Peng Ruan, Thomas Wiegelmann, Bernd Inhester Sami Solanki, Li Feng Max Planck Institute for Solar System Research Germany Modeling the 3D Coronal Plasma and Magnetic Field from STEREO/SECCHI and Magnetic Surface Data

Outline Methods of Magnetic Field Extrapolation Potential Field Model + Scaling Laws MHS Model

MDI Observation May 11, Jun. 7,

 j ×B=0 j =0, ∇ ×B =0 (Potential field model) j ∥ B, μ 0 j = ∇ ×B =α(r)B (Force-free model)  j ×B− ∇ p−ρ ∇ φ=0 (MHS)

SECCHI, STEREO-A, 4 wavelengths (2006-Dec-04)

Potential Field α=0.0 LFF α=0.1 (1/Solar radius) LFF α=0.5

Scaling Laws E H (s).... heating term E R (s).... radiative loss term E C (s)....conductive term Analytical approximation E H (s)=E 0 exp[-(s-s 0 )/s H ] Temperature.....T=T(s, S H ) Pressure p=p (s, S H ) Density n~p/T Taken from Aschwanden and Schrijver, 2002 E H (s)-E R (s)- E C (s)=0

For reconstruction:

Temperature distribution in the solar corona cut through longitude Ø=40 o

T. Neukirch(1995)’s MHS model j = α B +∇ F(B, φ ) ×∇ φ Force-free part: α B Non force-free part: ∇ F(B, φ ) ×∇ φ ∇ ×B = μ 0 j j ×B − ∇ p−ρ ∇ φ =0

MHS force=0 MHS force>0

The perturbation pressure and density might be larger than the background. This is unreasonable. j ×B− ∇ p−ρ ∇ φ=0 j ×B− ∇ p P −ρ P ∇ φ=0 − ∇ p 0 −ρ 0 ∇ φ=0 Background Perturbation

Relaxation L= ∫ [ B -2 ┃ ( ∇ ×B ) ×B ┃ 2 + ( ∇ ·B ) 2 ]d 3 x T. Wiegelmann, et al (2007)

Summary and Outlook

Thank you

Decomposition of B in spherical harmonics with coefficients a nm, b nm We match the line-of-sight component B●e LoS to observed data D Linear Force-Free Magnetic Field: