1. 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

2. The Ohio State University
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

3. Atomic Astrophysics: Stellar Structure
Envelope:
RZ + CZ
Isolated
atoms +
plasma
interactions
Atmosphere
+ Corona
Convection
Zone (CZ)
(Seaton, Yu,
Mihalas,
Pradhan
1994)
Radiative
Zone (RZ)
Nuclear Core
Drake et al (Nature 436/Chandra)

4. Radiation controls heat transport in solar interior
T(eV) ne (cm-3) r/R0
x1025
x1023
x1022
x1022
boundary position depends on transport
measured with helioseismology
0.55
0.90
0.7133
Solar model : J.N. Bahcall et al, Rev. Mod. Phys. 54, 767 (1982)
Courtesy:
Jim Bailey,
Sandia
radiation
convection
Transport depends on opacity, composition, ne, Te

5. 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 < 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.

6. “What’s 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
 % 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?

7. The Opacity Project (1983-2007)
Stellar Opacities and Atomic Data (NORAD)
The Opacity Project ( )
 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)

8. 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 u=hn/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.

9. First complete results 1994  OP1
The Opacity Project:
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 > 0.01 g/cc
(perturbed atom approximation)
New OP work includes both (Mendoza etal 2007)
OPSERVER: On-line “customized opacities”
(Ohio Supercomputer Center) 

10. Opacity Project (OP 2007) and OPAL Rosseland Mean Opacities

11. OP vs. OPAL  % Differences in Rosseland Mean Opacities
Delahaye & Pinsonneault (2006)
Log R = -3
OLD (OP1)
Envelope EOS only, and Without
Inner-shell
Processes
New OP
Extended
EOS, and including
Base of the Solar Convection Zone
Maximum difference
OP-OPAL ~ 3%
However…….

12. 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) .

13. 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 ApJ 625, 563

14. 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) ?

16. Courtesy: Jim Bailey

22.  Re-examination of OP opacities and atomic physics

23. Primary Atomic Processes in Plasmas
Electron Impact Excitation
Autoionization
Resonance
Dielectronic Recombination
Photoionization
Radiative Recombination
The Coupled-Channel R-matrix method provides a self-consistent and
unified treatment of all processes with one single wavefunction expansion

24. 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 (RR+DR) (Nahar and Pradhan 2004)
All significant effects may be included
Infinite series of resonances are considered

25. Relativistic and Non-Relativistic R-matrix Codes For Atomic Processes
(Ohio Supercomputer Center)
BPRM codes
Capable of large-scale
calculations
with high precision
and self-consistency,
BUT
SUPERSTRUCTURE
used for most OP data
Not
R-matrix Codes

26. 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)

27. Benchmarking Photoionization of O III: Comparison of R-Matrix Theory (Nahar 2003) and Synchrotron Experiment (Bijeau etal 2003)
Experiment
Experiment includes
the ground state and
metastable states
of O III in the beam
Theory

28. 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

29. 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

30. 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

31. 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”

32. Textbook Atomic Astrophysics and Spectroscopy Anil 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