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Summary of UCB MURI workshop on vector magnetograms

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- 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

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…

- Tests ability to drive an MHD calculation from boundary
- Boundary values of variables guaranteed to be physically consistent

- 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

- 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.

Apply a velocity field to an image consisting of random hash – can LCT correctly recover the velocity?

Here, it did correctly find the applied horizontal velocity field…

Vx

Vy

2 images of Bz taken at a horizontal plane of one of Bill Abbett’s flux emergence simulations:

Note LCT velocity is very wrong in the outer regions…

LCT

actual

- 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

- 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/

- Stay tuned! Simulations are running even as we speak….