Accurate Stellar Opacities and the Solar Abundance Problem

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Accurate Stellar Opacities and the Solar
Abundance Problem

• The Mihalas Symposium
• On
• Recent Directions In Astrophysical
  Quantitative
• Spectroscopy And Radiation Hydrodynamics
• Anil Pradhan
• The Ohio State University
• Collaborators Sultana Nahar, Max Montenegro,
  Franck Delahaye, Werner Eissner, Chiranjib Sur,
  Hong Lin Zhang

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Multi-Disciplinary Role of Atomic Astrophysics
From Stellar Interiors to Cancer Research

• Symposium on Atomic Astrophysics and Spectroscopy
  (Kodaikanal, Jan 27-31, 2009)
• Anil Pradhan
• The Ohio State University
• Atomic Astrophysics Biophysics
• Sultana Nahar, Max Montenegro, Yan Yu,
  Eric Silver,
• Chiranjib Sur, Werner Eissner, Russ
  Pitzer, Mike Mrozik
• Justin Oelgoetz, Hong Lin Zhang Jian
  Wang, Kaile Li,
• 
  Neil Jenkins

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Atomic Astrophysics Stellar
Structure
Stellar Envelope RZ CZ Isolated atoms
plasma interactions
Atmosphere Corona
Convection Zone (CZ)
(Seaton, Yu, Mihalas, Pradhan 1994)
Radiative Zone (RZ)
Nuclear Core
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Radiation controls heat transport in solar
interior

• boundary position depends on transport
• measured with helioseismology

Solar model J.N. Bahcall et al, Rev. Mod. Phys.
54, 767 (1982)
Courtesy Jim Bailey, Sandia
convection
radiation
Transport depends on opacity, composition, ne, Te
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Astrophysical Opacities

• Relationship between opacity and abundances
• Opacity depends on composition
• - Abundances of all astrophysically abundant
  elements H Ni in all ionization stages
• Atomic data needed for all radiative processes
• -- Bound-bound (oscillator strengths),
  bound-free (photoionization), free-free,
  scattering
• Two independent projects ? Agree lt 5
• -- The Opacity Project (Seaton et al. 1994)
• -- Livermore OPAL opacities (Rogers and
  Iglesias 1992)
• Solved outstanding astrophysical problems
• -- Cepheid pulsation ratios, base of the
  convection zone, etc.

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Whats wrong with the Sun ? (Bahcall)

• Problems with solar abundances !!
• Latest determination of solar abundances
  (Asplund et.al. 2005) measurements and 3D hydro
  NLTE models yield
• ? 30- 40 lower abundances of C, N, O, Ne, Ar
• than standard abundances (Grevesse and
  Sauval 1998)
• But the new abundances have problems with
  accurate Helioseismology data (sound speed, BCZ,
  Y-abundance, etc.)
• ? Higher mean opacities by 10-20 might
  reconcile helioseismology and new low-Z
  abundances (Bahcall et.al. 2004, Basu and Antia
  2008)
• However, such enhancements are ruled out by new
  opacities calculations by both the Opacity
  Project and OPAL !! What is to be done?

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Stellar Opacities and Atomic Datawww.astronomy.oh
io-state.edu/pradhan www.astronomy.ohio-state.edu
/nahar (NORAD)

• The Opacity Project (1983-2007)
• ? Approximately 30 atomic and astrophysicists
• (UK, US, Canada, France, Germany,
  Venezuela)
• ? Stellar opacities and radiative
  accelerations
• ? Large-scale radiative atomic calculations
• ? Iron Project ( collisional calculations
  with fine structure)
• Mihalas-Hummer-Dappen (MHD) equation-of-state
• ? Chemical picture
• ? Isolated atoms
• ? plasma interactions with occupation
  probability formalism
• Atomic data for all abundant elements H-Ni
• ? LS coupling
• ? No relativistic effects (no
  intercombination E1 transitions)
• ? Recent improvements (Seaton 2007, and
  references therein)

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Mean and Monochromatic Opacity
For a chemical mixture with relative abundances
fi, the Rosseland mean opacity (RMO) is given by
? 1/kR m? B(u) / k(u) du ?
Harmonic Mean ? where uhn/kT B(u)
15/p4 u4 exp(-u)/1 exp(-u)2 and the
opacity cross section of the mixture k(u) ?
fi ki(u) ? Summed over all elements,
ions, transitions is the sum of the
monochromatic opacities of each ion.
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The Opacity Project 1983-2005

• First complete results 1994 ? OP1
• (SYMP Seaton, Yu, Mihalas, Pradhan, MNRAS,
  266, 805, 1994)
• OP1 results for stellar envelope opacities
  without
• ? inner-shell processes
• ? stellar core EOS for r gt 0.01 g/cc
• (perturbed atom approximation)
• New OP work includes both (Mendoza etal 2007)
• OPSERVER On-line customized opacities
• (Ohio Supercomputer Center)
• ?http//opacities.osc.edu

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Opacity Project (OP 2007) and OPAL Rosseland
Mean Opacities
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OP vs. OPAL ? Differences in Rosseland Mean
Opacities
Log R -3
OLD (OP1) Envelope EOS only, and
Without Inner-shell Processes New
OP Extended EOS, and including Inner-shell
Processes
Base of the Solar Convection Zone
Maximum difference OP-OPAL 3
However.
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Radiative Acceleration
The radiative acceleration for the ith element in
terms of the Rosseland Mean Opacity is grad m
kR gi F/(cmi) Where the
non-dimensional parameter ? gi ? simta/s
du ? depends on the momentum transfer
cross section simta si(u) 1- exp(-u)
ai(u) .

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Radiative Accelerations OP vs OPAL

• Comparison OP-OPAL
• For a given stellar structure which Simulates
  HB or intermediate mass stars
• Trend Z Diff .

BCZ (Base of Convection Zone)

Delahaye Pinsonneault 2005 ApJ 625, 563
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Causes ?

• Frequency resolution, EOS, atomic physics
• Current OP and OPAL data similar in absolute
  accuracy
• ? Most of the data from atomic structure CI
  codes
• ? Only a relatively small subset of OP
  atomic data is from R-matrix calculations, most
  from SUPERSTRUCTURE or variants
• Issues and Questions
• Benchmark cross sections and opacities with
  experiments ?
• New Calculations with relativistic Breit-Pauli
  R-matrix (BPRM) methodology Iron Project and
  Beyond ?
• Missing Opacity ?
• Unaccounted physics (high-density EOS,
  resonances) ?

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Courtesy Jim Bailey
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? Re-examination of OP opacities and atomic
physics
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Primary Atomic Processes in Plasmas
Electron Impact Excitation
Autoionization
Dielectronic Recombination
Resonance
Photoionization
Radiative Recombination
The Coupled-Channel R-matrix method provides a
self-consistent and unified treatment of all
processes with one single wavefunction expansion
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Coupled Channel R-Matrix Theory

Total wavefunction expansion in terms of
coupled ion levels for (e ion) bound or free
continuum states

• Ab initio treatment of important atomic
• processes with the same expansion Eq.(1)
• Electron impact excitation, radiative
  transitions,
• and a self-consistent and unified treatment of
  photoionization and (e ion) recombination,
  including radiative and dielectronic (RRDR)
  (Nahar and Pradhan 2004)
• All significant effects may be included
• Infinite series of resonances are considered

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Relativistic and Non-Relativistic R-matrix Codes
For Atomic Processes
(Ohio Supercomputer Center)
BPRM codes Capable of large-scale calculations wit
h high precision and self-consistency,
BUT
SUPERSTRUCTURE used for most OP data Not
R-matrix Codes
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Sample re-calculation of opacities using the BPRM
codes Monochromatic opacity of Fe IV (Nahar and
Pradhan 2005)
Breit-Pauli R-Matrix (BPRM)
OP LS Coupling
Huge amount of BPRM atomic data for each ion
(e.g. 1.5 million f-values for Fe IV)
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Benchmarking Photoionization of O IIIComparison
of R-Matrix Theory (Nahar 2003) and Synchrotron
Experiment (Bijeau etal 2003)
Experiment includes the ground state and
metastable states of O III in the beam
Experiment
Theory
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Missing Opacity ?

New BPRM calculation
Large photoexcitation-of -core (PEC) resonances
and enhanced background
Opacity Project
Pressure broadening of autoionizing
resonances Has not yet been considered In
opacities calculations
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Atomic Physics -- Resonances

• Each atomic transition corresponds to (at least)
  two ionization stages of an element, in the
• ? ion and (e ion) autoionizing resonance
• All inner-shell radiative transitions correspond
  to
• (e ion) autoionizing photoexcitation-of-core
  (PEC) resonances (Ci) nl ? (Cj) nl
• Resonances treated as bound states in atomic
  structure codes used in opacities calculations
• Pressure broadening of resonances neglected

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Equation-of-State

• MHD EOS was not designed for high densities
• (stellar envelopes not cores)
• To extend the MHD EOS to high densities in deep
  interiors, the present OP work employs the
  expedient
• ? ad hoc cut-off for occupation probability w
  0.001
• ? OP EOS is much harder than OPAL EOS, by up
  to orders of magnitude

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Conclusion Astrophysical Opacities

• Absolute Precision of all available opacities
  (OP, OPAL, Kurucz, etc.) is similar (atomic
  structure codes)
• (Probably) covergence in terms of completeness
  but not accuracy
• Stellar opacities have not yet been computed
  using state-of-the-art atomic physics
  (relativistic R-matrix)
• Calculations for radiative accelerations and
  laboratory experiments reveal problems with
  monochromatic opacities
• New opacities calculations for a few ions show
  significant differences with OP opacities
• The solar abundance problem requires 1
  accuracy ? an order of magnitude more effort ?
• More realistic EOS at high densities
• Textbook Atomic Astrophysics and Spectroscopy

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Textbook Atomic Astrophysics and
SpectroscopyAnil Pradhan and Sultana Nahar
(Cambridge University Press 2009)

• CONTENTS (Chapters)
• Introduction
• Atomic Structure
• Radiative Transitions
• Theory of Atomic Processes
• Electron-Ion Collisions
• Photoionization and Recombination
• Multi-Wavelength Emission Lines
• Absorption Lines and Radiative Transfer
• Stellar Properties, Opacities and Spectra
• Nebulae and H II Regions
• Active Galactic Nuclei
• Cosmology

Atomic Physics
Astrophysics