Summary of ucb muri workshop on vector magnetograms
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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)

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Summary of ucb muri workshop on vector magnetograms
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



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
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



Velocities why it is essential to know them
Velocities: Why it is essential to know them: potential field models

  • 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


We are exploring several methods for finding the velocity of magnetized plasma
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
LCT tests show it works some times and not others… magnetized plasma:

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


Recovered velocity fields
Recovered velocity fields… magnetized plasma:

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

Vx

Vy


Here it doesn t work so well
Here it doesn’t work so well: magnetized plasma:

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
Comparison of LCT and actual horizontal velocity fields: magnetized plasma:

Note LCT velocity is very wrong in the outer regions…

LCT

actual


This illustrates some serious shortcomings to lct
This illustrates some serious shortcomings to LCT: magnetized plasma:

  • 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
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/


Result of applying dana s method to ar8210
Result of applying Dana’s method to AR8210: equation applied at boundary plane:


And so what happens in mhd simulations of ar8210
And so what happens in MHD simulations of AR8210? equation applied at boundary plane:

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


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