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