Magnetic Field Topology in Prominences

Lionello et al., ApJ 581, p.718

Purpose

Proof of concept: generate a realistic prominence from real data.

(Though not necessarily with real flows and field evolution!)

Hypotheses & Hidden Assumptions

• Prominence material suspended in dips.

  -- cf., Karpen et al., 2001, ApJ v. 553, p. 85: "Are Magnetic Dips Necessary for Prominence Formation?"

• Flux rope topology is correct one -- cf., sheared arcade.

Method

1. Start with a magnetogram -- Fig. 1
   
   

2. Extrapolate a potential field from B_z
   
   

3. Introduce shear: spin your poles for a while!
   
   
   
   where velocity stream function depends on B_z
   
   

4. Solve the usual MHD equations, relaxing to equilibrium.

5. Not content to leave well enough alone, cancel some normal flux:
   
   "[W]e apply electric field at z=0... as described in Linker et al. (2001)." What's this?!
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   This is similar to Longcope's MEF approach, but doesn't use "ME" to constrain velocity.
   
   
   
   
   • Start from induction eqn:
     
     
     
     
   • Decompose E_t =-(v x B)_t/c on RHS using Linker/Longcope formalism:
     
     
     
     
   • Lionello's velocity implies v_z = 0. Moreover, B_t is ignored.
     
     
   • Further, Linker et al. (2001) set $\Phi = 0$.
     
     
     
     Hence, one equation & one unknown: no need for add'l constraint.
   
   
   
   
   
   
   
   
   
   
   
   
   

6. Relax this flux-cancelled mess, and voila: A FLUX ROPE! -- with dips!

7. Solve a passel of conservation equations for field lines' thermodynamic structure.

8. Generate some plots and pretty pictures, and call it a paper.

Results

Field line solutions with:

• no dip/concentration

• one dip/concentration

• an off center dip/concentration

• two dips/concentrations

Conclusions

• Through elaborate field evolution, the authors can generate something that looks like a flux-rope prominence.

• Catalog of Shortcomings:

  1. contrived method of introducing shear; but cf. MURI

  2. unrealistic method of evolving B: B_t, v_z ignored

  3. didn't solve MHD/TH simultaneously -- no big deal?

  4. no eruption in sight -- but given purpose, is this a fault?

Figures

1. a) H? image from NSO Sacramento Peak showing a filament on 1996 September 23 at 14:35 UT. (b) NSO Kitt Peak Magnetogram for 1996 September 23 (start time 17:32 UT, stop time 18:26 UT). (c) Initial flux distribution for the calculation. It was extracted and smoothed from an NSO Kitt Peak Synoptic Magnetogram for CR 1913 (the active region was observed around 17:20 UT on 1996 August 29). (d) Final flux distribution derived from the NSO Kitt Peak Synoptic Magnetogram for CR 1914 (observed around 23:57 UT on 1996 September 25).
   
   
   
   
   
   
   
   
   
   

2. Results from the MHD calculation of the prominence magnetic field. (a) A twisted magnetic field with the initial flux distribution. (b) The magnetic flux evolves to the new state during the MHD calculation, forming a magnetic flux rope. Arcade-like field lines surround the flux rope.
   
   
   
   
   
   
   
   
   
   

3. Height profile as a function of the distance along the field line for magnetic field lines with dips. Some field lines have more than one dip.
   
   
   
   
   
   
   
   
   
   

4. (a) Height profile as a function of the distance along the field line for an arcade field line that cannot develop a stable condensation. (b) Temperature profile. (c) Density profile. Notice that no dip is present to sustain an eventual condensation.
   
   
   
   
   
   
   
   
   
   

5. (a) Height profile as a function of the distance along the field line for a flux rope field line that develops a condensation. (b) Temperature profile. (c) Density profile. The condensation appears in the dip of the field line. For a more asymmetric case, see Fig. 6.
   
   
   
   
   
   
   
   
   
   

6. (a) Height profile as a function of the distance along the field line for a flux rope field line that develops a condensation. (b) Temperature profile. (c) Density profile. The condensation appears in the dip of the field line. For a more symmetric case, see Fig. 5.
   
   
   
   
   
   
   
   
   
   

7. (a) Height profile as a function of the distance along the field line for a flux rope field line that develops two condensations. (b) Temperature profile. (c) Density profile. The condensations appear in the dips of the field line.
   
   
   
   
   
   
   
   
   
   

8. (a) Location of the concave upward portions of the magnetic field lines (magnetic dips). These are the places where filament material is more likely to reside. Actual filament location in the Sacramento Peak H? images for comparison: (b) August 29, 15:55 UT; (c) August 20, 15:13 UT; (d) September 23, 15:04 UT; (e) September 24, 14:58 UT; (f) September 25, 15:09 UT; (g) September 26, 15:45 UT.
   
   
   
   
   
   
   
   
   
   

9. Evolution of the concave upward portion of the magnetic field (dips) during the MHD calculation viewed from the side. The planes are colored according to the intensity of the magnetic flux. The percentage of emerged flux is shown in the top left corner of each image. The dips rise as the surface magnetic field evolves from the configuration, as in Fig. 1c to that in Fig. 1d.

• The Paper