Large-scale Magnetohydrodynamic Numerical Simulations on the Solar Flux Emergence and the Formation of Active Region

2D and 3D MHD Simulations on the Solar Flux Emergence from -20,000 km: Large-scale Dynamics and Small-scale Observational FeaturesShin Toriumi & Takaaki Yokoyama

Department of Earth and Planetary Science, University of TokyoFEW 2011: 22 Aug 2011qRT2Dconvective collapse1Preceding StudiesEmergence in the convection zoneMHD (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. Introduction2Preceding Studies

Aim of this StudyLarge-scale emergence from -20,000 km of CZ to the coronaSmall-scale / fine structures at the surface1. Introduction

Emergence in the Convection ZoneMoreno-Insertis (1996)

Emergence from the Photosphere to the CoronaMagara (2001)cf. Abbett & Fisher (2003)31. Introduction2D Parametric Surveys (Toriumi & Yokoyama 2010, 2011a)Conditions of the magnetic flux tube at -20,000 km3D Experiment (Toriumi & Yokoyama 2011b, in prep)Applying conditions obtained in 2D surveys

Observational StudyComparison with the AR observation4

2. 2D Parametric Surveys

x/H0z/H0z/H0y/H0Axial and Cross-sectional Calculations (Toriumi & Yokoyama 2010, 2011a)Two-step Emergence

52. 2D Parametric SurveysDensity, Field lines, Velocity Vectors (Toriumi & Yokoyama 2010)

H062. 2D Parametric Surveys

Density, Field lines, Velocity Vectors (Toriumi & Yokoyama 2011a)H07

2. 2D Parametric Surveys

x/H0z/H0z/H0y/H0Axial and Cross-sectional Calculations (Toriumi & Yokoyama 2010, 2011a)Two-step Emergence

Results : (at -20,000 km)Field Strength : 104 GTotal Flux : 1021-1022 MxTwist Intensity : > 2.510-4 km-182. 2D Parametric SurveysEmergence from -20,000 kmDecelerate around the surface to make a flat structure.B = 104 G, = 1021-1022 Mx, Twist > 2.510-4 km-1

Mechanism of DecelerationPlasma on the rising sheet cannot pass through the surface.Combination of different regions is essential.

3D ExperimentVariations are assumed to be uniform in 2D experiments. 3D experiment is necessary.It requires large grid numbers: N = 106 109.H09

3. 3D ExperimentInitial ConditionTaken from 2D parametric studiesBtube= 2.0104 G, = 6.31020 Mx, q = 5.010-4 km-1N = 5122561024H0 = 200 km-400 x/H0 +400z/H0+250-200y/H0-200+200LX = 160,000 km LZ = 90,000 kmLY = 80,000 kmFlux Tubeat -20,000 km103. 3D ExperimentResultsField 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.H0 = 200 km0 = 25 sB0 = 300 GSurface113. 3D ExperimentResultsPhotospheric line-of-sight field (Bz) and selected field lines.

H0 = 200 km0 = 25 sB0 = 300 G

Multiple separations of both polarities and a shearing motion.

The size of AR is decided by the flat tube beneath.124. DiscussionComparison with ObservationSeparations 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.4. DiscussionPicture 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.

4. DiscussionWavelength 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 tubes radius) exp(-r2/Rtube2)

Therefore;

= L = Rtube (: a few)

= 3000 km Rtube = 1000 km

?

SurfaceSurfaceL5. Observational StudyHinode Observation of AR 10926 (Dec. 2006)Evaluate the wavelength (= distance between the Vertical Sheets)Fourier transformation of the small-scale elements

?165. Observational StudyHinode Observation of AR 10926 (Dec. 2006)Evaluate the wavelength (= distance between the Vertical Sheets)Fourier transformation of the small-scale elements

?175. Observational StudyResults

A = 5000 kmB = 3000 kmA is the distance between the elements parallel to the vertical sheets.

B is the distance across the sheets:

B= 3000 kmAB185. Observational StudyComparison with Numerical ResultsDistance between the vertical sheets: = 3000 km.

According to the numerical results: = Rtube (: a few)

Flux tube forming AR 10296 had a radius of the order of 1000 km in the deeper CZ.

Rtube 1000 km196. Summary2D Parametric SurveysConditions of the flux tube at -20,000 km3D ExperimentTwo-step emergenceSeparations and a shearing motion of magnetic elementsComparison with AR observationPicture of the flux emergence, formation of active region, and small-scale elementsHinode AnalysisWavelength perpendicular to the field linesInitial tubes radius20Fin.Thank you for your attention!