1. Shin Toriumi & Takaaki Yokoyama Department of Earth and Planetary Science, University of Tokyo FEW 2011: 22 Aug 2011

2.  Preceding Studies Emergence in the convection zone ○ MHD (Schuessler 1979, Longcope 1996, etc.) ○ Thin flux tube approximation (Spruit 1981, Fan 1993, etc.) ○ Anelastic approximation (Gough 1969, Abbett 2000, Jouve 2009, etc) Emergence from the photosphere to the corona ○ MHD (Shibata 1989, Fan 2001, Isobe 2007, Pariat 2009, etc.) ○ Radiative MHD (Cheung 2008, Rempel 2009, Martinez-Sykora 2008, etc.) 1. Introduction

3.  Preceding Studies  Aim of this Study Large-scale emergence from -20,000 km of CZ to the corona Small-scale / fine structures at the surface 1. Introduction Emergence in the Convection Zone Moreno-Insertis (1996) Emergence from the Photosphere to the Corona Magara (2001) cf. Abbett & Fisher (2003)

4. 1. Introduction  2D Parametric Surveys (Toriumi & Yokoyama 2010, 2011a) Conditions of the magnetic flux tube at -20,000 km  3D Experiment (Toriumi & Yokoyama 2011b, in prep) Applying conditions obtained in 2D surveys  Observational Study Comparison with the AR observation

5. 2. 2D Parametric Surveys x/H0x/H0 z/H0z/H0 z/H0z/H0 y/H0y/H0  Axial and Cross-sectional Calculations (Toriumi & Yokoyama 2010, 2011a) “Two-step Emergence”

6. 2. 2D Parametric Surveys Density, Field lines, Velocity Vectors (Toriumi & Yokoyama 2010)

7. 2. 2D Parametric Surveys Density, Field lines, Velocity Vectors (Toriumi & Yokoyama 2011a)

8. 2. 2D Parametric Surveys x/H0x/H0 z/H0z/H0 z/H0z/H0 y/H0y/H0  Axial and Cross-sectional Calculations (Toriumi & Yokoyama 2010, 2011a) “Two-step Emergence”  Results : (at -20,000 km) Field Strength : 10 4 G Total Flux : 10 21 -10 22 Mx Twist Intensity : > 2.5×10 -4 km -1

9. 2. 2D Parametric Surveys  Emergence from -20,000 km Decelerate around the surface to make a flat structure. B = 10 4 G, Φ = 10 21 -10 22 Mx, Twist > 2.5×10 -4 km -1  Mechanism of Deceleration Plasma on the rising sheet cannot pass through the surface. Combination of different regions is essential.  3D Experiment Variations are assumed to be uniform in 2D experiments. → 3D experiment is necessary. It requires large grid numbers: N = 10 6 → 10 9.

10. 3. 3D Experiment  Initial Condition Taken from 2D parametric studies B tube = 2.0×10 4 G, Φ = 6.3×10 20 Mx, q = 5.0×10 -4 km -1 N = 512×256×1024 H 0 = 200 km -400 x/H 0 +400 z/H0z/H0 +250 -200 y/H0y/H0 +200 L X = 160,000 km L Z = 90,000 km L Y = 80,000 km Flux Tube at -20,000 km

11. 3. 3D Experiment  Results Field strength in (x/H 0 0) is plotted. Makes a flat structure beneath the surface. Secondary emergence due to the magnetic buoyancy instability. H 0 = 200 km τ 0 = 25 s B 0 = 300 G Surface

12. 3. 3D Experiment  Results Photospheric line-of-sight field (B z ) and selected field lines. H 0 = 200 km τ 0 = 25 s B 0 = 300 G Multiple separations of both polarities and a shearing motion. The size of AR is decided by the flat tube beneath.

13. 4. Discussion  Comparison with Observation Separations and a shearing motion of magnetic elements. Agree with observation of AR 5617 by Strous & Zwaan (1999). They suggested the “Vertical Sheet” model. “Vertical Sheet” model: Each emergence occurs in a vertical sheet, while sheets are aligned in a parallel fashion.

14. 4. Discussion  Picture of Flux Emergence and the Formation of Active Region (1) The rising tube decelerates to make a flat structure. (1) Secondary emergence to the corona. Multiple separations occur due to the magnetic buoyancy instability. Compare with the “vertical sheet” model. (1) As inner fields emerge, foot points shift to show a shearing motion, because the pitch angle of inner fields are smaller.

15. 4. Discussion  Wavelength of the Separations The surface of the rising tube is fluted due to the interchange instability. L ≒ (density transition scale) cf. Chandrasekhar 1961 ≒ R tube (initial tube’s radius) ∵ δρ ∝ exp(-r 2 /R tube 2 ) Therefore; λ ⊥ = L = αR tube (α: a few) λ ⊥ = 3000 km R tube = 1000 km Surface λ⊥λ⊥ L

16. 5. Observational Study  Hinode Observation of AR 10926 (Dec. 2006) Evaluate the wavelength λ ⊥ (= distance between the Vertical Sheets) Fourier transformation of the small-scale elements

17. 5. Observational Study  Hinode Observation of AR 10926 (Dec. 2006) Evaluate the wavelength λ ⊥ (= distance between the Vertical Sheets) Fourier transformation of the small-scale elements

18. 5. Observational Study  Results λ A = 5000 km λ B = 3000 km λ A is the distance between the elements parallel to the vertical sheets. λ B is the distance across the sheets: λ ⊥ ≒ λ B = 3000 km A B

19. 5. Observational Study  Comparison with Numerical Results Distance between the vertical sheets: λ ⊥ = 3000 km. According to the numerical results: λ ⊥ = αR tube (α: a few) Flux tube forming AR 10296 had a radius of the order of 1000 km in the deeper CZ. R tube ≒ 1000 km λ⊥λ⊥

20. 6. Summary  2D Parametric Surveys Conditions of the flux tube at -20,000 km  3D Experiment Two-step emergence Separations and a shearing motion of magnetic elements Comparison with AR observation Picture of the flux emergence, formation of active region, and small-scale elements  Hinode Analysis Wavelength perpendicular to the field lines Initial tube’s radius

21. Thank you for your attention!