1. Ward Manchester University of Michigan
Coupling of the Coronal and Subphotospheric Magnetic Field in Active Regions by Shear Flows Driven by The Lorentz Force
Ward Manchester
University of Michigan

2. Outline
Universal feature of active regions that produce CMEs: magnetic shear
Source of magnetic shear: a subtle combination of the Lorentz force and gravitational pressure stratification of the solar atmosphere
Examples of shearing motions in flux ropes, and magnetic layers
Picture of magnetic activity that couples the subphotospheric magnetic field to the corona

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

4. 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 ApJ 595, 1231 )
Break-out model: Imposed shearing motions and reconnection above the arcade in a quadruple system (Antiochos 1999 ApJ 510, 485)

5. Emergence of a 3D flux rope
Manchester, Gombosi, De Zeeuw and Fan , ApJ 610, 588

6. Flux Rope Emerging From the Convection Zone into the Corona
Buoyant section of the flux rope reduced by a factor of two

7. Spontaneous Shearing Motions
Opposite sides of the flux rope move in opposite directions as the flux rope expands.
Motions are driven by the Lorentz force!

8. Development and Eruption of Magnetic Shear Core

9. 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

11. Dynamic Coupling By Shear Flows

12. Shearing During Flux Emergence From a Magnetic Layer

13. Comparison of Shear Velocity
The image on the left, the shear velocity at the mid-plane of the simulation is shown.
On the right, Doppler velocity maps of active regions at the limb made with SUMER
Chae et al. 2000, ApJ 533, 535,

14. Conclusions
Shearing motions are a consequence of the Lorentz force that arises as the magnetic field expands in a highly stratified atmosphere which naturally explains:
Magnitude of the shear velocity in the photosphere, chromosphere and corona that occur at a characteristic fraction of the local Alfven speed.
Shearing motions transport axial flux into expanding portion of flux rope or arcade and acts to return the axial component to constant values along field lines
These shear flows strongly couple the low b corona to the high b photosphere and convection zone

15. Fundamental Assumptions
The Sun possesses a gravitational field that results in large pressure stratification of the atmosphere
Non-force-free magnetic structures pass that through the photosphere into the corona to form active regions are MUCH larger than pressure scale height at the photosphere (140 km)
Magnetic fields possess a horizontal axial component in addition to an azimuthal component
The Lorentz force represented as (curl B) X B reverses direction across the expanding structure
Very general as it applies to flux ropes, arcades and magnetic layers

16. Thank You