Simulated Solar Plages Robert Stein, David Benson - Mich. State Univ. USA Mats Carlsson - University of Oslo, NO Bart De Pontieu - Lockheed Martin Solar.

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Presentation transcript:

Simulated Solar Plages Robert Stein, David Benson - Mich. State Univ. USA Mats Carlsson - University of Oslo, NO Bart De Pontieu - Lockheed Martin Solar & Astrophysics Lab., USA Goran Scharmer - Royal Swedish Academy of Sciences, SE Aake Nordlund - Copenhagen University, DK

Movie by Mats Carlsson

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

Conservation Equations Mass Momentum Energy Magnetic Flux

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

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

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

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

Solve Transfer Equation for each bin i

Equation of State Tabular EOS includes ionization, excitation H, He, H 2, other abundant elements

Boundary Conditions Ghost zones loaded Density: top hydrostatic, bottom logarithmic Velocity: symmetric (normal derivative =0) Energy (per unit mass): top = slowly evolving average, bottom fixed entropy in inflows Magnetic (Electric field): top -> potential, bottom -> fixed value in inflows, damped in outflows

Fluid Parcels reaching the surface Radiate away their Energy and Entropy Z S E  Q 

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

Magnetic Field Lines - initially vertical

Magnetic Field & Velocity surface) Up Down

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

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

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

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

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

Center to Limb Movie by Mats Carlsson

G-Band Center to Limb Appearance

Individual features

Magnetic field

Vertical velocity

Height where tau=1

Temperature structure

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

G-band images from simulation at disk center & towards limb (by Mats Carlsson) Notice: Dark bands moving across granules

Temperature fluctuations + Velocity

The End