accurate stellar opacities and the solar abundance problem the mihalas symposium on recent...
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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
Multi-Disciplinary Role of Atomic Astrophysics: From Stellar
Interiors to Cancer ResearchSymposium on Atomic Astrophysics and
Spectroscopy (Kodaikanal, Jan 27-31, 2009)
Anil PradhanThe 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
Drake et al. 2005 (Nature 436/Chandra)
Atomic Astrophysics: Stellar Structure
Nuclear Core
RadiativeZone (RZ)
ConvectionZone (CZ)
Atmosphere+ Corona
StellarEnvelope:RZ + CZ
Isolated atoms + plasmainteractions(Seaton, Yu, Mihalas,Pradhan1994)
Radiation controls heat transport in solar interior
T(eV) ne (cm-3) r/R0
1360 6x1025
293 4x1023
182 9x1022
54 1x1022
radiation convection
• boundary position depends on transport• measured with helioseismology
Solar model : J.N. Bahcall et al, Rev. Mod. Phys. 54, 767 (1982)
Transport depends on opacity, composition, ne, Te
0.55
0.90
0.7133
0Courtesy:Jim Bailey,Sandia
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.
“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
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?
Stellar Opacities and Atomic Datawww.astronomy.ohio-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)
Mean and Monochromatic Opacity
For a chemical mixture with relative abundances fi, the Rosseland mean opacity (RMO) is given by
1/R = B(u) / (u) du Harmonic Mean
where u=h/kT
B(u) = [15/4] u4 exp(-u)/[1 – exp(-u)]2
and the opacity cross section of the mixture
(u) = fi i(u) Summed over all elements, ions, transitions
is the sum of the monochromatic opacities of each ion.
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 > 0.01 g/cc
(perturbed atom approximation)
• New OP work includes both (Mendoza etal 2007)
• OPSERVER: On-line “customized opacities”
(Ohio Supercomputer Center)
ttp:::hop t s:os :: : uaci ie ced
Opacity Project (OP 2007) and OPAL Rosseland Mean Opacities
Delahaye & Pinsonneault (2006)
OP vs. OPAL % Differences in Rosseland Mean Opacities
Log R = -3
Base of the Solar Convection Zone
OLD (OP1)Envelope EOS only, and WithoutInner-shellProcessesNew OPExtendedEOS, and includingInner-shell Processes
Maximum difference OP-OPAL ~ 3%
However…….
Radiative Acceleration
The radiative acceleration for the ith element in terms of the Rosseland Mean Opacity is
grad =R i F/(ci) Where the non-dimensional parameter i = i
mta/ du depends on the momentum transfer cross section
imta = i(u) [1- exp(-u)] – ai(u) .
Comparison OP-OPAL
For a given stellar structure which Simulates HB or intermediate mass stars
Trend: Z Diff .
Delahaye & Pinsonneault 2005 ApJ 625, 563
Radiative Accelerations: OP vs OPALRadiative Accelerations: OP vs OPAL
~ BCZ(Base ofConvectionZone)
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) ?
Courtesy: Jim Bailey
Re-examination of OP opacities and atomic physics
Primary Atomic Processes in Plasmas
Electron Impact Excitation
Radiative Recombination
Photoionization
Autoionization
Dielectronic RecombinationResonance
The Coupled-Channel R-matrix method provides a self-consistent and unified treatment of all processes with one single wavefunction expansion
Coupled Channel R-Matrix Theory
• 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
Total wavefunction expansion in terms of coupled ion levels for(e + ion) bound orfree continuum states
Relativistic and Non-Relativistic R-matrix Codes For Atomic Processes
BPRM codesCapable of large-scalecalculationswith high precisionand self-consistency, BUT
(Ohio Supercomputer Center)
SUPERSTRUCTUREused for most OP data
Not R-matrix Codes
Sample re-calculation of opacities using the BPRM codes:Monochromatic opacity of Fe IV (Nahar and Pradhan 2005)
Huge amount of BPRM atomic data for each ion (e.g. 1.5 million f-values for Fe IV)
Breit-PauliR-Matrix (BPRM)
OP LS Coupling
Benchmarking Photoionization of O III:Comparison of R-Matrix Theory (Nahar 2003)
and Synchrotron Experiment (Bijeau etal 2003)
Experiment includesthe ground state and metastable states of O III in the beam
Experiment
Theory
Missing Opacity ?
New BPRM calculation
Opacity Project
Large photoexcitation-of-core (PEC) resonances and enhanced background
Pressure broadening ofautoionizing resonancesHas not yet been consideredIn opacities calculations
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
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
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”
Textbook
Atomic Astrophysics and SpectroscopyAnil Pradhan and Sultana Nahar
(Cambridge University Press 2009) CONTENTS (Chapters)1. Introduction2. Atomic Structure3. Radiative Transitions4. Theory of Atomic Processes5. Electron-Ion Collisions6. Photoionization and Recombination7. Multi-Wavelength Emission Lines8. Absorption Lines and Radiative Transfer9. Stellar Properties, Opacities and Spectra10. Nebulae and H II Regions11. Active Galactic Nuclei12. Cosmology
Atomic Physics
Astrophysics