Photospheric MHD simulation of solar pores

Robert CameronAlexander VöglerVasily Zakharov

Manfred Schüssler

Max-Planck-Institut für Sonnensystemforschung Katlenburg-Lindau, Germany

MSI Workshop

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

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 12 Mm1.4

Mm

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 codeMPS (Alexander Vögler): Radiative Transfer

Hyper Diffusivities

Results

Intensity|B| (tau=1)

Bvert (tau=1) Uvert (tau=1)

Vertical StructureP

ore

sim

ulat

ion

Qui

et S

un S

imul

atio

nO

bser

ved

pore

s (S

utte

rlin)

Sim

ulat

ions

Vertical Structure 2: Energy transport

Temperature Vertical Field

Z=-240

Z=-360

Z=-480

Vertical Structure 2: Energy transport

Temperature at a fixed geometrical height (3 copies)

Vertical Structure 2: Energy transport

Intensitylog(Tau constant geometrical depth)

Vertical magnetic field (Tau=1 surface)

Intensity Tau=1,Tau=0.1

Reference frame

Slice

Magnetic field linesMagnetic energyTau=1 level

Temperature contoursTemperatureTau=1 level

Radial Structure

TAU=1

TAU=0.1

Radial Structure

TAU=1

TAU=0.1

Topology

From bottom to topFrom top to bottomInverse U loops

Evolution

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

Evolution

Intensity v size

A view from the side

500nm

=0.7 0.5 0.2

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.