1. Photospheric MHD simulation of solar pores Robert Cameron Alexander Vögler Vasily Zakharov Manfred Schüssler Max-Planck-Institut für Sonnensystemforschung Katlenburg-Lindau, Germany MSI Workshop

2. 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

3. 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 12 Mm 1.4 Mm

4. The MURaM code Finite Differences Fixed, uniformly spaced mesh (288 x 288 x 100) Forth order in space Runge-Kutta Hyper Diffusivities Short Characteristic method for radiation University of Chicago: Basic MHD code MPS (Alexander Vögler): Radiative Transfer Hyper Diffusivities

5. Results Intensity |B| (tau=1) B vert (tau=1) U vert (tau=1)

6. Vertical Structure Pore simulation Quiet Sun Simulation Observed pores (Sutterlin) Simulations

7. Vertical Structure 2: Energy transport Temperature Vertical Field Z=-240 Z=-360 Z=-480

8. Vertical Structure 2: Energy transport Temperature at a fixed geometrical height (3 copies)

9. Vertical Structure 2: Energy transport Intensity log(Tau constant geometrical depth ) Vertical magnetic field (Tau=1 surface)

10. Intensity Tau=1,Tau=0.1

11. Reference frame

12. Slice Magnetic field lines Magnetic energy Tau=1 level Temperature contours Temperature Tau=1 level

13. Radial Structure TAU=1 TAU=0.1

14. Radial Structure TAU=1 TAU=0.1

15. Topology From bottom to top From top to bottom Inverse U loops

16. Evolution Flux decay from pore Average field strength (depends on how pore is defined)

17. Evolution Intensity v size

18. A view from the side 500nm  =0.7 0.5 0.2

19. 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.