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Published byHilary Daniels Modified over 8 years ago
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Solar Convection Simulations Robert Stein, David Benson - Mich. State Univ. Aake Nordlund - Niels Bohr Institute
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Movie by Mats Carlsson
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METHOD Solve conservation equations for: mass, momentum, internal energy & induction equation
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Conservation Equations Mass Momentum Energy Magnetic Flux
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Numerical Method Spatial differencing –6 th -order staggered finite difference, 3 points either side Spatial interpolation –5 th order, staggered Time advancement –3 rd order Runga-Kutta
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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
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5 Rays Through Each Surface Grid Point Interpolate source function to rays at each height
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Opacity is binned, according to its magnitude, into 4 bins.
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Solve Transfer Equation for each bin i
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Equation of State Tabular EOS includes ionization, excitation H, He, H 2, other abundant elements
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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
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Fluid Parcels reaching the surface Radiate away their Energy and Entropy Z S E Q
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Observables
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Granulation
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Solar velocity spectrum MDI doppler (Hathaway) TRACE correlation tracking (Shine) MDI correlation tracking (Shine) 3-D simulations (Stein & Nordlund) v ~ k v ~ k -1/3
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Velocity Spectrum
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Line Profiles Line profile without velocities. Line profile with velocities. simulation observed
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Convection produces line shifts, changes in line widths. No microturbulence, macroturbulence. Average profile is combination of lines of different shifts & widths. average profile
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P-Mode Excitation Triangles = simulation, Squares = observations (l=0-3) Excitation decreases both at low and high frequencies
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SUPER- GRANULATION SCALE CONVECTION
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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 Mm 100 km horizontal, 12-75 km vertical resolution
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Initialization Double horizontally + small fraction stretched : Uz at 0.25 Mm Snapshots of methods + composite (?)
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Initialization Double horizontally + small fraction stretched : Uz at 17.3 Mm
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Mean Atmosphere Temperature, Density and Pressure (10 5 dynes/cm 2 ) (10 -7 gm/cm 2 ) (K)
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Mean Atmosphere Ionization of He, He I and He II
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Energy Fluxes ionization energy 3X larger energy than thermal
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Convective Flux, 48 Mm wide, after 2 hours
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Problem
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MAGNETO- CONVECTION
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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
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Magnetic Field Lines - initially vertical
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G-band images from simulation at 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
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Comparison with observations Simulation, mu=0.6 Observation, mu=0.63
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Center to Limb Movie by Mats Carlsson
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G-Band Center to Limb Appearance
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G-band image & magnetic field contours (-.3,1,2 kG)
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Magnetic Field & Velocity (@ surface) Up Down
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G-band Bright Points = large B, but some large B dark
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G-band & Magnetic Field Contours:.5, 1, 1.5 kG (gray) 20 G (red/green)
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Individual features
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Magnetic field
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Vertical velocity
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Height where tau=1
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Temperature structure
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Magnetic concentrations: cool, low low opacity. Towards limb, radiation emerges from hot granule walls behind. On optical depth scale, magnetic concentrations are hot, contrast increases with opacity
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Temperature Gradients largest next to magnetic concentrations
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Magnetic Field & Velocity High velocity sheets at edges of flux concentration
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Temperature + B contours (1, 2, 3, kG)
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Temperature & Magnetic Field (contours 1, 2 kG)
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Temperature & Velocity
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Magnetic Field & Velocity
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Temperature & Velocity
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Micropore Formation Small granule is squeezed out of existence Magnetic flux moves into location of previous granule
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G-band images from simulation at disk center & towards limb (by Mats Carlsson) Notice: Dark bands moving across granules
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Temperature fluctuations + Velocity
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Boundary Conditions Magnetic structure depends on boundary conditions 1)Inflows at bottom advect horizontal field in 2)At bottom: boundary magnetic field vertical At top: B tends toward potential
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B Swept to Cell Boundaries
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Magnetic Field Lines - fed horizontally
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Flux Emergence & Disappearance 12 34 Emerging flux Disappearing flux
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The End
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