1. 3D simulations of solar emerging flux ISOBE Hiroaki Plasma seminar 2004/04/28

2. What is emerging flux? 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

3. Hα(Hida/DST) EUV (TRACE)

4. 2D simulation Parker instability =>Expansion due to magnetic pressure => formation of Ω-shaped loop in the corona.

5. 3 dimensionality Evidence for emergence of twisted flux tube such as Sigmoid.

6. Matsumoto et al. 1993 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.

7. Matsumoto et al. 1998

8. Fan 2001 (ApJL)

9. Magara & Longcope 2001 Fully compressible, ideal MHD Emergence of twisted flux tube Outer loop is close to potential, while inner loop exhibits sigmiod-like structure.

10. Magara & Longcope 2003 Measurement of MHD helicity injection by the emerging flux using the method presented by Kusano et al. (2002)

11. A Model for Dynamic Evolution of Emerging Magnetic Field in the Sun Magara, T 2004, ApJ, 605, 480 3D simulation of twisted flux tube Modeling of the height evolution of field line with various shape.

12. Model setup Ideal MHD. Hydrostatic initial atmoshere, twisted flux in the convection zone. Grid: 100x100x100 (only 1/4 of the domain is solved) *unit of legnth = 2×scale height at z=0

13. Snapshot of outer/inner field lines Outer filed line expand like a wide fan. Inner field line extends mainly in the vertical direction and keeps parallel to the original axis.

14. Mechanism of different behavior of outer/inner filed lines 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.

15. Modeling of emergence of field line 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

16. Derivation of equation 1. density profile

17. Derivation of equation 2. JxB force Magnetic field strehgth B is approximated to have z dependance like eq.(19)

18. Derivation of equation 3. ↑equation to be solved, where v A i=Bi/(4πρ i ), κ:curvature of the fied line, H: scale height of B. H, z i, and Bi are obtaine by fitting of the simulation reslut: H=21, z i=10, Bi=0.13

19. Result for outer field line Solution of the model equation. Result of simulation.

20. Result for different types of field line typeA: constant κ typeB: κincrease with time typeC: κdecrease with time

21. Results 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?

22. Chirality of field lines If initial twist is left-handed, inner field line (dark gray) exhibits backward-S shape, while outer fied line (light gray) exhibits S shape.

23. Whichfield lines are brighten? Field lines with stronger current at their footpoints are drawn in lighter color. Inner field lines are bright and backward-S is seen.

25. The Emergence of a Magnetic Flux Tube into a Preexisting Coronal Arcade Fan, Y. & Gibson, S.E., 2003, ApJ, 589, L105 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.

26. Model setup 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

27. Result(1) Rapid rise starts after kink instability sets in.

28. Result (2) Strong current sheet is formed and exhibits inverse-S

29. A Coupled Model for the Emergence of Active Region Magnetic Flux into the Solar Corona Abbett, W.P. & Fisher G.H., 2003, ApJ, 582, 475 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.)

30. Simulation domains 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.

31. Result (1) MHD Potential field No twist q=0.25 q=0.5 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.

32. Result (2) 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)

33. Result (3) 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

34. Result (4) Some field lines exhibit sigmoidal structure. But the chirality depends on field lines.

36. My simulations 1.With convection Emergence of twisted flux tube from vigorously convecting convection zone Emerging flux loses its coherence by the turbulent convective flow.

37. Reconnection with pre-existing field 3D version of Yokoyama & Shibata 1995 Fast reconnection by anomalous resistivity=> jet formation.

38. Formation of 3D structure by magnetic Rayleigh-Taylor instability

39. Effect of lateral expansion Confinement by strong coronal field (Miyagoshi-san’s calculation).

40. λ= 5 10 100 2 dimensional If λis small, convective interchange mode and lataral expansion prevent the emergence into the corona λ