Improved Improved phenomenological equation phenomenological equation

of stateof state in the chemical picture in the chemical picture

byby

Regner TrampedachRegner TrampedachMt. Stromlo Observatory, Australian National Mt. Stromlo Observatory, Australian National

UniversityUniversity

8/19/048/19/04

The Holistic StarThe Holistic Star

• ...from the convective, radiatively cooled surface layers

• ...to the relativistically degenerate core

• All observations are of the photosphere

• Photosphere is boundary condition of star

• All observed p-/g-modes go through the surface layers

The Dynamic SunThe Dynamic Sun

Vertical Temperature cut ofVertical Temperature cut ofηη - -BooBoo

Spectroscopy with Spectroscopy with simulationssimulations• No micro-/macro-

turbulence

• Assymetric lines

• => proper => proper recog-nition of recog-nition of NiI-blendNiI-blend• Lower [OI] Lower [OI] abundabund

• Agreement Agreement btw. OI, [OI] btw. OI, [OI] and OH and OH

Input PhysicsInput Physics

• Equation of State (EOS)Equation of State (EOS)– Pressure for hydro-static supportPressure for hydro-static support– Response to temperature-/density-Response to temperature-/density-

changeschanges

• Opacity: ff + bf + bb + CIAOpacity: ff + bf + bb + CIA– radiative transfer =>radiative transfer =>

– radiative heating: radiative heating: qqradrad,,λλ = = ρκ ρκ λ λ ((JJλλ--SSλ λ ))

Equation of StateEquation of StateTwo main purposes:Two main purposes:

• Thermodynamic properties of plasmaThermodynamic properties of plasma– Pressure, internal energyPressure, internal energy– Adiabatic exponentAdiabatic exponent

• Foundation of opacity calculationsFoundation of opacity calculations– ionization and dissociation balancesionization and dissociation balances– population of electronic- and roto-population of electronic- and roto-

vibrational-statesvibrational-states

The OP/MHD- and OPAL-The OP/MHD- and OPAL-projectsprojects• Prompted by a plea by Simon (1982)Prompted by a plea by Simon (1982)

• Pulsations byPulsations byκκ -mechanism didn’t agree -mechanism didn’t agree with observationswith observations

• Substantial disagreement with Substantial disagreement with helioseismic structure of the Sunhelioseismic structure of the Sun

MHD Equation of StateMHD Equation of State

• Explicitly includes hundreds of Explicitly includes hundreds of energy-levels for each energy-levels for each ion/atom/moleculeion/atom/molecule

• Use occupation probabilities, Use occupation probabilities, wwii, to , to

account for destruction of states account for destruction of states from “collisions” with other particles:from “collisions” with other particles:

Micro-field DistributionsMicro-field Distributions

• Ionization by fluctuating fields from Ionization by fluctuating fields from passing ions/electronspassing ions/electrons

• With a state, With a state, ii, being destroyed by a field , being destroyed by a field of critical strength, of critical strength, FFcrcr, the probability of , the probability of it surviving is it surviving is

wwi i = Q= Q((FFcr cr )) = =∫∫00FFcrcr PP((FF )d)dFF

• Changed from linear fit to Changed from linear fit to QQ-MHD, -MHD, Nayfonov, DNayfonov, Dääppen, Hummer & Mihalas (1999).ppen, Hummer & Mihalas (1999).

Micro-Field Effects in the Micro-Field Effects in the SunSun

___ OPAL___ MHD2000- - old Q (Fcd)

Quantum effectsQuantum effects

• Quantum diffractionQuantum diffractionfrom Heisenberg’sfrom Heisenberg’suncertainty relationuncertainty relation

• Exchange Exchange interactioninteractionfrom Pauli’s from Pauli’s exclusionexclusionprincipleprinciple

Exchange Interactions in the Exchange Interactions in the SunSun

___ OPAL___ MHD2000- - no Exch

Interaction with Neutral Interaction with Neutral ParticlesParticles

• Original MHD used hard-sphere Original MHD used hard-sphere interacts.interacts.

• How How dodo hard spheres interact?hard spheres interact?

Through electric forces, of course...Through electric forces, of course...

• Assume Gaussian (s-orbital) Assume Gaussian (s-orbital) rr22ee--rr//rrαα

e e---distribution.-distribution.

Effective charges in the SunEffective charges in the Sun

___ OPAL___ MHD2000- - const. Z

Coulomb InteractionsCoulomb Interactions

• The 1The 1stst order term is the Debye-H order term is the Debye-Hüückel ckel term term FFDHDH/(/(NkTNkT)= )= −-Λ −-Λ /3 ./3 .

• Including this, was the largest Including this, was the largest improvement over earlier work.improvement over earlier work.

• Results in negative Results in negative FFtottot for large for large Λ Λ !!!!!!

• MHD included a MHD included a ττ -factor to avoid this.-factor to avoid this.

• Include higher-order terms by factor Include higher-order terms by factor gg((Λ Λ ).).

Coulomb InteractionsCoulomb Interactions

• OPAL includes OPAL includes terms up to terms up to nn 5/25/2

• Now Including Now Including results from Monte-results from Monte-Carlo and hyper-Carlo and hyper-netted-chain netted-chain simulations.simulations.

• Analytical Analytical ggFF((ΛΛ ) )

differentiated and differentiated and fitted to fitted to ggUU((ΛΛ ).).

gU

gF

Coulomb Interactions in the Coulomb Interactions in the SunSun

___ OPAL___ MHD2000- - Debye-H

Additional ChangesAdditional Changes

• Relativistic effects – affects stellar Relativistic effects – affects stellar centrescentres– The Sun has a relativistically degenerate The Sun has a relativistically degenerate

corecore– well, - at least slightly...well, - at least slightly...

• MoleculesMolecules– 315 di-atomic and 99 poly-atomic (+ ions)315 di-atomic and 99 poly-atomic (+ ions)– Affects stellar atmospheres and the Affects stellar atmospheres and the

convection simulationsconvection simulations

Opacity According to OPOpacity According to OP

Confronting ExperimentConfronting Experiment

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

SummarySummary

• Developed new equation of stateDeveloped new equation of state– With larger range of validityWith larger range of validity– More complete physicsMore complete physics

• Will change Solar "standard" model Will change Solar "standard" model ...might help reconcile low ...might help reconcile low C,N,O Sun with helioseismology...C,N,O Sun with helioseismology...

• Haven't included crystallizationHaven't included crystallization - yet- yet

Prospects for the FutureProspects for the Future

• Calculate tables of MHD2000Calculate tables of MHD2000

• Use it as basis for new opacity Use it as basis for new opacity calculation using the newest cross-calculation using the newest cross-section datasection data

• Implement a new radiative transfer Implement a new radiative transfer scheme in the convection simulationsscheme in the convection simulations

• Build a grid of convection models, using Build a grid of convection models, using the new EOS, opacities and radiative the new EOS, opacities and radiative transfer schemetransfer scheme