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3D simulations of solar emerging flux

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3D simulations of solar emerging flux

ISOBE Hiroaki

Plasma seminar 2004/04/28

- Magnetic field: origin of solar activities such as sunspots, active regions, coronal heating, flares, coronal mass ejections, jets etc..
- Magnetic field is generated by the dynamo action in the solar interior and rise to the surface by magnetic buoyancy.

- Dynamics of the emergence of the magnetic flux into the atmosphere is impotant to understand: formation of sunspots of active region, energy accumlation and triggering of flares, jets and other ecplosive phenomena.

Shibata et al. 1989

Hα(Hida/DST)

EUV (TRACE)

Parker instability =>Expansion due to magnetic pressure => formation of Ω-shaped loop in the corona.

- Evidence for emergence of twisted flux tube such as Sigmoid.

- 3D, fully compressible, ideal MHD
- Noliner development of interchange and undular (Parker) mode
- Extraction of the gas from the loop top by the undular mode is necessary for the emergence into the corona.

- Fully compressible, ideal MHD
- Emergence of twisted flux tube
- Outer loop is close to potential, while inner loop exhibits sigmiod-like structure.

Measurement of MHD helicity injection by the emerging flux using the method presented by Kusano et al. (2002)

- 3D simulation of twisted flux tube
- Modeling of the height evolution of field line with various shape.

*unit of legnth = 2×scale height at z=0

- Ideal MHD. Hydrostatic initial atmoshere, twisted flux in the convection zone.
- Grid: 100x100x100 (only 1/4 of the domain is solved)

- Outer filed line expand like a wide fan.
- Inner field line extends mainly in the vertical direction and keeps parallel to the original axis.

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

pressure

tension

gravity

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

model equation.

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.

- 3D isothermal (lowβ) MHD simulation of emerging flux tube into the corona with pre-existing magnetic arcade.
- Emerging flux strongly twisted and kink-unstable.
- The emergence is driven by the electric field at the lower boundary.

- Potential arcade in the initial corona.
- Resistivity is numerical.
- Emergence of twisted flux is driven by the electric fiedl at the lower boundary.
- grid: 240x160x200

Rapid rise starts after kink instability

sets in.

- Strong current sheet is formed and exhibits inverse-S

- 3D MHD simulation of emerging magnetic flux tube from convection zone into the corona.
- The convection zone and upper atmosphere is solved separately with different scheme, and the result of the convection zone calculation is used as the lower boundary of the upper calculation domain.
- (The numerical technique is interesting, the presented results are not so much.)

Photosphere-corona: Fully compressive MHD (ZEUS 3D).

64x64x64 grids (1grid=1Mm).

Interface

Convection zone: Anelastic MHD (ANMHD; Lantz & Fan 1999).

256x128x128 grids (1grid=1Mm).

Adiabatically stratified, depth=5.1 pressure scale heights.

MHD Potential field

No twist

- Potential approximation is not good when the flux tube twisted (not surprising).
- But the field are not force-free even in the case of q=0.

q=0.25

q=0.5

blue: θ=0

(force free)

black: θ=π/4

magenta: θ= π/2

θ: angle from potensial field.

Outer field lines differs more from force-free (hence more dynamic).

t=8.75)

After the vertical flow at the lower boundary diminished (no driving at the boudary), the field lines relax to more force-free.

t=9.25

Some field lines exhibit sigmoidal structure. But the chirality depends on field lines.

- Emergence of twisted flux tube from vigorously convecting convection zone
- Emerging flux loses its coherence by the turbulent convective flow.

- 3D version of Yokoyama & Shibata 1995
- Fast reconnection by anomalous resistivity=> jet formation.

Confinement by strong coronal field (Miyagoshi-san’s calculation).

λ= 5 10 100

λ

If λis small, convective interchange mode and lataral expansion prevent the emergence into the corona

2 dimensional