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Nonlinear Force Free Field Extrapolations for AR 10486 Pre and Post Flare

Nonlinear Force Free Field Extrapolations for AR 10486 Pre and Post Flare. J.McTiernan 19-Jul-2006. Some Jargon:. Force-free field: JxB = 0, current J is parallel to B Alpha: constant of proportionality, J = α B Linear Force-free field: α is a spatial constant

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Nonlinear Force Free Field Extrapolations for AR 10486 Pre and Post Flare

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  1. Nonlinear Force Free Field Extrapolations for AR 10486Pre and Post Flare J.McTiernan 19-Jul-2006

  2. Some Jargon: • Force-free field: JxB = 0, current J is parallel to B • Alpha: constant of proportionality, J = αB • Linear Force-free field: αis a spatial constant • Non-linear Force-free field: αis not constant • Potential field: α= 0, J = 0, also called “current-free”

  3. Optimization method: Wheatland, Roumeliotis & Sturrock, Apj, 540, 1150 Objective: minimize the “Objective Function” We can write: If we vary B, such that dB/dt = F, and dB/dt = 0 on the boundary, then L will decrease.

  4. Optimization method: Wheatland, Roumeliotis & Sturrock, Apj, 540, 1150 Objective: minimize the “Objective Function” We can write: If we vary B, such that dB/dt = F, and dB/dt = 0 on the boundary, then L will decrease.

  5. Optimization method (cont): • Start with a box. The bottom boundary is the magnetogram, the upper and side boundaries are the initial field. Typically start with potential field or linear FFF, extrapolated from magnetogram. • Calculate F, set new B = B + F*dt (typical dt =1.0e-5). B is fixed on all boundaries. • “Objective function”, L, is guaranteed to decrease, but the change in L (ΔL) becomes smaller as iterations continue. • Iterate until ΔL approaches 0. • The final extrapolation is dependent on all boundary conditions and therefore on the initial conditions. • Requires a vector magnetogram, with 180 degree ambiguity resolved. • See Schrijver, et al. 2006, Solar Physics 235, 161 for comparison of methods, and limitations of NLFFF’s.

  6. The starting point is a potential field, extrapolated from Bz on the surface: Note that the potential field lines do not show shear in the field. Colors? The brighter lines have stronger Bz at the surface.

  7. Here is the NLFFF: These are the same field line starting points shown earlier. There are some differences.

  8. Bx By Bz Start with a VECTOR magnetogram With 180° amiguity resolved: MFSC data : D.Falconer 29-Oct-2003 18:31:00 UT And 29-Oct-2003 21:27:00 UT Pre-flare Post-flare Note “patchiness” in Bx, By; this is not so good.

  9. Pre flare field lines: Post flare field lines This is a blow-up of the flare region. The ‘start points’ of the field lines (on the left side) are the same in both images. (co-alignment is good to 5 arcsec). The post-flare lines look more like potential field lines.

  10. What about the pre and post flare magnetic energy? • Pre-flare energy = 2.466e33 ergs • Post-flare energy = 2.430e33 ergs • ΔE = -3.66e31 ergs. Is this significant? • Uncertainties from Monte Carlo calculation: • Assumed uncertainties: 25 G in Bz, 50 G in Bx, By • σΔE = 2.28e32 ergs • The energy change is negligible compared to the uncertainty.

  11. What about the flare footpoints? Pre flare VM is 2 hrs before the X flare. Post flare VM is < 1hr after peak. So the loops seen here may or may not correspond to our B field. TRACE image with RHESSI contours

  12. The footpoints move outwards in both directions: Can we find field lines that look as if they connect the footpoints? IVM Bz, with RHESSI 50 – 100 keV footpoints, at different times: A: 20:43:40 to 20:44:40UT B: 20:51:12 to 20:52:12UT C: 20:58:40 to 20:59:40UT

  13. Pre flare field lines: Post flare field lines Post-flare lines are much better than pre-flare lines when connecting footpoints.

  14. For the pre-flare field, lines from right-hand footpoints A and B end 20 arcsec below corresponding left-hand footpoints.

  15. For the post-flare field, lines from right-hand footpoints A and B end within 5-10 arcsec of the corresponding left-hand footpoints.

  16. The ‘post-flare loops’ are high 50 to 100 Mm. The pre-flare sheared field lines were lower, Less than 30 Mm. Post-flare Pre-flare

  17. Conclusions? Post-flare field looks more ‘potential’, but the difference in energy between the two magnetograms is not significant. “Post-flare loops” in the post-flare magnetogram are aligned in the same direction as the HXR footpoints, this was hard to see in the pre-flare magnetogram. Future work? Better alignment. Also try different ambiguity resolution. The NLFFF code is part of SSW, try: IDL>ssw_upgrade, /nlfff, /spawn See http://sprg.ssl.berkeley.edu/~jimm/fff/optimization_fff.html for documentation.

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