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Solar Convection Simulations

Solar Convection Simulations. Robert Stein, David Benson - Mich. State Univ. Aake Nordlund - Niels Bohr Institute. Movie by Mats Carlsson. METHOD. Solve conservation equations for: mass, momentum, internal energy & induction equation. Conservation Equations. Mass.

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Solar Convection Simulations

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  1. Solar Convection Simulations Robert Stein, David Benson - Mich. State Univ. Aake Nordlund - Niels Bohr Institute

  2. Movie by Mats Carlsson

  3. METHOD • Solve conservation equations for: mass, momentum, internal energy & induction equation

  4. Conservation Equations Mass Momentum Energy Magnetic Flux

  5. Numerical Method • Spatial differencing • 6th-order staggered finite difference,3 points either side • Spatial interpolation • 5th order, staggered • Time advancement • 3rd order Runga-Kutta

  6. Radiation Heating/Cooling • LTE • Non-gray, 4 bin multi-group • Formal Solution Calculate J - B by integrating Feautrier equations along one vertical and 4 slanted rays through each grid point on the surface. • Produces low entropy plasma whose buoyancy work drives convection

  7. 5 Rays Through Each Surface Grid Point Interpolate source function to rays at each height

  8. Opacity is binned, according to its magnitude, into 4 bins.

  9. Solve Transfer Equation for each bin i

  10. Equation of State • Tabular EOS includes ionization, excitationH, He, H2, other abundant elements

  11. Boundary Conditions • Current: ghost zones loaded by extrapolation • Density, top hydrostatic, bottom logarithmic • Velocity, symmetric • Energy (per unit mass), top = slowly evolving average • Magnetic (Electric field), top -> potential, bottom -> fixed value in inflows, damped in outflows • Future: ghost zones loaded from characteristics normal to boundary(Poinsot & Lele, JCP, 101, 104-129, 1992)modified for real gases

  12. t Z Fluid Parcelsreaching the surface Radiate away their Energy and Entropy r Q E S

  13. Observables

  14. Granulation

  15. 3-D simulations (Stein & Nordlund) v ~ k-1/3 MDI correlation tracking (Shine) MDI doppler (Hathaway) TRACE correlation tracking (Shine) v ~ k Solar velocity spectrum

  16. Velocity Spectrum

  17. Line Profiles observed simulation Line profile without velocities. Line profile with velocities.

  18. Convection produces line shifts, changes in line widths. No microturbulence, macroturbulence. Average profile is combination of lines of different shifts & widths. average profile

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

  20. SUPER-GRANULATION SCALE CONVECTION

  21. Initialization • Start from existing 12 x 12 x 9 Mm simulation • Extend adiabatically in depth to 20 Mm,no fluctuations in extended portion, relax for a solar day to develop structure in extended region • Double horizontally + small fraction of stretched fluctuations to remove symmetry,relax to develop large scale structures • Currently: 48x48x20 Mm100 km horizontal, 12-75 km vertical resolution

  22. Initialization Double horizontally + small fraction stretched : Uz at 0.25 Mm Snapshots of methods + composite (?)

  23. Initialization Double horizontally + small fraction stretched : Uz at 17.3 Mm

  24. Mean Atmosphere Temperature, Density and Pressure (K) (105 dynes/cm2) (10-7 gm/cm2)

  25. Mean Atmosphere Ionization of He, He I and He II

  26. Energy Fluxes ionizationenergy 3X larger energy than thermal

  27. Convective Flux, 48 Mm wide,after 2 hours

  28. Problem

  29. MAGNETO-CONVECTION

  30. Unipolar Field • Impose uniform vertical field on snapshot of hydrodynamic convection • Boundary Conditions: B -> potential at top, B vertical at bottom • B rapidly swept into intergranular lanes

  31. G-bandimages from simulationat disk center & towards limb(by Mats Carlsson) Notice: Hilly appearance of granules Striated bright walls of granules Micropore at top center Dark bands moving across granules

  32. Comparison with observations Observation, mu=0.63 Simulation, mu=0.6

  33. Center to Limb Movie by Mats Carlsson

  34. G-Band Center to Limb Appearance

  35. G-band image & magnetic field contours (-.3,1,2 kG)

  36. Magnetic Field & Velocity (@ surface) Down Up

  37. G-band Bright Points = large B, but some large B dark

  38. G-band & Magnetic Field Contours: .5, 1, 1.5 kG (gray) 20 G (red/green)

  39. Individual features

  40. Magnetic field

  41. Vertical velocity

  42. Height where tau=1

  43. Temperature structure

  44. Magnetic concentrations: cool, low r,low opacity.Towards limb,radiation emerges from hot granulewalls behind.On optical depth scale,magneticconcentrations are hot, contrast increases with opacity

  45. Magnetic Field &VelocityHigh velocity sheets at edges of flux concentration

  46. Temperature + B contours(1, 2, 3, kG)

  47. G-bandimages from simulationat disk center & towards limb(by Mats Carlsson) Notice: Dark bands moving across granules

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