Modeling Magnetic Reconnection in a Complex Solar Corona Dana Longcope Montana State University & Institute for Theoretical Physics

The Changing Magnetic Field TRACE 171: 1,000,000 K 8/10/01 12:51 UT 8/11/01 17:39 UT 8/11/01 9:25 UT (movie)(movie) THE CORONA PHOTOSPHERE

Is this Reconnection? TRACE 171: 1,000,000 K 8/10/01 12:51 UT 8/11/01 17:39 UT 8/11/01 9:25 UT (movie)(movie) THE CORONA PHOTOSPHERE

Outline 1.Developing a model magnetic field 2.A simple example of 3d reconnection 3.The general (complex) case --- approached via variational calculus. 4.A complex example

The Sun and its field Focus on the p-phere And the corona just above

Modeling the coronal field

Example: X-ray bright points EIT 195A image of “quiet” solar corona (1,500,000 K)

Example: X-ray bright points Small specks occur above pair of magnetic poles (Golub et al. 1977)

Example: X-ray bright points

When 2 Poles Collide All field lines from positive source P1 All field lines to negative source N1

Regions overlap when poles approach When 2 Poles Collide

Stress applied at boundary Concentrated at X-point to form current sheet Reconnection releases energy How it’s done in 2 dimensions

A Case Study TRACE & SOI/MDI observations 6/17/98 (Kankelborg & Longcope 1999)

The Magnetic Model  Poles  Converging: v = 218 m/sec  Potential field: - bipole - changing  1.6 MegaVolts (on separator)

Reconnection Energetics  Flux transferred intermittently:  Current builds between transfers  Minimum energy transfer:

Post-reconnection Flux Tube Flux Accumulated over Releases stored Energy Into flux tube just inside bipole (under separator) Projected to bipole location

Post-reconnection Flux Tube Flux Accumulated over Releases stored Energy Into flux tube just inside bipole (under separator)

A view of the model

More complexity From p-spheric field (obs). Find coronal coronal field Defines connectivity

Minimum Energy: Equilibrium Magnetic energy Variation: Fixed at photosphere:  Potential field

Minimization with constraints Ideal variations only  force-free field Constrain helicity ( w/ undet’d multiplier   constant-  fff

A new type of constraint… Photospheric field: f(x,y) -- the sources …flux in each domain

Domain fluxes Domain D ij connects sources P i & N j Flux in source i: Flux in Domain D ij Q: how are fluxes related: A: through the graph’s incidence matrix

The incidence matrix N s Rows: sources N d Columns: domains  Nc = Nd – Ns + 1 circuits

The incidence matrix

Reconnection possible allocation of flux…

Reconnection … another possibility

Reconnection Related to circuit in the domain graph Must apply 1 constraint to every circuit in graph

Separators: where domains meet 4 distinct flux domains

Separators: where domains meet 4 distinct flux domains Separator at interface

Separators: where domains meet 4 distinct flux domains Separator at interface Closed loop encloses all flux linking P2  N1

Minimum W subj. to constraint Constraint on P2  N1 flux Current-free within each domain  current sheet at separator

Minimum W subj. to constraint 2d version: boundary of 4 domains becomes current sheet

A complex example Ns = 20

A complex example Ns = 20  Nc = 33

The original case study Approximate p-spheric field using discrete sources

The domain of new flux Emerging bipole P01-N03 New flux connects P01-N07

Summary 3d reconnection occurs at separators Currents accumulate at separators  store magnetic energy Reconnection there releases energy Complex field has numerous separators