Simulations ofmagnetoconvectionand Solar-B

A. Vögler, A. Lagg, M. Schüssler, S.K. Solanki
Max Planck Institute for Solar System Research

Regimes of solar
magnetoconvection
quiet
Sun

plage

sunspotumbra

sunspot umbra
average B horizontal scale ofconvection decreases

 convective energy

transport decreases

plage‘quiet’ Sun
G-band image: VTT, Tenerife

MPS/UofC Radiation MHD (MURaM) CodeDeveloped by the MPS MHD group (A. Vögler, R. Cameron, S. Shelyag, M. Schüssler)in cooperation with F. Cattaneo, Th. Emonet, T. Linde (Univ. of Chicago)

http://www.mps.mpg.de/projects/solar-mhd/muram_site 3D compressible MHD
 cartesian fixed grid radiative transfer: short characteristics non-grey (opacitybinning), LTE partial ionisation (11 species)
 4th order centered spatial difference scheme explicit time stepping: 4th order Runge-Kutta Solar-B
 MPI parallelized (domain decomposition)
 and: extensive diagnostic tools to compare with observations(e.g. continuum, spectral line & polarization diagnostics)

Applications and Results of MURaM
 Structure and dynamics of photospheric flux concentrations(Vögler et al., 2003, 2005; Vögler & Schüssler 2003; Vögler 2003, 2004)

 Fractal dimension of magnetic patterns (Janssen et al. 2003)
 Effect of non-grey radiative transfer (Vögler et al. 2004) Nature of G-band bright points (Schüssler et al. 2003, Shelyag etal. 2004)

 Origin of facular brightening (Keller et al. 2004)
 Solar pores (Cameron et al., 2005)
 Magnetic flux in internetwork fields (Khomenko et al. 2005a, b)
 Nature of umbral dots (Schüssler & Vögler 2006)
 Decay of mixed-polarity fields (Vögler et al, in prep.) Flux emergence (Cheung et al., in prep.) CLV of facular brightness (Zakharov et al. in prep.)“High Resolution” Simulations<Bz> = 200 G;

Grid: 576 x 576 x 100 (10 km horiz. cell size)

Brightness

Magnetic field.

Bz

vz

Details ofthin
magneticflux
sheet

THorizontal cuts near surface level

IC
Vögler et al. 2005

3D view of a thin flux sheet
Perspective view

Face-on view• Quasi 2-dimensional above
the surface• Loss of coherence beneaththe surface
Vögler et al. 2005
Steiner et al. 1998

Steiner et al. 1994Facular brightening
LimbCenter(continuum image: SST, La Palma θ=60° λ=488nm)
Recent observations reveal:  3D appearance of faculae extension up to 0.5”
(Lites et al. 2004)
 narrow dark lanes centerward offaculae

Facular brightening
Simulation: B0=400 G

Observation

θ=60°

θ=0°
Facula: narrow layer of hot material onside and top of adjacent granule
Dark lane: - cool & tenuous material in adjacent
flux concentration- cool & dense material above
neighbouring granulecontinuum intensity at 488 nm

magnetic field strength(Keller et al. 2004)

G-band spectrum synthesis
G-Band (Fraunhofer): spectral range from 4295 to 4315 Å
contains many temperature-sensitive molecular lines (CH)241 CH lines + 87 atomic lines

For comparison with observations, we define as G-band
intensity the integral of the spectrum obtained from thesimulation data:
4315 A[Shelyag, 2004]

IG =∫ I (λ )dλ4295 A

G-band: Simulation vs. Observation

Simulation (20 km resolution)
Schüssler et al. 2003
Shelyag et al. 2003

Observation(~100 km resolution)(SST, La Palma,Scharmer et al. 2002)Bz & G-band radiance in simulations
and observations
G-band brightness ~ continuum brightness
However, different constants of proportionality for“magnetic” and “non-magnetic” features

Magnetic

Magnetic flux
invisible in G- Magneticband?

<B> = 200 G

SST measurement<B> = 10 G
Zakharov [2006]

Magneto-convection in a sunspot umbra● Suppressed energy transport Æ dark
● Convective transport required to sustain raditative energy output● Umbral dots a manifastation of convection ?
(e.g. overstable oscillations, intrusion of QS plasma)Time evolution of the brightness pattern
Quiet Sun
<B>= 0Sunspot umbra<B>= 2500 G

5800 km

Extreme plage<B>= 800 G

Vertical cuts through an upflow umbral plumecolors: temperature, vmax = 3 km/s

τR = 1Bz

perpendicular
to the dark lane

Temp

along to the dark laneNear-surface layers of an upflow plume
cut perpendicular
to the dark lane

τR = 1
isotherms„Piling-up″ of plasma
below the cusp:→ τ=1 surface elevated→ central parts cut throughlower temperature→ dark lane appears(≈ 15% contrast)

What next…?
Large scales:• (small) Sunspots• extension to chromosphere

Small scales:• role of the surface dynamo• penumbral fine structure

Comparison with Solar-B SOT data