Nonlinear Force Free Field Models for AR 10486

J.McTiernan, H.Hudson (SSL/UCB) T.Metcalf (LMSAL)

Abstract:In this work we present a nonlinear force free field (NLFFF) extrapolation from the chromospheric vector magnetogram of AR10486 taken before the X11 flare of 29 October 2003. The extrapolation is used to interpret the different source patterns and motions seen in RHESSI images of the flare. In particular we examine the footpoint motion observed in the flare by RHESSI.. This work is funded by NASA contract NAS 5-98033

Optimization method (cont):

• Iterative process, starts with potential field, extrapolated from magnetogram.

• Be sure that B does not change on the boundary

• Calculate F, set new B = B + F*dt (typical dt =1.0e-4)

• “Objective function”, L, is guaranteed to decrease, but the change in L (dL) becomes smaller as you go.

• Keep going until dL approaches 0.

Optimization method (cont):

• At the start, the field is only non-potential at the bottom boundary. Non-potentiality propagates outward as the iterations increase.

• Iterations end long before non-potentiality reaches upper boundary – the non-potentiality in the “final” field is concentrated near the lower boundary in the 30000 km above the chromosphere.

• It is important to note that the final extrapolation is dependent on the boundary conditions and the initial conditions. We choose to use the potential field because we believe that the field is roughly potential far from active regions. Other initial and boundary conditions are currently being tested.

Figure 1:

This is the IVM chromospheric magnetogram obtained on 29-Oct-2003 at 1846 UT. Blue contours are for negative Bz (Bz is radial field here, not line of sight). Red contours are for positive Bz. The small arrows denote the direction of the transverse field.

Figure 2:

These are selected magnetic field lines plotted from the NLFFF extrapolation. The image is of Bz, and has been rotated by the solar P angle, to make comparison to images easier. (For the rotation and alignment of the vector magnetogram we used an MDI magnetogram taken at 1828 UT on 29-Oct-2003. The uncertainty in co-alignment is approximately 5 arcsec – the pixel size of the binned magnetogram used for the extrapolation is 4.4 arcsec.) Two sets of long, sheared field lines are visible on the plot. These are very low-lying lines, less than 10000 km above the chromosphere.

Figure 3:

These are field lines for the potential field extrapolation.

Figure 4:

The image is a TRACE 195 A image taken during the solar flare. The black contours are the 6 – 12 keV RHESSI image. This is probably thermal emission associated with the bright looptops in the arcade. The red contours are of the 50 – 100 keV, associated with nonthermal emission at footpoints. Note that the TRACE loops shown look similar to some of the sheared field lines in Figure 2. They are not in the same position, though.

Figure 5:

This is the separatrix image obtained using the NLFFF extrapolation for AR 10486, with the dark filaments denoting the magnetic separatrices. (See e.g., Metcalf, et al. 2003 ApJ, 595, 483). The contours are RHESSI images in the 50 to 100 keV energy band, for three different times. The contours marked ‘A’ are from 20:44 UT, the contours marked ‘B’ are from 20:51 UT and the contours marked ‘C’ are from 20:59 UT. The footpoints are close to separatrices, and move outward along the separatrices with time, as seen by Metcalf et al. 2003. The upper footpoint jumps between separatrices between times ‘A’ and ‘C’.

Conclusions:

• The NLFFF Optimization model seems to give reasonable results with non-potentiality in the solution concentrated near the lower boundary. The effects of shear are evident and long filament-like field lines are seen.

• Flare HXR footpoints are mostly associated with magnetic separatrices, and move along the separatrices with time.

• The NLFFF field has 1.66 times the energy of the potential field