1. Solar Convection: What it is & How to Calculate it. Bob Stein

2. The Sun is Dynamic, Convection is the Driver  Transports Energy  Transports Angular Momentum  Generates Magnetic Fields by Dynamo  Excites Acoustic and Magnetic Waves

3. The Solar Surface Hot gas rises (floats up) -> Brighter Cool gas sinks (pulled down by gravity) -> Darker ~ 1000 km Convection (boiling water)

4. The Solar Surface

5. The Solar Surface Convection Sunspots: Magnetic fields, Cooler -> Darker

6. Observed as Doppler Shift at the solar surface

7. Magnetic Field

8. The Sun in X-Rays

9. The Solar Wind

10. Models & Observations SIMULATION Calculate Observables OBSERVATIONS Disagree improve physics Agree investigate causes

11. Comparison Simulations vs. Observations Images Intensity distribution Spectrum Line profiles Magnetic Field distribution Resonant Oscillations

12. Emergent Intensity

13. Intensity Histogram

14. Line Profiles Average Profile Iron: Majority species Equilibrium populations Heavy-> small Doppler width Weak lines

15. Field Distribution simulationobserved Both simulated and observed distributions are stretched exponentials.

16. P-Mode Excitation Triangles = simulation, Squares = observations (l=0-3) Excitation decreases both at low and high frequencies

17. Causes: convection

18. Convection is Driven by Radiative Cooling at Surface: Fluid Radiates away its Energy & Entropy -> Denser -> pulled down by Gravity Z S E  Q 

19. Stratified convective flow: diverging upflows, turbulent downflows Velocity arrows, temperature fluctuation image (red hot, blue cool)

20. Stein & Nordlund, ApJL 1989

21. Downflows: cell size increases with depth

22. Vorticity: Downdrafts are Turbulent

23. Turbulent downdraft

24. Never See Hot Gas

25. Causes: Oscillations

26. Simulation Modes

27. Oscillations Excited by Turbulent Pressure & Entropy Fluctuations Entropy Fluctuations

28. Peak Excitation ~ 5 minutes

29. Turbulent Pressure > Entropy Fluctuations

30. Oscillations Excited close to Surface

31. Causes: Magnetic Field

32. Magnetic Field Reorganization

33. Exponential Distribution

37. Magnetic Field Lines

38. Methodology

39. Equations: Conservation of Mass Conservation of Momentum Conservation of Energy Induction

40.  E P p y, V y, B y P z, V z, B z ExEx EyEy EzEz Variables Staggered in Space Center: i,j,k Faces: i-1/2,j-1/2,k-1/2

41. Spatial Derivatives: 6 th order Finite Difference

42. Time Advance: 3 rd order Runge-Kutta n=1-3

44. Characteristic Boundary Conditions Unique Conservative Equations Non-unique Wave-like Equations

45. Characteristic Equations

46. Characteristic Boundary Conditions Boundary Conditions on OUTGOING characteristics is the Characteristic Equations evaluated using one-sided derivatives For INCOMING characteristics the normal derivatives in the characteristic directions must be evaluated using the physics boundary conditions.

47. For (non-magnetic) Gas

48. The End