1. Summary of UCB MURI workshop on vector magnetograms Have picked 2 observed events for targeted study and modeling: AR8210 (May 1, 1998), and AR8038 (May 12, 1997) “Plan of Action” formulated (see http://solarmuri.ssl.berkeley.edu/~fisher/public/pre sentations/vmgram-workshop-2002/. for details http://solarmuri.ssl.berkeley.edu/~fisher/public/pre sentations/vmgram-workshop-2002/ Have started modeling AR8210 – It is difficult! Challenges: Generating initial conditions self- consistently, deriving physically consistent velocity fields at photosphere, real versus numerical time scales

2. MDI magnetogram of AR8210

3. This active region was extremely well observed, was responsible for a number of flares and CMEs, and has a fascinating evolution across the solar disk…

4. First step: Drive MHD model with “fake” data of flux emergence from another MHD simulation Tests ability to drive an MHD calculation from boundary Boundary values of variables guaranteed to be physically consistent

5. Test calculations of flux emergence and comparisons with potential field models

6. Velocities: Why it is essential to know them: Physically consistent evolution at bottom plane in a simulation: Terms on LHS describe evolution driven by horizontal motion; RHS describes evolution due to flux emergence or submergence This requires knowledge of vector components of B and v. How do we determine v self-consistently from a sequence of vector magnetograms? Price for ignoring the problem: Incorrect coronal magnetic topology

7. We are exploring several methods for finding the velocity of magnetized plasma: Stokes Profiles could be used to get v z Local Correlation Tracking (LCT) can find a velocity field v  (But is it correct?) Vertical component of induction equation provides a constraint equation on v from a sequence of vector magnetograms (but solution is under-constrained) Kusano et al. used combination of LCT and vertical induction equation to solve for v z Longcope has developed a solution by adding an additional constraint: minimize the horizonal kinetic energy. Method appears to work in some cases, but not yet thoroughly tested.

8. LCT tests show it works some times and not others… Apply a velocity field to an image consisting of random hash – can LCT correctly recover the velocity?

9. Recovered velocity fields… Here, it did correctly find the applied horizontal velocity field… VxVx VyVy

10. Here it doesn’t work so well: 2 images of B z taken at a horizontal plane of one of Bill Abbett’s flux emergence simulations:

11. Comparison of LCT and actual horizontal velocity fields: Note LCT velocity is very wrong in the outer regions… actual LCT

12. This illustrates some serious shortcomings to LCT: In order for local correlation tracking to work, there must be some “structure” in the image There is (at least one) arbitrary constant (e.g. the “tile size”) which must be specified a-priori LCT cannot give any information about vertical velocities LCT will incorrectly determine the horizontal velocity when magnetic flux is emerging or submerging

13. Try an alternative approach based on ideal MHD induction equation applied at boundary plane: Magnetic quantities known from sequence of vector magnetograms This equation provides an (underdetermined) constraint on the velocity field. With additional assumptions, a physically consistent velocity field can be found. Details of Longcope’s proposed solution available at http://solarmuri.ssl.berkeley.edu/~dana/public/presenta tions/ http://solarmuri.ssl.berkeley.edu/~dana/public/presenta tions/

15. Result of applying Dana’s method to AR8210:

16. And so what happens in MHD simulations of AR8210? Stay tuned! Simulations are running even as we speak….