Simulation of Flux Emergence from the Convection Zone

Simulation of Flux Emergence from the Convection Zone

Fang Fang1, Ward Manchester IV1, William Abbett2 and Bart van der Holst1

1 Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, MI 48105

2 Space Sciences Laboratory, University of California, Berkeley, CA 94720

2Flux Emergence WorkshopAug 23rd, 2011

Outline• Introduction• Simulation Steps• Results

– Coupling of the Magnetic Flux and Convective Flows• Vertical Flows• Horizontal Flows

– Magnetic Flux Cancellation– Magnetic and Energy Fluxes

• Conclusions


Emergence of Solar Magnetic Flux

Parnell et al. 2009

The power-law distribution implies that either all surface magnetic features are generated by the same mechanism, or that they are dominated by surface processes leading to a scale-free distribution.


MHD Equations• Solve modified MHD equations with BATSRUS

• Qe: Energy source term, including radiative cooling and coronal heating (Abbett 2007)

• Tabular Equation of State (Rogers 2000)• Closed Lower Boundary


Simulation Domain

Vertical stratification of density and temperatureDomain of 30×30×42 Mm3 With 56 million cells

Flux Rope


Convection Zone

Convective granules with dimension of 1 Mm, upflowing speed of 1 km/s

Intergranular plasma with downflowing speed of 2 km/s

The movie above shows the 1-hour evolution of the structure of Uz at the photosphere.


Initial Magnetic Flux Rope

Initial flux rope at Z = -10 Mm surrounded by downflowing (blue) and upflowing (red) plasma.



– Coupling of the Magnetic Flux and Convective Flows

• Vertical Flows• In the convection zone• In the near-surface layers


Emergence of the Magnetic Flux

The movie shows the structure of Bx on the X = 0 plane, the cross-section cut of the flux rope.

The flux rope approaches the photosphere at 2.5 hours after the initialization.QuickTime™ and a

BMP decompressorare needed to see this picture.


The Emerged Flux Rope


Formation of the Sunspots - 1

The large-scale downflows in the convection zone forms and maintains the bipoles.

The movie shows the evolution of Uz on the Y=0 plane with lines indicating the magnetic field lines.

QuickTime™ and aBMP decompressor

are needed to see this picture.


Formation of the Sunspots - 2

3D magnetic field lines colored by the local Uz.


Convective Collapse - 1

Convective Collapse

Uz at t = 4:50:00 Bz at t = 4:50:00 Bz at t = 5:22:00


Convective Collapse - 2

Downward flows produces a bulb of plasma with lower temperature, leading to a pressure imbalance with the surrounding plasma. The flux tube collapses as a result of the pressure imbalance and equilibrates with higher magnetic field up to 2 kG.

The movie shows the evolution of Bz on the Y=0 plane with lines indicating the magnetic field lines.





– Coupling of the Magnetic Flux and Convective Flows• Vertical Flows

• Horizontal Flows• Separating motion of the bipoles

• Rotation of the magnetic pores

• Shearing motion along the PILs


Coalescence at the photosphere

The movie shows the structure of Bz field with arrows representing the horizontal velocity field.

The coalescence of the small-scale fluxes into the major pores facilitates the accumulation of the magnetic flux on the surface and therefore the formation of the large pores.




Rotation of the Sunspots at the Photosphere

The movie above shows the structure of Bz at the phtosphere, with arrows representing the horizontal velocity field.

The positive pore shows highly sheared flows and magnetic field lines.

The negative pore presents a coherent rotation.




Horizontal flow in Convection Zone

The movie above shows Bz structure at z = -3 Mm with arrows representing the horizontal velocity field.

Large scale horizontal converging flow constrains the total area of the emerged flux and prevents the pores from separation.

The negative polarity also shows a coherent pattern of rotation at Z= -3 Mm.




Depth of the Rotation of Sunspot

The movie shows Uy on X-Z plane with black lines showing the magnetic field lines.

The coherent rotation starts to extend downward at t = 4 hrs and approaches the depth of 10 Mm in 0.5 hours. The negative polarity shows a very coherent pattern of rotation, while on the positive pore on the left, the rotation is not obvious.




Lorentz Force

Uy at t = 4:21:00 Uy at t = 5:13:00 By at t = 5:13:00


Horizontal Motion in the Corona

The movies show the structure of Bz field with arrows representing the horizontal velocity field (left) and magnetic field (right) in corona.






Magnetic Flux

Total Initial Axial Flux : 1.52 1021 MxZ = -3 Mm: max = 1.32 1021 Mx (87%)Z = 0 Mm: max = 6.85 1020 Mx (45%)Z = 3 Mm: max = 4.13 1020 Mx (27%)

Temporal evolution of the total magnetic fluxes


Magnetic and Energy Fluxes

Energy flux associated with horizontal motions dominates in the energy transfer from convection zone into the corona. At photosphere, the total energy transport is 71031 ergs in 8 hrs.

The magnetic flux emerges at the surface as bipoles with upflowing motion, then they are quickly pulled apart by the horizontal flows, and concentrate in the downdrafts.


Large-Scale Flux CancellationAt time t=5 hours, two opposite polarities are pushed together by the horizontal flow. The convergence of these two polarities can produce highly-sheared magnetic field structure, strong gradient of magnetic field strength, and maybe shearing flow.

The movie shows the evolution of photospheric Bz field with arrows representing the horizontal velocity field.




Transverse Field during Flux Cancellation

Wang et al. 2011

The transverse magnetic field intensifies along the PIL after the flux cancellation.




Conclusions• The simulation illustrates the features during the flux

emergence: o Dipoles are formed and maintained by the downflow

drafts in the deep convection zone.o Sunspot rotation driven by Lorentz force is observed

both at the photosphere and in the convection zone.• The energy flux into the coronal is mainly dominated by

fluxes associated with the horizontal (shearing and rotating) motion.


References• Abbett, W. P. 2007, ApJ, 665, 1469• Parnell, C. E., DeForest, C. E., Hagenaar, H. J.,

Johnston, B. A., Lamb, D. A., & Welsch, B. T. 2009, ApJ, 698, 75

• Rogers, F. J. 2000, Physics of Plasmas, 7, 51• Wang, S., Liu, C., Liu, R., Deng, N., Liu, Y., &

Wang, H. 2011, ArXiv e-prints

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Simulation of Flux Emergence from the Convection Zone