1. Chip Manchester, Fang Fang, Bill Abbett, Bart van der Holst Patterns of Large- Scale Flux Emegence Patterns of Large- Scale Flux Emegence

2. Outline Much more advanced simulations of flux emergence in a realistic convection zone and corona (Abbett 2007) Much more advanced simulations of flux emergence in a realistic convection zone and corona (Abbett 2007) Confirm earlier simulations and show that shear flows driven by the Lorentz force are extremely robust. Confirm earlier simulations and show that shear flows driven by the Lorentz force are extremely robust. Shear flows dominate the transport of magnetic energy from the convection zone into the corona Shear flows dominate the transport of magnetic energy from the convection zone into the corona Lorentz-force driven shear flow are a mechanism by which energy builds up for CMEs, flares, filament eruptions Lorentz-force driven shear flow are a mechanism by which energy builds up for CMEs, flares, filament eruptions

3. Emergence of a 3D Flux Rope in a Simple Polytropic Atmosphere Fan 2001, Manchester et al. 2004

4. The Lorentz Force Drives the Shearing!! Shearing motions transport Bx flux into the expanding portion of the flux rope and tends to return Bx to constant values along field lines to restore force balance

5. Current Sheet Formation Shear Afven waves cause axial flux to accumulate where the rope expands Shear Afven waves cause axial flux to accumulate where the rope expands The sheared core lifts off and erupts forming a current sheet The sheared core lifts off and erupts forming a current sheet In Parker’s picture, localized expansion along the length of the rope, causes torsional Alfven waves that transport azimuthal flux In Parker’s picture, localized expansion along the length of the rope, causes torsional Alfven waves that transport azimuthal flux Cosmical Magnetic Fields 1979

6. Flux Rope Eruption Rope eruption occurs with the passage of a shear Alfven wave Rope eruption occurs with the passage of a shear Alfven wave Fang et al. ApJ 2010 714, 1649

7. Separation of Flux Rope at Sigmoid Current Sheet To the left, an iso-surface of current density and field lines are shown over the photosphere colored to show Bz. Right: Eruption of flux rope into the corona.

8. Larger Scale Simulations Large simulation recovers similar results Large simulation recovers similar results

9. Realistic Simulation of Flux Emergence Model from upper convection zone to corona Abbett 2007 Model from upper convection zone to corona Abbett 2007 Parameterized radiative losses Parameterized radiative losses OPAL EOS OPAL EOS Magnetic Flux proportional coronal heating Magnetic Flux proportional coronal heating Fang et al. ApJ 2010 714, 1649

10. Realistic Convection Zone Model vertical velocity shown in gray scale vertical velocity shown in gray scale

11. Emphemeral Region Scale 10 18-19 Mx

12. Magnetic Field Evolution at the Photosphere Development of sheared field at the photosphere Development of sheared field at the photosphere

13. Comparison of EIS Shear Velocity The image on the left is an EIS Doppergram of AR10930 observed December 2006 over the western limb of the Sun. The image on the right shows shear flows ½ driven by the Lorentz ½ siphon flow parallel to B

14. Magnetic Pore Scale Magnetic Pore Scale 6x10 20 Mx 30Mm scale

15. Flow Patterns are Much More Complicated White line = PIL Color = Ux

16. Photospheric Energy Flux Total energy from horizontal flows is 1x10 30 ergs 1% necessary for CMEs and X-class flares Total energy from horizontal flows is 1x10 30 ergs 1% necessary for CMEs and X-class flares Manchester et al. 2004 Fang et al. 2010

17. Magnetic Shear in AR6982 Falconer 2001 JGR 106, 25185

18. MHD Code: BATSRUS (SC/EE/IH/GM) Block Adaptive Tree Solar-wind Roe-type Upwind Scheme Block Adaptive Tree Solar-wind Roe-type Upwind Scheme Conservative finite-volume method Conservative finite-volume method Shock-capturing Total Variation Diminishing schemes Shock-capturing Total Variation Diminishing schemes Explicit, implicit & explicit/implicit time stepping Explicit, implicit & explicit/implicit time stepping Semi-relativistic MHD equations Semi-relativistic MHD equations Splitting the magnetic field into B 0 + B 1 Splitting the magnetic field into B 0 + B 1 Various methods to control the divergence of B Various methods to control the divergence of B AMR & data structure AMR & data structure Adaptive self-similar blocks Adaptive self-similar blocks Octree data structure Octree data structure Parallel implementation Parallel implementation Fortran-90 with MPI Fortran-90 with MPI Near-perfect scaling to >1500 PEs (explicit time-stepping) Near-perfect scaling to >1500 PEs (explicit time-stepping) Good scaling to ~256 PEs with implicit time-stepping Good scaling to ~256 PEs with implicit time-stepping Highly portable (SGI Origin, Altix, Compaq, PC clusters, X-serve clusters, etc) Highly portable (SGI Origin, Altix, Compaq, PC clusters, X-serve clusters, etc)

19. SWMF Performance  Key algorithms to achieve this speed:  Concurrent/mixed execution of components.  Adaptive grid in BATSRUS (SC, IH and GM).  Implicit time stepping in SC/Heat Conduction.

20. Global Magnetosphere Ionosphere Electrodynamics Inner Magnetosphere Radiation belts Solar Energetic Particles Upper Atmosphere Solar Corona Eruptive Event Generator Inner Heliosphere The SWMF is freely available at http://csem.engin.umich.edu Polar Wind Plasmasphere Photosphere to Corona SWMF

21. Conclusions Flux emergence from a realistic convection zone into the corona. Flux emergence from a realistic convection zone into the corona. Shearing mechanism is extremely robust and persists even in a granular convection zone Shearing mechanism is extremely robust and persists even in a granular convection zone Shear flows are slower and more structured than in the idealized polytropic model. Shear flows are slower and more structured than in the idealized polytropic model. Shear velocities are in better agreement with observations of the photosphere and low corona. Shear velocities are in better agreement with observations of the photosphere and low corona. The large scale pattern of magnetic shear in active regions is found, which increases with proximity to the neutral line The large scale pattern of magnetic shear in active regions is found, which increases with proximity to the neutral line Transport of magnetic energy from the convection zone to the corona is dominated by horizontal flows Transport of magnetic energy from the convection zone to the corona is dominated by horizontal flows No Eruptions yet. Scaled to the size of an AR, shear flows would easily provide 10 32 ergs. No Eruptions yet. Scaled to the size of an AR, shear flows would easily provide 10 32 ergs. Beginning simulations of 60x90 Mm & 10 22 Mx Beginning simulations of 60x90 Mm & 10 22 Mx

22. Thank You

23. Recent CME Models That Impose Shear Magnetic Arcade Models Imposed shearing of foot points with magnetic reconnect at the base of the arcade (Amari et al. 2003 ApJ 595, 1231 ) Imposed shearing of foot points with magnetic reconnect at the base of the arcade (Amari et al. 2003 ApJ 595, 1231 ) Break-out model: Imposed shearing motions and reconnection above the arcade in a quadruple system (Antiochos 1999 ApJ 510, 485) Break-out model: Imposed shearing motions and reconnection above the arcade in a quadruple system (Antiochos 1999 ApJ 510, 485)

24. Velocity and Magnetic Shear in AR 10486 Source of the Halloween Events Velocity Shear Yang et al. 2004, ApJ 617 L151, Magnetic Shear Liu et al. 2005, ApJ 622, 722 Velocity Shear Yang et al. 2004, ApJ 617 L151, Magnetic Shear Liu et al. 2005, ApJ 622, 722