March 2004 LWS Meeting 1

Structure and Evolution ofCoronal Magnetic Fields

A. A. van BallegooijenHarvard-Smithsonian Center for Astrophysics

Cambridge, MA

March 2004 LWS Meeting 2

Basic Questions

• How is magnetic energy injected into the corona?• How is it stored there?• How is it released (e.g., in flares and CMEs)?

Answering these questions requires knowledge of• the geometry of the coronal magnetic field• its evolution subject to photospheric forcing and energy dissipation

March 2004 LWS Meeting 3

Evidence for Stressed Coronal Fields (1) Photospheric vector magnetograms show sheared magnetic fields near the neutral line:

From: Lites (2004)Advanced StokesPolarimeter (ASP),April 8, 2000

March 2004 LWS Meeting 4

Evidence for Stress Coronal Fields (2)Yohkoh SXT images show S-shaped structures (sigmoids),indicating the coronal field is sheared and/or twisted:

Rust & Kumar 1996(ApJ 464, L199)

March 2004 LWS Meeting 5

Evolution of Coronal Magnetic Stress• Helicity injection by emergence of sheared or twisted fields through the photosphere (timescale ~ 1 day). e.g., Pevtsov, Maleev & Longcope 2003 (ApJ 593, 1217)

• Helicity injection by shearing flows acting on photospheric footpoints of coronal loops. e.g., DeVore 2000 (ApJ 539, 944); Chae 2001 (ApJ 560, L95)

• Concentration of axial fields by converging flows toward the neutral line.• In a sheared field, photospheric flux cancellation involves magnetic reconnection, creating a helical flux rope. e.g., Mackay & van Ballegooijen 2001 (ApJ 560, 445)

• Taylor-like relaxation to minimum energy state. e.g., Nandy, Hahn, Canfield & Longcope 2003 (ApJ 597, L73)

March 2004 LWS Meeting 6

Model of Flux Rope Formation

t=0

Assumptions:•Coronal field evolves in ideal MHD, relaxes to nonlinear force free field (magneto-frictional method).• Initial field is weakly sheared.• Photosphere flux is subject to diffusion and differential rotation (no helicity injection).• Flux cancellation at the neutral line involves magnetic reconnection, produces a flux rope after ~ 3 days.

t=3 daysFrom: Mackay & van Ballegooijen (2001)

March 2004 LWS Meeting 7

Model of Flux Rope FormationProblem: it work too well. After 10 days, the flux rope becomeshighly twisted, inconsistent with observed vector fields:

This suggests that poloidal flux is annihilated inside flux rope.

March 2004 LWS Meeting 8

Modeling Coronal Magnetic Fields

Models based on observations taken at one instant of time:1. Potential fields or linear force-free fields based on observed radial magnetic field at the photosphere.2. Nonlinear force-free fields based on observed a) photospheric vector field (e.g., Bleybel et al 2002) b) Hα filament (e.g., van Ballegooijen 2004) c) coronal loop structures (method TBD). This requires nonlinear relaxation methods.

March 2004 LWS Meeting 9

Example #1: Field ExtrapolationLinear and nonlinear force-free fields based on Imaging VectorMagnetograph data from Mees Solar Observatory:

From: Bleybel et al. 2002 (A&A 395, 685)

Yohkoh SXT image

BBrr

α=×∇

)(rr

αα =

constant=α

March 2004 LWS Meeting 10

Example #2: Flux Rope Model

Relax to force-free state usingmagneto-frictional method(van Ballegooijen 2004).

Based on data from ASP andMDI, April 8, 2000.

Flux rope inserted into apotential field describingoverlying coronal arcade(not shown).

Mxaxi19106.7 ×=Φ

19106.7 ×Axial flux of rope:

poloidal flux:

10105.1 ×

Mx

Mx/cm

March 2004 LWS Meeting 11

Example #2: Flux Rope ModelVector field from ASP Vector field from model

March 2004 LWS Meeting 12

Theory/Modeling Software for SDO

Need software tools for the following tasks:• derive maps of photospheric (vector) field from HMI data• combine datasets into global maps representing vector or radial field at one instant of time (estimate backside fields)• construct 3D models (e.g., using magneto-frictional method)• compare results with solar image data: - trace field lines passing through user-defined starting points - project field lines onto AIA images for comparison with observed coronal loop and filaments• adjust 3D model to improve fit.

March 2004 LWS Meeting 13

Theory/Modeling Software

The AIA Team proposes to develop• a standard file format for 3D coronal magnetic models• software for reading such files into IDL• software for comparing models with AIA image data

Goal is to provide an interface with MHD models of theextended corona and inner heliosphere.

March 2004 LWS Meeting 14

Conclusions

• The magneto-frictional method provides a useful tool for computing nonlinear force-free fields containing flux ropes.• Need to develop methods for fitting 3D magnetic models to observed coronal loop structures.