Simulation of Flux Emergence from the Convection Zone Fang Fang 1, Ward Manchester IV 1, William Abbett 2 and Bart van der Holst 1 1 Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, MI Space Sciences Laboratory, University of California, Berkeley, CA 94720

2 Flux 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

3 Flux Emergence WorkshopAug 23rd, 2011 Emergence of Solar Magnetic Flux Parnell et al 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.

4 Flux Emergence WorkshopAug 23rd, 2011 MHD Equations Solve modified MHD equations with BATSRUS Q e : Energy source term, including radiative cooling and coronal heating (Abbett 2007) Tabular Equation of State (Rogers 2000) Closed Lower Boundary

5 Flux Emergence WorkshopAug 23rd, 2011 Simulation Domain Vertical stratification of density and temperature Domain of 30×30×42 Mm 3 With 56 million cells Flux Rope

6 Flux Emergence WorkshopAug 23rd, 2011 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.

7 Flux Emergence WorkshopAug 23rd, 2011 Initial Magnetic Flux Rope Initial flux rope at Z = -10 Mm surrounded by downflowing (blue) and upflowing (red) plasma.

8 Flux Emergence WorkshopAug 23rd, 2011 Outline Introduction Simulation Steps Results – Coupling of the Magnetic Flux and Convective Flows Vertical Flows In the convection zone In the near-surface layers

9 Flux Emergence WorkshopAug 23rd, 2011 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.

10 Flux Emergence WorkshopAug 23rd, 2011 The Emerged Flux Rope

11 Flux Emergence WorkshopAug 23rd, 2011 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.

12 Flux Emergence WorkshopAug 23rd, 2011 Formation of the Sunspots - 2 3D magnetic field lines colored by the local Uz.

13 Flux Emergence WorkshopAug 23rd, 2011 Convective Collapse - 1 Convective Collapse Uz at t = 4:50:00 Bz at t = 4:50:00Bz at t = 5:22:00

14 Flux Emergence WorkshopAug 23rd, 2011 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.

15 Flux Emergence WorkshopAug 23rd, 2011 Outline Introduction Simulation Steps Results – 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

16 Flux Emergence WorkshopAug 23rd, 2011 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.

17 Flux Emergence WorkshopAug 23rd, 2011 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.

18 Flux Emergence WorkshopAug 23rd, 2011 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.

19 Flux Emergence WorkshopAug 23rd, 2011 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.

20 Flux Emergence WorkshopAug 23rd, 2011 Lorentz Force Uy at t = 4:21:00 Uy at t = 5:13:00By at t = 5:13:00

21 Flux Emergence WorkshopAug 23rd, 2011 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.

22 Flux Emergence WorkshopAug 23rd, 2011 Magnetic Flux Total Initial Axial Flux : 1.52  Mx Z = -3 Mm:  max = 1.32  Mx (87%) Z = 0 Mm:  max = 6.85  Mx (45%) Z = 3 Mm:  max = 4.13  Mx (27%) Temporal evolution of the total magnetic fluxes

23 Flux Emergence WorkshopAug 23rd, 2011 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 7  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.

24 Flux Emergence WorkshopAug 23rd, 2011 Large-Scale Flux Cancellation At 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.

25 Flux Emergence WorkshopAug 23rd, 2011 Transverse Field during Flux Cancellation Wang et al The transverse magnetic field intensifies along the PIL after the flux cancellation.

26 Flux Emergence WorkshopAug 23rd, 2011 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.

27 Flux Emergence WorkshopAug 23rd, 2011 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