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2D and 3D MHD Simulations on the Solar Flux Emergence from -20,000 km: Large-scale Dynamics and Small-scale Observationa

2D and 3D MHD Simulations on the Solar Flux Emergence from -20,000 km: Large-scale Dynamics and Small-scale Observational Features. Shin Toriumi & Takaaki Yokoyama Department of Earth and Planetary Science, University of Tokyo FEW 2011: 22 Aug 2011. 1. Introduction. Preceding Studies

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2D and 3D MHD Simulations on the Solar Flux Emergence from -20,000 km: Large-scale Dynamics and Small-scale Observationa

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  1. 2D and 3D MHD Simulations on the Solar Flux Emergence from -20,000 km: Large-scale Dynamics and Small-scale Observational Features • Shin Toriumi & Takaaki Yokoyama • Department of Earth and Planetary Science, University of Tokyo FEW 2011: 22 Aug 2011

  2. 1. Introduction • Preceding Studies • Emergence in the convection zone • MHD (Schuessler 1979, Longcope1996, 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.)

  3. 1. Introduction • 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 Emergence from the Photosphere to the Corona Emergence in the Convection Zone cf. Abbett & Fisher (2003) Magara (2001) Moreno-Insertis (1996)

  4. 1. Introduction • 2D ParametricSurveys (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 • Axial and Cross-sectional Calculations (Toriumi & Yokoyama 2010, 2011a) • “Two-step Emergence” z/H0 z/H0 x/H0 y/H0

  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 • Axial and Cross-sectional Calculations (Toriumi & Yokoyama 2010, 2011a) • “Two-step Emergence” • Results : (at -20,000 km) • Field Strength : 104G • Total Flux: 1021-1022Mx • Twist Intensity : > 2.5×10-4 km-1 z/H0 z/H0 x/H0 y/H0

  9. 2. 2D Parametric Surveys • Emergence from -20,000 km • Decelerate around the surface to make a flat structure. • B = 104 G, Φ = 1021-1022Mx, 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 = 106 → 109.

  10. 3. 3D Experiment Flux Tube at -20,000 km • Initial Condition • Taken from 2D parametric studies • Btube= 2.0×104 G, Φ = 6.3×1020Mx, q = 5.0×10-4 km-1 • N = 512×256×1024 • H0 = 200 km LX = 160,000 km LZ = 90,000km +250 LY = 80,000km z/H0 +200 y/H0 -200 -200 -400 x/H0+400

  11. 3. 3D Experiment • Results • Field strength in (x/H0 < 0 and y/H0 > 0) is plotted. Makes a flat structure beneath the surface. Secondary emergence due to the magnetic buoyancy instability. Surface H0 = 200 km τ0 = 25 s B0 = 300 G

  12. 3. 3D Experiment • Results • Photospheric line-of-sight field (Bz) and selected field lines. Multiple separations of both polarities and a shearing motion. The size of AR is decided by the flat tube beneath. H0 = 200 km τ0 = 25 s B0 = 300 G

  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 • The rising tube decelerates to make a flat structure. • Secondary emergence to the corona. Multiple separations occur due to the magnetic buoyancy instability.Compare with the “vertical sheet” model. • As inner fields emerge, foot points shift to show a shearing motion, because the pitch angle of inner fields are smaller.

  15. 4. Discussion λ⊥? • Wavelength of the Separations • The surface of the rising tube is fluted due to the interchange instability. L≒ (density transition scale) cf. Chandrasekhar 1961 ≒ Rtube (initial tube’s radius) ∵δρ ∝ exp(-r2/Rtube2) • Therefore; λ⊥ = L = αRtube (α: a few) λ⊥ = 3000 km Rtube = 1000 km Surface λ⊥ Surface 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 λ⊥?

  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 λ⊥?

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

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

  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! Fin.

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