Convection Simulation of an A-star By Regner Trampedach Mt. Stromlo Observatory, Australian National University 8/19/04

Hydro-dynamics Solve Euler equations Solve Euler equations Conservation of: Conservation of: – Mass: dρ / dt = - u ∙ ∇ ρ - ρ ∇ ∙ u – Momentum: ρ du / dt = - ρ u ∙ ∇ u + ∇ (T - P gas ) + ρ g – Energy: dE / dt = - ∇ ∙ uE + (T - P gas ) ∇ ∙u + ρ q rad Regular horizontal and optimized vertical grid Regular horizontal and optimized vertical grid

Radiation Dynamics Simplified by only needing forward solution Simplified by only needing forward solution More expensive by factor N x × N y × N φ × N t More expensive by factor N x × N y × N φ × N t Binning the rad. transfer according to opacity => speed-up by N bin /N λ, N bin = 4 Binning the rad. transfer according to opacity => speed-up by N bin /N λ, N bin = 4 Binning is calibrated against 1D average sim. Binning is calibrated against 1D average sim. About to change to Sparse/Selective OS About to change to Sparse/Selective OS More stable + accurate and converges More stable + accurate and converges

Assumptions No rotation No magnetic fields (Scaled) Solar abundances Uniform gravitational field No diffusion No radiative levitation of individual species LTE EOS and radiation

A few collaborators Convection-code: Robert F. Stein, Michigan State University Å ke Nordlund, Copenhagen Observatory Å ke Nordlund, Copenhagen Observatory Equation of State: Werner D ä ppen, University of Southern California Radiative Transfer: Martin Asplund, Mt. Stromlo Observatory Asteroseismology: J ø rgen Christensen-Dalsgaard, Aarhus Univ. Dali Georgobiani, Stanford Dali Georgobiani, Stanford and many more...

The Dynamic Sun

Vertical Temperature cut of η -Boo

Solar Line Calculation Abundance analysis Abundance analysis –Agreement between FeI, FeII and meteoritic –Lower C, N and O abundances – at odds with helioseismology Synthetic spectra/line-profiles Synthetic spectra/line-profiles –No free parameters, e.g., micro-/macro-turb. –Agree both in shape (bisectors) and shifts

The A-star simulation 7300 K, logg=4.3, [Fe/H] = K, logg=4.3, [Fe/H] = × 100 × 82 grid-points 100 × 100 × 82 grid-points ×11.45×13.10 Mm ×11.45×13.10 Mm About 5 pressure scale-heights About 5 pressure scale-heights 5.6 and 6.4 decades of pressure and density 5.6 and 6.4 decades of pressure and density 19 mins. with 50 s resolution 19 mins. with 50 s resolution p-modes with Π =12 mins., A=1.5 km/s p-modes with Π =12 mins., A=1.5 km/s

3D-1D( α =1) > ρ -inversion > ρ -inversion > T-gradient > T-gradient More structure in photosphere More structure in photosphere < u and P turb < u and P turb Seperate conv. Zones Seperate conv. Zones Diff. internal structure Diff. internal structure

3D-1D( α =2) Largerρ, T Largerρ, T > T-gradient > T-gradient More structure in photosphere More structure in photosphere > P turb -peak > P turb -peak No overshoot No overshoot Very Different internal struct. Very Different internal struct.

A vertical cut in the A-star simulation T: 1700 – K log ρ : Convective

A Local Temperature Inversion T: 1700 – K log ρ : Convective

T -inversion Up to K Up to K Factor 10 density invers. Factor 10 density invers. Related to ionization? Related to ionization?

Summary Have changed lower boundary to accomodate radiative zone Have changed lower boundary to accomodate radiative zone Have included optically thick radiative transfer Have included optically thick radiative transfer Have started running a simulation on the border between A and F Have started running a simulation on the border between A and F

Prospects for the Future Calculate new and improved EOS-tables Calculate new and improved EOS-tables Use it as basis for new opacity calculation using the newest cross-section data Use it as basis for new opacity calculation using the newest cross-section data Implement an improved radiative transfer scheme in the convection simulations Implement an improved radiative transfer scheme in the convection simulations Build a grid of convection models, using the new EOS, opacities and rad. Transfer Build a grid of convection models, using the new EOS, opacities and rad. Transfer Expanding coverage in (T eff, g, Z ) Expanding coverage in (T eff, g, Z )