Accurate Stellar Opacities and the Solar Abundance Problem

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 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, Justin Oelgoetz, Hong Lin Zhang Russ Pitzer, Mike Mrozik Jian Wang, Kaile Li, Neil Jenkins

Atomic Astrophysics: Stellar Structure Stellar Envelope: RZ + CZ Atmosphere + Corona Isolated atoms + plasma interactions Convection Zone (CZ) (Seaton, Yu, Mihalas, Pradhan 1994) Radiative Zone (RZ) Nuclear Core Drake et al. 2005 (Nature 436/Chandra)

Radiation controls heat transport in solar interior T(e. V) ne (cm-3) • boundary position depends on transport • measured with helioseismology r/R 0 54 1 x 1022 0. 90 182 9 x 1022 0. 7133 293 4 x 1023 0. 55 Solar model : J. N. Bahcall et al, Rev. Mod. Phys. 54, 767 (1982) 1360 6 x 1025 0 radiation convection Transport depends on opacity, composition, ne, Te Courtesy: 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 3 D 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 Data www. 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 E 1 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/k. R = m B(u) / k(u) du Harmonic Mean where u=hn/k. T B(u) = [15/p 4] u 4 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.

The Opacity Project: 1983 -2005 • First complete results 1994 OP 1 (SYMP: Seaton, Yu, Mihalas, Pradhan, MNRAS, 266, 805, 1994) • OP 1 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) http: //opacities. osc. edu

Opacity Project (OP 2007) and OPAL Rosseland Mean Opacities

OP vs. OPAL % Differences in Rosseland Mean Opacities Log R = -3 Base of the Solar Convection Zone Maximum difference OP-OPAL ~ 3% However……. Delahaye & Pinsonneault (2006) OLD (OP 1) Envelope EOS only, and Without Inner-shell Processes New OP Extended EOS, and including Inner-shell Processes

Radiative Acceleration The radiative acceleration for the ith element in terms of the Rosseland Mean Opacity is grad = m k. R 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).

Radiative Accelerations: OP vs OPAL Comparison OPOPAL For a given stellar structure which Simulates HB or intermediate mass stars Trend: Z Diff. ~ BCZ (Base of Convection Zone) Delahaye & Pinsonneault 2005 Ap. J 625, 563

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 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

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

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

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)

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

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

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 Spectroscopy Anil Pradhan and Sultana Nahar (Cambridge University Press 2009) CONTENTS (Chapters) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 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