulation using 3D AMR code Lynch et al • “Create” prominence by simple boundary flows • Reproduces standard features of CMEs/flares

17. Breakout Model • 3D simulation by Roussev et al (2008) of 04/21/02 event • Complex topology with flux transfer prior to eruption • Generalized breakout process

18. Cancellation Model • Loss of equilibrium/ flux cancellation: • Reconnection/emergence at photosphere converts downward to upward tension • Produces twisted flux rope in corona, prior to eruption • Rope loses equilibrium, jumps upward • Subsequent flare reconnection accelerates ejection • Van Ballejooigen, Forbes, Mikic/Linker, Amari, …

19. Flux Cancellation Model • Analytic model by Forbes et al • Detailed simulation of 05/12/97 event (Titov et al)

20. Aneurism Model • Ideal instability (kink-like) • Part rather than remove overlying field • Need twisted flux rope • Sturrock, Fan, Kliem, …

21. Aneurism Model • 3D simulation by Fan et al. • System driven only by flux “emergence” • Kink or torus instability depending on overlying field • So far only idealized configurations

22. Models for CME Initiation • Apparently have three mechanisms that can produce explosive CMEs in 3D simulations: • Reconnection (Breakout), loss-of-equilibrium (flux cancellation), ideal instability • All require sheared prominence field • All produce twisted flux rope as a result of eruption • Flux cancellation and ideal instability require twisted flux rope before eruption

23. 64K Question • What is the pre-eruption structure of the prominence field? • Clearly has strong shear • Does it have twist (twisted flux rope topology) • NRL VAULT image of 06/16/02, 20K material, spatial resolution < 200 km • Little evidence for twist in either structure or motions, but exact topology still unclear • See Rob’s movies!