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Advances in Atomic Processes and X-Ray Diagnostics for Astrophysical Plasmas

This paper explores the latest developments in atomic processes, theories, and datasets relevant to X-ray diagnostics in astrophysical plasmas. Key topics include particle distributions in laboratory and astrophysical sources, resonances, and electron distribution functions. It discusses advanced theoretical frameworks such as close coupling and distorted wave methods, as well as significant projects like the Opacity Project and Iron Project. Insights into the spectral formation and analysis of various plasma sources are also presented, with applications to stellar coronae and active galactic nuclei.

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Advances in Atomic Processes and X-Ray Diagnostics for Astrophysical Plasmas

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  1. Atomic Processes, Theory, and DataFor X-Ray Plasmas Anil Pradhan, Sultana Nahar Guo-Xin Chen (ITAMP), Franck Delahaye Justin Oelgoetz, Hong Lin Zhang (LANL) (www.astronomy.ohio-state.edu/~pradhan) X-ray Diagnostics For Astrophysical Plasmas November 15-17, 2004 ITAMP, Harvard-Smithsonian Center For Astrophysics

  2. Atomic Processes, Theories, and Data • Processes: Particle Distributions in Lab and Astro Sources (Lab Astrophysics)  Resonances and Electron Distribution Functions in EBIT experiments • Theories: Electron Impact Excitation  Close Coupling vs. Distorted Wave • Data: Opacity Project and Iron Project  Excitation, Photoionization, Recombination, A-coefficients  X-ray Spectral Models • He-like ions in transient plasmas (e.g. X-Ray flares)  The Movie !

  3. Relativistic and Non-Relativistic R-matrix Codes For Atomic Processes Large-scale calculations with high precision and self-consistency

  4. Atomic Data For X-Ray Spectral Diagnostics • Laboratory Plasmas Sources: - Electron-Beam-Ion-Traps (EBIT) - Tokamaks - Magnetic Z-pinch and other ICF devices • Astrophysical Sources - Stellar Coronae - Active Galactic Nuclei - Supernova remnants • Are all these plasma sources the same ? • Are the line intensities and ratios the same ?

  5. Spectral Formation In Astro and Lab Sources • Particle Distribution: - Maxwellian  Most astrophysical cases - Non-Maxwellian  Tokamaks during heating phase (ECH, NBI, etc.), ‘runaway electrons’ in high-energy tail - Gaussian  EBIT (mono-energetic beam) - Bi-Maxwellian  Electron-ion storage rings • Radiation Field: - Stellar UV continuum  Blackbody Planck Function - Black Hole accretion  AGN, Non-thermal power-law L ~ E-a • Ionization Equilibrium or Non-Eqm: - Stationary - Transient (time-dependent)

  6. Benchmarking Laboratory and Astrophysical X-Ray Sources:Electron Impact Excitation (Chen etal., 2003) Ne- like

  7. Resonance and relativistic effects in prominent x-ray transitions

  8. Coupled Channel R-Matrix Theory vs. Distorted Wave Coupled Channel Distorted Wave • Includes only initial and final • channels in Eq. (1); no summation • Neglects channel coupling • Resonance states (intermediate • channels) NOT included in • wavefunction expansion • Limited number of resonances • may be considered in the • isolated resonance approximation • May not be adequate for highly • charged ions (weak transitions, • resonance effects) • 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) Review: Nahar and Pradhan (2004) • Significant effects are included • Infinite series of resonances are considered

  9. Resonance Effects on the 3F/3C Line Ratio R-Matrix 3F Collision Strength Line Ratio vs. Te Filled Squares - DW Filled Circles – Distorted Wave

  10. Fe XVII 3F/3C Line Ratio vs. Temperature: Theory and Observations Beiersdorfer et.al., ApJ, 2004 Chen et.al. (JPB,36,453,2003) The measured 3F/3C value ~ 0.7 from tokamaks and EBIT agrees with theory

  11. Fe XVII Collision Strengths:Resonances up to n = 3 and n = 4 complexes Filled Poiints: Distorted Wave Blue: Gaussian Average Red: n =3 resonances

  12. Line Ratios and Electron Distribution Functions (EDF) in X-Ray Sources • All Fe XVII cross sections averaged over both EDFs – Maxwellian and Gaussian (Chen and Pradhan 2004) • Different sets of line ratios computed from collisional-radiative model including n = 4 levels • Solution to 3s/3d problem: • 3s/3d = (3F+3G+3H) / (3C+3D+3E) • Line ratios are source-specific • Tokamak, EBIT, and astrophysical measurements depend on EDFs • EBIT results are gaussian; for benchmarking need: • - Precise beam shapes • - Higher resolution (many more energies) • Oscillations due to distribution of resonances • Recombination-Cascades

  13. Fe XVII 3s/3d Ratio: Theory and ObservationsChen and Pradhan (2004) • Maxwellian average – solid line; Gaussian average – solid red line • Filled Blue – LLNL EBIT; Open Blue – NIST EBIT • Open red circles – Solar (T~ 4MK); Filled green – Capella (Chandra); • Open green – “ (XMM) • Extreme left – other measurements

  14. Unified electron-ion recombination (RR+DR): R-Matrix Theory and Experiments Maxwellian Averaged Rate Gaussian Averaged X-sections Expt Theory Expt Rates agree to < 20% Theory: Pradhan et.al. (ApJL, 549, L265, 2001) Expt: Savin et.al. (ApJS, 123, 687, 1999)

  15. R-Matrix Opacity/Iron/RmaX Project Data(Links From www.astronomy.ohio-state.edu/~pradhan) • Collisional Data For all Fe ions (also Fe-group) • Radiative Data Photoionization Cross Sections and Transition Probablities for most astrophysically abundant ions, including inner-shell photo-excitation, opacities etc. • New self-consistent photoionization and unified (RR+DR) electron-ion recombination cross sections and rates for over 50 ions (S. Nahar and collaborators), e.g. for X-ray applications - Li-, He-like: CIV/CV, OVI/OVII,…..,FeXXIV/FeXXV - Including total and level-specific recombination rate coefficients up to n<=10 - Unified recombination cross sections  DR spectrum • Electronic On-line Database: TIPTOPBASE and OPSERVER(C. Mendoza and collaborators)

  16. Code XRAD – Theoretical X-ray Absorption Spectrum • The Opacity Project and Iron Project Data (> 107 lines) • Ab initio data (theoretical energies, f-values, photoionization xsects, etc.) Fe L-shell opacity, ~ 1 keV features • Completeness of atomic data • General behavior and features • No detailed fitting

  17. XRAD Simulation of AGN MCG6-15-30 • Code XRAD uses ab initio • theoretical energies • No fitting of individual • features • Vary Te, Ne, Nz • Overall features obtained XRAD XSPEC OBS

  18. Code HELINE (Oelgoetz and Pradhan 2001,2004)Stationary and Transient Spectra of He-like Ions Time-Dependent Coupled Equations for Level Populations Collisional Ionization, Recombination, and Photoexcitation (thermal and non-thermal radiation fields) Collisional, Photoionized, and Hybrid Plasmas For Fe XXV the Helium “triplet” becomes a “quartet” with dielectronic satellites f,i,r z,x,y,w

  19. The 6.7 keV Ka complex of Fe XXVIonization Fractions of Iron In Different Plasma Sources Black Body Non-thermal Power-Law Coronal Eqm. Log Te

  20. Time-dependent Temperature, Radiation, and Ionization Fractions Electron Temperature Te(t) Example: X-Ray flare in accretion disc around a Black Hole Ionization Parameter U(t) = L / Ne Ionization Fractions coll. Ionization Te(t) + Photoionization U(t) ASTRO-E2 Hybrid: Te(t) & U(t) Time (Seconds)

  21. Time Evolution of Transient Plasmas Collisional (Lab) Photoionized Hybrid (Astrophysical) Dielectronic satellites dominate at early times in collisional case; very weak in photoionized case. Recombination dominates in all cases at late times t = 480 s t = 1080 s t = 1320 s t = 1560 s t = 1920 s Spectral Inversion z  w t = 2400 s Photon Energy (keV)

  22. Time-Dependent Photoionization and Collisional Ionization:The 6.7 KeV Ka Complex of He-like Fe XXV(Oelgoetz and Pradhan 2004)

  23. Time-Dependent Photoionization and Collisional Ionization:The 6.7 KeV Ka Complex of He-like Fe XXV(Oelgoetz and Pradhan 2004) PHOTOZN (U ~ 100) DOMINATES AT EARLY TIMES; DI-ELEC. SAT. (DES) q (1s2s2p) STRONG w q r t v,u y z

  24. Time-Dependent Photoionization and Collisional Ionization:The 6.7 KeV Ka Complex of He-like Fe XXV(Oelgoetz and Pradhan 2004) w IONIZN LAGS BEHIND RECOMBN; SMALL DES z y x j,r k

  25. Time-Dependent Photoionization and Collisional Ionization:The 6.7 KeV Ka Complex of He-like Fe XXV(Oelgoetz and Pradhan 2004) SPECTRAL INVERSION Z <--> W DURING RECOMBN PHASE AT LATE TIMES z x w y

  26. Conclusion • The Iron Project and the RmaX Project are providing large-scale atomic data of high accuracy using the R-matrix method for electron impact excitation, photoionization, unified electron-ion recombination, and transition probabilities in a self-consistent ab initio formulation • TIPTOPBASE  Electronic database • Spectral diagnostics and interpretation of plasma conditions my be source-specific • Electron distribution functions need to be known • Relativistic and resonance effects are crucial • Transient X-ray sources require new physical approximations, independent of global or local energy balance

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