simulations of solar magneto-convection
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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)
Thank you for your att...
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