3D simulations of solar emerging flux. ISOBE Hiroaki Plasma seminar 2004/04/28. What is emerging flux?. Magnetic field: origin of solar activities such as sunspots, active regions, coronal heating, flares, coronal mass ejections, jets etc..
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Plasma seminar 2004/04/28
Shibata et al. 1989
Parker instability =>Expansion due to magnetic pressure => formation of Ω-shaped loop in the corona.
Measurement of MHD helicity injection by the emerging flux using the method presented by Kusano et al. (2002)
*unit of legnth = 2×scale height at z=0
The inner field line cannot expand laterally because it is surrounded tightly by adjacent twisted field lines, while the outer field line can expand freely.
To model the height evolution of the apex of the filed line, the momentum equation for the plasma element at the middle of the emerging filed line is solved.
Magnetic field strehgth B is approximated to have z dependance like eq.(19)
↑equation to be solved, where vAi=Bi/(4πρi), κ:curvature of the fied line, H: scale height of B.
H, zi, and Bi are obtaine by fitting of the simulation reslut:
H=21, zi=10, Bi=0.13
Solution of the
Result of simulation.
typeA: constant κ
typeB: κincrease with time
typeC: κdecrease with time
A B C
Type A continues to expand. Type B approaches to quasi-static state. Density is larger and tension is less important in type C: good model for prominence?
If initial twist is left-handed, inner field line (dark gray) exhibits backward-S shape, while outer fied line (light gray) exhibits S shape.
Field lines with stronger current at their footpoints are drawn in lighter color.
Inner field lines are bright and backward-S is seen.
Rapid rise starts after kink instability
Photosphere-corona: Fully compressive MHD (ZEUS 3D).
64x64x64 grids (1grid=1Mm).
Convection zone: Anelastic MHD (ANMHD; Lantz & Fan 1999).
256x128x128 grids (1grid=1Mm).
Adiabatically stratified, depth=5.1 pressure scale heights.
MHD Potential field
magenta: θ= π/2
θ: angle from potensial field.
Outer field lines differs more from force-free (hence more dynamic).
After the vertical flow at the lower boundary diminished (no driving at the boudary), the field lines relax to more force-free.
Some field lines exhibit sigmoidal structure. But the chirality depends on field lines.
Confinement by strong coronal field (Miyagoshi-san’s calculation).
λ= 5 10 100
If λis small, convective interchange mode and lataral expansion prevent the emergence into the corona