Improved%20phenomenological%20equation%20of%20state%20in%20the%20chemical%20picture

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Improved phenomenological equation of state in
the chemical picture

• by
• Regner Trampedach
• Mt. Stromlo Observatory, Australian National
  University
• 8/19/04

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The 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

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The Dynamic Sun
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Vertical Temperature cut of? -Boo
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Spectroscopy with simulations

• No micro-/macro-turbulence
• Assymetric lines

• gt proper recog-nition of NiI-blend

• Lower OI abund
• Agreement btw. OI, OI and OH

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Input Physics

• Equation of State (EOS)
• Pressure for hydro-static support
• Response to temperature-/density-changes
• Opacity ff bf bb CIA
• radiative transfer gt
• radiative heating qrad,? ?? ? (J?-S? )

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Equation of StateTwo main purposes

• Thermodynamic properties of plasma
• Pressure, internal energy
• Adiabatic exponent
• Foundation of opacity calculations
• ionization and dissociation balances
• population of electronic- and roto-vibrational-sta
  tes

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The OP/MHD- and OPAL-projects

• Prompted by a plea by Simon (1982)
• Pulsations by? -mechanism didnt agree with
  observations
• Substantial disagreement with helioseismic
  structure of the Sun

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MHD Equation of State

• Explicitly includes hundreds of energy-levels for
  each ion/atom/molecule
• Use occupation probabilities, wi, to account for
  destruction of states from collisions with
  other particles

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Micro-field Distributions

• Ionization by fluctuating fields from passing
  ions/electrons
• With a state, i, being destroyed by a field of
  critical strength, Fcr, the probability of it
  surviving is
  wi Q(Fcr ) ?0Fcr P(F
  )dF
• Changed from linear fit to Q-MHD, Nayfonov,
  Däppen, Hummer Mihalas (1999).

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Micro-Field Effects in the Sun
___ OPAL ___ MHD2000 - - old Q (Fcd)
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Quantum effects

• Quantum diffractionfrom Heisenbergsuncertainty
  relation

• Exchange interactionfrom Paulis
  exclusionprinciple

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Exchange Interactions in the Sun
___ OPAL ___ MHD2000 - - no Exch
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Interaction with Neutral Particles

• Original MHD used hard-sphere interacts.
• How do hard spheres interact?
• Through electric forces, of course...
• Assume Gaussian (s-orbital) r2e-r/ra
  e--distribution.

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Effective charges in the Sun
___ OPAL ___ MHD2000 - - const. Z
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Coulomb Interactions

• The 1st order term is the Debye-Hückel term
  FDH/(NkT) --? /3 .
• Including this, was the largest improvement over
  earlier work.
• Results in negative Ftot for large ? !!!
• MHD included a t -factor to avoid this.
• Include higher-order terms by factor g(? ).

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Coulomb Interactions in the Sun
___ OPAL ___ MHD2000 - - Debye-H
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Additional Changes

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

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Opacity According to OP
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Confronting Experiment

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

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Summary

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

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Prospects for the Future

• Calculate tables of MHD2000
• Use it as basis for new opacity calculation using
  the newest cross-section data
• 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