Improved phenomenological equation of state in the chemical picture by Regner Trampedach Mt. Stromlo Observatory, Australian National University 8/19/04

The Holistic Star...from the convective, radiatively cooled surface layers...from the convective, radiatively cooled surface layers...to the relativistically degenerate core...to the relativistically degenerate core All observations are of the photosphere All observations are of the photosphere Photosphere is boundary condition of star Photosphere is boundary condition of star All observed p-/g-modes go through the surface layers All observed p-/g-modes go through the surface layers

The Dynamic Sun

Vertical Temperature cut of η -Boo

Spectroscopy with simulations No micro-/macro- turbulence No micro-/macro- turbulence Assymetric lines Assymetric lines => proper recog- nition of NiI- blend => proper recog- nition of NiI- blend Lower [OI] abund Lower [OI] abund Agreement btw. OI, [OI] and OH Agreement btw. OI, [OI] and OH

Input Physics Equation of State (EOS) Equation of State (EOS) –Pressure for hydro-static support –Response to temperature-/density-changes Opacity: ff + bf + bb + CIA Opacity: ff + bf + bb + CIA –radiative transfer => –radiative heating: q rad, λ = ρκ λ (J λ -S λ )

Equation of State Two main purposes: Thermodynamic properties of plasma Thermodynamic properties of plasma –Pressure, internal energy –Adiabatic exponent Foundation of opacity calculations Foundation of opacity calculations –ionization and dissociation balances –population of electronic- and roto-vibrational- states

The OP/MHD- and OPAL- projects Prompted by a plea by Simon (1982) Prompted by a plea by Simon (1982) Pulsations by κ -mechanism didn’t agree with observations Pulsations by κ -mechanism didn’t agree with observations Substantial disagreement with helioseismic structure of the Sun Substantial disagreement with helioseismic structure of the Sun

MHD Equation of State Explicitly includes hundreds of energy- levels for each ion/atom/molecule Explicitly includes hundreds of energy- levels for each ion/atom/molecule Use occupation probabilities, w i, to account for destruction of states from “collisions” with other particles: Use occupation probabilities, w i, to account for destruction of states from “collisions” with other particles:

Micro-field Distributions Ionization by fluctuating fields from passing ions/electrons Ionization by fluctuating fields from passing ions/electrons With a state, i, being destroyed by a field of critical strength, F cr, the probability of it surviving is w i = Q(F cr ) = ∫ 0 F cr P(F )dF With a state, i, being destroyed by a field of critical strength, F cr, the probability of it surviving is w i = Q(F cr ) = ∫ 0 F cr P(F )dF Changed from linear fit to Q -MHD, Nayfonov, D ä ppen, Hummer & Mihalas (1999). Changed from linear fit to Q -MHD, Nayfonov, D ä ppen, Hummer & Mihalas (1999).

Micro-Field Effects in the Sun ___ OPAL ___ MHD old Q (F cd )

Quantum effects Quantum diffraction from Heisenberg’s uncertainty relation Quantum diffraction from Heisenberg’s uncertainty relation Exchange interaction from Pauli’s exclusion principle Exchange interaction from Pauli’s exclusion principle

Exchange Interactions in the Sun ___ OPAL ___ MHD no Exch

Interaction with Neutral Particles Original MHD used hard-sphere interacts. Original MHD used hard-sphere interacts. How do hard spheres interact? How do hard spheres interact? Through electric forces, of course... Through electric forces, of course... Assume Gaussian (s-orbital) r 2 e -r/r α e - -distribution. Assume Gaussian (s-orbital) r 2 e -r/r α e - -distribution.

Effective charges in the Sun ___ OPAL ___ MHD const. Z

Coulomb Interactions The 1 st order term is the Debye-H ü ckel term F DH /(NkT)= −-Λ /3. The 1 st order term is the Debye-H ü ckel term F DH /(NkT)= −-Λ /3. Including this, was the largest improvement over earlier work. Including this, was the largest improvement over earlier work. Results in negative F tot for large Λ !!! Results in negative F tot for large Λ !!! MHD included a τ -factor to avoid this. MHD included a τ -factor to avoid this. Include higher-order terms by factor g(Λ ). Include higher-order terms by factor g(Λ ).

Coulomb Interactions OPAL includes terms up to n 5/2 OPAL includes terms up to n 5/2 Now Including results from Monte-Carlo and hyper-netted-chain simulations. Now Including results from Monte-Carlo and hyper-netted-chain simulations. Analytical g F ( Λ ) differentiated and fitted to g U ( Λ ). Analytical g F ( Λ ) differentiated and fitted to g U ( Λ ). gUgU gFgF

Coulomb Interactions in the Sun ___ OPAL ___ MHD Debye-H

Additional Changes Relativistic effects – affects stellar centres Relativistic effects – affects stellar centres –The Sun has a relativistically degenerate core –well, - at least slightly... Molecules Molecules –315 di-atomic and 99 poly-atomic (+ ions) –Affects stellar atmospheres and the convection simulations

Opacity According to OP

Confronting Experiment From Nahar, S. N., 2003, Phys. Rev. A (submitted)

Summary Developed new equation of state Developed new equation of state –With larger range of validity –More complete physics Will change Solar "standard" model...might help reconcile low C,N,O Sun with helioseismology... Will change Solar "standard" model...might help reconcile low C,N,O Sun with helioseismology... Haven't included crystallization Haven't included crystallization - yet - yet

Prospects for the Future Calculate tables of MHD2000 Calculate tables of MHD2000 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 a new radiative transfer scheme in the convection simulations Implement a new radiative transfer scheme in the convection simulations Build a grid of convection models, using the new EOS, opacities and radiative transfer scheme Build a grid of convection models, using the new EOS, opacities and radiative transfer scheme