Summary of UCB MURI workshop on vector magnetograms

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/presentations/vmgram-workshop-2002/ . for details • 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 vz • 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 vz • 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… Vx Vy

10. Here it doesn’t work so well: 2 images of Bz 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… LCT actual

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/presentations/

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….