Photospheric MHD simulation of solar pores

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Photospheric MHD simulation of solar pores
MSI Workshop

• Robert Cameron
• Alexander Vögler
• Vasily Zakharov
• Manfred Schüssler
• Max-Planck-Institut für Sonnensystemforschung
• Katlenburg-Lindau, Germany

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Equations

• Compressible non-ideal MHD with radiation
• Momentum equation, Lorentz force and artificial
  viscosity
• Continuity equation
• Induction equation, with proper diffusion
• Energy equation, with non-gray radiation
• Equation of state, including partial ionization

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Setup

• Box size 288 x 288 x 100 grid points
• Boundary conditions
• Vertical field above box
• OR
• Potential field above box
• Initial Conditions
• Two total fluxes considered (today only
  larger case considered).
• Simulate 2-D to get near equilibrium then
  create 3-D initial condition.
• Injection of some opposite polarity flux in
  some runs

1.4 Mm
12 Mm
12 Mm
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The MURaM code
University of Chicago Basic MHD code MPS
(Alexander Vögler) Radiative Transfer
Hyper Diffusivities

• Finite Differences
• Fixed, uniformly spaced mesh (288 x 288 x 100)
• Forth order in space
• Runge-Kutta
• Hyper Diffusivities
• Short Characteristic method for radiation

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Results
Intensity
B (tau1)
Bvert (tau1)
Uvert (tau1)
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Vertical Structure
Pore simulation Quiet Sun Simulation Observed
pores (Sutterlin)
Simulations
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Vertical Structure 2 Energy transport
Temperature Vertical Field
Z-240
Z-360
Z-480
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Vertical Structure 2 Energy transport
Temperature at a fixed geometrical height (3
copies)
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Vertical Structure 2 Energy transport
log(Tau constant geometrical depth)
Intensity
Vertical magnetic field (Tau1 surface)
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Intensity Tau1,Tau0.1
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Reference frame
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Slice
Temperature contours Temperature Tau1 level
Magnetic field lines Magnetic energy Tau1 level
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Radial Structure
TAU1
TAU0.1
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Radial Structure
TAU1
TAU0.1
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Topology
From bottom to top From top to bottom Inverse U
loops
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Evolution
Average field strength (depends on how pore is
defined)
Flux decay from pore
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Evolution

• Intensity v size

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A view from the side
500nm ?0.7 0.5 0.2
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Main conclusions

• Thermal properties of pore similar to
  observations
• Magnetic fields and magnetic field gradient
  sensitive to definition of the pores edge.
• Energy transport involves plumes which are dark
  at surface (?)
• Topology is becoming interesting (but the pore is
  still small).
• Side views have reasonable enhancements, but is
  quite smooth.