simulations of solar magneto-convection

Simulations of solarSimulations of solar magneto-convection magneto-convection

Alexander Vögler Alexander Vögler

Max-Planck-Institut für AeronomieMax-Planck-Institut für Aeronomie

Katlenburg-Lindau, GermanyKatlenburg-Lindau, Germany

MPRS Seminar Lindau, Dezember 17, 2003 MPRS Seminar Lindau, Dezember 17, 2003

What is magneto-convection?What is magneto-convection?

The simulation codeThe simulation code

Simulations of photospheric Simulations of photospheric

magneto-convection magneto-convection

Outlook Outlook

OutlineOutline

What is magneto-convection?What is magneto-convection?

The simulation codeThe simulation code

Simulations of photospheric Simulations of photospheric

magneto-convection magneto-convection

Outlook Outlook

OutlineOutline

Interaction between convective flows and magnetic Interaction between convective flows and magnetic

field in an electrically well-conducting fluidfield in an electrically well-conducting fluid

High Reynolds numbers: nonlinear dynamics, High Reynolds numbers: nonlinear dynamics,

structure and pattern formationstructure and pattern formation

Key processesKey processes

What is magneto-convection?What is magneto-convection?

Generation of magnetic fields: self-excited dynamoGeneration of magnetic fields: self-excited dynamo

(Re)distribution of magnetic flux(Re)distribution of magnetic flux

Dynamics: waves, instabilitiesDynamics: waves, instabilities

Energetics: interference with convective energy transport, Energetics: interference with convective energy transport,

non-thermal heatingnon-thermal heating

Magneto-convection in the Magneto-convection in the photosphere photosphere

We simulate surface layers

Regimes of Regimes of magneto-magneto-

convection in the convection in the photosphere photosphere

<B> increases: <B> increases: quiet Sun quiet Sun plage plage umbraumbra

horizontal scale of horizontal scale of convection decreasesconvection decreases

convective energy convective energy transport decreasestransport decreases

G-band image: KIS/VTT, Obs. del Teide, Tenerife & M. Sailer, Univ. Obs. Göttingen

sunspot umbrasunspot umbra

plageplage

‘‘quiet’ sunquiet’ sun

Thermal convection

• Schwarzschild/Ledoux criterion for onset of convection:

ad with

pd

Td

ln

ln

• In diffusive systems, the Rayleigh number must exceed a critical value

critRaRa with

adRa

ln/ln Tln/ln

: mean molecular weight

: thermal diffusivity

: kinematic viscosity

Thermal convection in the photosphere

• cooling layer around visible surface

superadiabatic T-gradient at =1

Temperature drop due to

radiative cooling

• radiative cooling drives strong downflows

Effects of magnetic fields

Convection Magneto-Convection

• flux expulsion: Lorentz force suppresses motions in strong fields

• convective field amplification: radiative cooling

partial evacuation

superequipartition fields

What is magneto-convection?What is magneto-convection?

The simulation codeThe simulation code

Simulation of photosphericSimulation of photospheric

magneto-convection magneto-convection

Outlook Outlook

OutlineOutline

Realistic solar simulations:Realistic solar simulations: what is required ? what is required ?

3D3D full compressibilityfull compressibility partial ionizationpartial ionization

non-local, non-grey radiative transfernon-local, non-grey radiative transfer open boundariesopen boundaries

sufficiently big box (covering the relevant spatial scales)sufficiently big box (covering the relevant spatial scales)

and:and: extensive diagnostic tools to compare with extensive diagnostic tools to compare with observations (continuum & spectral line & polarization observations (continuum & spectral line & polarization diagnostics, diagnostics, tracer particles, etc.) tracer particles, etc.)

The MPAe/UofC Radiation MHD (MURAM)The MPAe/UofC Radiation MHD (MURAM) CodeCode

3D compressible MHD3D compressible MHD cartesian gridcartesian grid 4th order centered spatial difference scheme4th order centered spatial difference scheme explicit time stepping: 4th order Runge-Kuttaexplicit time stepping: 4th order Runge-Kutta MPI parallelized (domain decomposition)MPI parallelized (domain decomposition)

radiative transfer: short characteristics radiative transfer: short characteristics non-grey (opacity binning), LTE non-grey (opacity binning), LTE

partial ionisation (11 species)partial ionisation (11 species) Hyperdiffusivities for stabilizationHyperdiffusivities for stabilization open lower boundary conditionopen lower boundary condition

Basis CodeBasis Code (Univ. of Chicago) (Univ. of Chicago)

Extensions for solar applicationsExtensions for solar applications (MPAe)(MPAe)

Energy equationEnergy equation

Momentum equationMomentum equation

Continuity equationContinuity equation

Induction equationInduction equation

The MHD EquationsThe MHD Equations

Radiative Transfer Radiative Transfer Equation Equation

Non-grey treatment of radiative Non-grey treatment of radiative transfertransfer

frequencies are grouped into frequency bins according to the height in the atmosphere frequencies are grouped into frequency bins according to the height in the atmosphere

where where = 1 = 1 is reached is reached

Multigroup method: Multigroup method: (Nordlund 1982, Ludwig 1992, Vögler et al. 2003)

transfer equation is solved for each bin separately:

-> calculation of• bin-averaged opacities • bin-integrated source function

Non-grey treNon-grey treatmentatment necessary for necessary for accurate radiative heating rates: accurate radiative heating rates:

2D magnetic flux-sheet model2D magnetic flux-sheet model

heightheightTTinin < T< Texex

ρρinin < < ρρexex

BB22/8/8 = p = pexex-p-pinin

Non-grey treNon-grey treatmentatment necessary for necessary for accurate radiative heating rates: accurate radiative heating rates:

2D magnetic flux-sheet model2D magnetic flux-sheet model

Grey RT can lead to qualitatively incorrect Grey RT can lead to qualitatively incorrect heating ratesheating rates

Effect of line-opacities on directional Effect of line-opacities on directional heating/cooling:heating/cooling:

grey casegrey case non-grey casenon-grey case

What is magneto-convection?What is magneto-convection?

The simulation codeThe simulation code

Simulations of photospheric Simulations of photospheric

magneto-convection magneto-convection

Outlook Outlook

OutlineOutline

Simulation of a solar plage regionSimulation of a solar plage region

start convection without magnetic fieldstart convection without magnetic field

initially vertical magnetic field introduced after initially vertical magnetic field introduced after convection has become quasi-stationaryconvection has become quasi-stationary

initial field strength: initial field strength: BB00= 200 G = 200 G

BB00

Grid Resolution:Grid Resolution:

288 x 288 x 100288 x 288 x 1006 Mm6 Mm

6 Mm6 Mm1.4 Mm1.4 Mm

600 km600 km

800 km800 km=1=1

BBzz

strong strong fields fields coloredcolored

IICC

vvzz

6000 km6000 km1τ Plage runBB00 = 200 G = 200 G

BBzzB >B > 500500 …… 1000 1000 …… 15001500

GG

BBzz

TT IICC

vvzzBBzz

TT IICC

vvzz

horizontal cuts horizontal cuts near surface levelnear surface level

BBzz

TT IICC

vvzzBBzz

TT IICC

vvzz

horizontal cuts horizontal cuts near surface levelnear surface level

Plage run

v vs. Bz

B vs. inclin.(B)

• strong fields inhibit motionsstrong fields inhibit motions

• downflows downflows preferred in preferred in regions of strong field regions of strong field

• strong fields are verticalstrong fields are vertical

• weak fields: orientation weak fields: orientation more evenly more evenly distributeddistributed

Statistical properties in Statistical properties in a a layer aroundlayer around

Relation between flux concentrations Relation between flux concentrations and continuum intensityand continuum intensity

Continuum intensity:Continuum intensity:

I >I > 1.0 1.0 …… 1.21.2 <I><I>

Field strength:Field strength:

B >B > 500 500 …… 1000 1000 … … 1500 1500 … … 17001700

GG

Plage Plage runrun

Plage runPlage run

ProbabilitProbability distribution of field y distribution of field strength atstrength at

brightbright featuresfeatures

darkdark featuresfeatures

Vertical cut through Vertical cut through a sheet-like a sheet-like structurestructure

• partial evacuation partial evacuation depression of surface depression of surface

level level

• lateral heating from hot lateral heating from hot wallswalls

Brightness Brightness enhancement of small enhancement of small

structuresstructures

Radiation Flux & Radiation Flux & TemperatureTemperature

IIcc

BBzz

TemperatureTemperatureField StrengthField Strength

Vertical cut through a Vertical cut through a microporemicropore

II

BBzz

Emergent IntensityEmergent Intensity

Canopy structure in the upper Canopy structure in the upper photospherephotosphere

yellow: magnetic field linesgrey: surface of optical depth unity (visible “solar surface”)

Upper photosphere:Upper photosphere:

Strong horizontal flows inside field Strong horizontal flows inside field concentrationsconcentrations

magnetic fieldmagnetic field temperaturetemperature

z = 100 kmz = 100 km z = 540 kmz = 540 km

Magnetic field & horizontal velocitiesMagnetic field & horizontal velocities

Vortical flow inside Vortical flow inside magnetic field magnetic field concentrationconcentration

Net circulation of Net circulation of converging granular flows converging granular flows around magnetic element around magnetic element

Plage runPlage run

600 km600 km

300 km300 km

0 km0 km

-300 km-300 km Vertical structure of magnetic Vertical structure of magnetic flux concentrationsflux concentrations

depthdepth

B0=10 G50 G

200 G800 G

From weak to strong fields: Intensity and vertical field

10 G10 G 50 G50 G

200 G200 G 800 G800 G

Probability distribution of field strength

Grid resolutionGrid resolution288 x 288288 x 288576 x 576576 x 576

10 G10 G 50 G50 G

200 G200 G 800 G800 G

Distribution of magnetic flux

10 G10 G 50 G50 G

200 G200 G 800 G800 G

Distribution of magnetic energy

Convection in a strong field: B0 = 800 G

vertical magnetic field intensity

reduction of horizontal length scales

isolated bright upflows ( umbral dots ?? )

Convection in a strong field: B0 = 800 G

Bz vs |v|*sgn(vz) Intensity vs |B|

strong upflows in weak field regions

high intensity contrast (22-25 %) due to bright upflows

Bz vs vhor

horizontal motions strongly suppressed

Convection in a bipolar region:decay of magnetic flux

vertical magnetic field

+200 G

weak fields

-200 G

0 G

Convection in a bipolar region:decay of surface flux

2

2

2

2

y

B

x

B

t

Bt

)/exp( tB

122 ))(( yxt kk

Exponential decay:

scmt /105.1 212sec3000

Convection in a bipolar region:decay of magnetic energy

sec650001

sec300011

)/exp( tEMAG

• The energy decays at the same rate as the flux:

•The decay rates are consistent with an effective „turbulent“ diffusivity:

xyx kkk 2221101 )(2.2

Convection in a bipolar region:Distribution of magnetic energy

energy distributionfor successive times

normalized distributions

• Distribution of magnetic energy is time-independent

• About 30% of the energy stored in weak fields

time = 0 ... 100 min

Larger domains Larger domains meso/supergranulation meso/supergranulation

(( S. Shelyag) S. Shelyag)

What else, what next ... ?What else, what next ... ?

Extended height range: Extended height range: convection zone convection zone chromosphere chromosphere

Larger magnetic structures: large pores, sunspotsLarger magnetic structures: large pores, sunspots

(( R. Cameron) R. Cameron)

Formation of bipolar regions by flux emergence Formation of bipolar regions by flux emergence (( M. Cheung) M. Cheung)

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