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

MDI magnetogram of AR8210

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…

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

Test calculations of flux emergence and comparisons with potential field models

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

)()(

Bv zzt

vBBz

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.

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?

Recovered velocity fields…

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

Vx Vy

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:

Comparison of LCT and actual horizontal velocity fields:

Note LCT velocity is very wrong in the outer regions…

actual LCT

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

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/

)()(

Bv zz

z vBt

B

Result of applying Dana’s method to AR8210:

And so what happens in MHD simulations of AR8210?

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