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Convection Convection Simulation of an A-Simulation of an A-
starstar
ByBy
Regner TrampedachRegner TrampedachMt. Stromlo Observatory, Australian National Mt. Stromlo Observatory, Australian National
UniversityUniversity
8/19/048/19/04
Hydro-dynamicsHydro-dynamics
• Solve Euler equationsSolve Euler equations• Conservation of:Conservation of:
– Mass: Mass: ddρ ρ //ddtt = -= -uu ∙∙∇∇ ρρ --ρρ ∇∇ ∙∙uu– Momentum: Momentum: ρρ dduu //ddtt = -= -ρρ uu ∙∙∇∇ uu ++∇∇ ((TT -- PPgasgas))
++ρρ gg– Energy: Energy: ddEE //ddtt = - = -∇∇ ∙∙uuEE + + ((TT -- PPgasgas))∇∇ ∙∙uu
++ρ ρ qqradrad
• Regular horizontal and optimized vertical Regular horizontal and optimized vertical gridgrid
Radiation DynamicsRadiation Dynamics
• Simplified by only needing forward solutionSimplified by only needing forward solution
• More expensive by factor More expensive by factor NNxx××NNyy××NNφ φ ××NNtt
• Binning the rad. transfer according to Binning the rad. transfer according to opacity => speed-up by opacity => speed-up by NNbin bin /N/Nλ λ , N, Nbinbin = 4= 4
• Binning is calibrated against 1D average Binning is calibrated against 1D average sim.sim.
• About to change to Sparse/Selective OSAbout to change to Sparse/Selective OS
• More stable + accurate and convergesMore stable + accurate and converges
AssumptionsAssumptions
No rotationNo rotation
No magnetic fieldsNo magnetic fields
(Scaled) Solar abundances(Scaled) Solar abundances
Uniform gravitational fieldUniform gravitational field
No diffusionNo diffusion
No radiative levitation of individual No radiative levitation of individual speciesspecies
LTE EOS and radiationLTE EOS and radiation
A few collaboratorsA few collaborators
Convection-code: Convection-code: Robert F. Stein, Michigan State Robert F. Stein, Michigan State UniversityUniversity
ÅÅke Nordlund, Copenhagen Observatoryke Nordlund, Copenhagen Observatory
Equation of State:Equation of State: Werner D Werner Dääppen, University of Southern ppen, University of Southern CaliforniaCalifornia
Radiative Transfer: Radiative Transfer: Martin Asplund, Mt. Stromlo Martin Asplund, Mt. Stromlo ObservatoryObservatory
Asteroseismology:Asteroseismology: J Jøørgen Christensen-Dalsgaard, Aarhus rgen Christensen-Dalsgaard, Aarhus Univ.Univ.
Dali Georgobiani, StanfordDali Georgobiani, Stanford
and many more...and many more...
The Dynamic SunThe Dynamic Sun
Vertical Temperature cut ofVertical Temperature cut ofηη --BooBoo
Solar Line CalculationSolar Line Calculation
• Abundance analysisAbundance analysis– Agreement between FeI, FeII and Agreement between FeI, FeII and
meteoriticmeteoritic– Lower C, N and O abundances – at odds Lower C, N and O abundances – at odds
with helioseismologywith helioseismology
• Synthetic spectra/line-profilesSynthetic spectra/line-profiles– No free parameters, e.g., micro-/macro-No free parameters, e.g., micro-/macro-
turb.turb.– Agree both in shape (bisectors) and shiftsAgree both in shape (bisectors) and shifts
The A-star simulationThe A-star simulation
• 73007300 K, logK, loggg=4.3, [Fe/H] = 0.0=4.3, [Fe/H] = 0.0
• 100100××100100××82 grid-points82 grid-points
• 11.4511.45×11.45×13.10×11.45×13.10 MmMm
• About 5 pressure scale-heightsAbout 5 pressure scale-heights
• 5.6 and 6.4 decades of pressure and 5.6 and 6.4 decades of pressure and densitydensity
• 19 mins. with 5019 mins. with 50 s resolutions resolution
• p-modes with p-modes with Π Π ==1212 mins., A=1.5mins., A=1.5 km/skm/s
3D-1D(3D-1D(αα =1)=1)• >>ρρ -inversion-inversion
• > > TT-gradient-gradient
• More structure More structure in photospherein photosphere
• < < uu and and PPturbturb
• Seperate conv. Seperate conv. ZonesZones
• Diff. internal Diff. internal structurestructure
3D-1D(3D-1D(αα =2)=2)• LargerρLargerρ , ,TT• > > TT-gradient-gradient
• More structure More structure in photospherein photosphere
• > > PPturbturb-peak-peak
• No overshootNo overshoot
• Very Different Very Different internal struct.internal struct.
A vertical cut in the A-star A vertical cut in the A-star simulationsimulation
T: 1700 – 72500T: 1700 – 72500 K logK logρρ : -6.2 - 0.4 : -6.2 - 0.4
Convective
A Local Temperature InversionA Local Temperature Inversion
T: 1700 – 72500T: 1700 – 72500 K logK logρρ : -6.2 - 0.4 : -6.2 - 0.4
Convective
TT-inversion-inversion
• Up to 10Up to 10 000000
KK
• Factor 10 Factor 10 density density invers.invers.
• Related to Related to ionization?ionization?
SummarySummary
• Have changed lower boundary to Have changed lower boundary to accomodate radiative zoneaccomodate radiative zone
• Have included optically thick Have included optically thick radiative transferradiative transfer
• Have started running aHave started running a simulation on simulation on the border between A and Fthe border between A and F
Prospects for the FutureProspects for the Future• Calculate new and improved EOS-tablesCalculate new and improved EOS-tables
• Use it as basis for new opacity calculation Use it as basis for new opacity calculation using the newest cross-section datausing the newest cross-section data
• Implement an improved radiative transfer Implement an improved radiative transfer scheme in the convection simulationsscheme in the convection simulations
• Build a Build a gridgrid of convection models, using of convection models, using the new EOS, opacities and rad. Transferthe new EOS, opacities and rad. Transfer
• Expanding coverage in (Expanding coverage in (TTeffeff, , gg, , ZZ ))