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Diffuse X-ray Emitting Plasma in the Galactic Center

Diffuse X-ray Emitting Plasma in the Galactic Center. Michael Muno (UCLA/Hubble Fellow). References (or, the really useful slide) (or, people who are more qualified to give this lecture).

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Diffuse X-ray Emitting Plasma in the Galactic Center

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  1. Diffuse X-ray Emitting Plasma in the Galactic Center Michael Muno (UCLA/Hubble Fellow)

  2. References(or, the really useful slide)(or, people who are more qualified to give this lecture) • R. Mewe “Atomic Physics of Hot Plasmas”, in X-ray Spectroscopy in Astrophysics, eds. Van Paradijs & Bleeker, Springer, 1988. • D. A. Liedhal, “Spectral Properties of Photoionized and Transient Plasmas”, ibid. • Lecture notes from F. Paerels • R. L. Liboff, Introductory Quantum Mecahnics, Addison-Wesley, 1992

  3. Outline • Introduction to spectral modeling • The physics of plasma models • Continuum processes • Interactions between electrons and ions • Ionization balance and line radiation • Lines from one- and two-electron ions • The mysterious hot plasma in the Galactic center

  4. N E X-rays from the Galactic Center: Point Sources in a Sea of Diffuse Emission Wang, Gotthelf, & Lang 2002; NASA/UMass 30 pc

  5. We can measure: Temperature (kT) Density (n) Ionization state Luminosity (L) We can derive: Pressure (P = nkT) Energy (E = 1/3 PV) Lifetime (E/L) These are used to find a source for the plasma: Supernova shocks winds from massive stars magnetic reconnection How Do We Discover the Origin of the Hot Plasma?

  6. The X-ray Spectrum

  7. Spectral Fitting (XSPEC, ISIS, Sherpa) Spectral Model (line rates, collisional cross sections) Data + Physical Model (geometry, kT, n) Instrumental Response Synthetic Spectrum Comparison (chi-squared)

  8. Spectral Fitting (XSPEC, ISIS, Sherpa) Spectral Model (line rates, collisional cross sections) Data + Physical Model (geometry, kT, n) Instrumental Response Synthetic Spectrum Comparison (chi-squared)

  9. The Spectral Model • Continuum: • Bremsstrahlung • Free-bound • Two-photon • Line emission • Dielectronic recombination

  10. Continuum Emission gtot has contributions from Bremsstrahlung, free-bound, and two-photon processes • Spectrum turns over at a frequency hn = kT. • Continuum intensity depends on n2.

  11. g Z+z g Z+z g g Z+z e- e- Two-photon (e.g. from 2s 2S1/2 for H) e- Free-bound Bremsstrahlung Continuum Processes

  12. Temperature Dependence • Bremsstrahlung dominates at high kT & low n • Free-bound dominates at low kT & high n • Two photon is only seen when collisional de-excitation is negligible, i.e. at low densities. Å

  13. Line Emission: Basic Energetics (Al, P, Cl, K, and metals like Sc and Mn are rare)

  14. How Do Electrons Photons, and Ions Interact? Part 1. e- e- e- e- e- Collisional excitation / de-excitation Collisional ionization Three-body recombination No photons, but changes energy levels or ionization state.

  15. How Do Electrons Photons, and Ions Interact? Part 2. e- e- Photoexcitation / Radiative decay Photo-ionization Radiative recombination Photons cause changes energy levels or ionization state.

  16. “spectator” e- e- e- a satellite line Auger ionization How Do Electrons Photons, and Ions Interact? Part 3. e- or e- Dielectronic recombination leads to. . . More two-electron processes, but a bit more complex. I had such nice symmetry. Too bad two-e- excitations are rare. . .

  17. e- e- Auger ionization How Do Electrons Photons, and Ions Interact? Part 4. e- or Collisional or photo-excitation leads to. . . fluorescence Processes important in low-ionization states.

  18. Solving Ionization Balance • Ionization cross sections are determined using perturbation theory and experiments. • Recombination rates are determined from ionization cross sections, using the principle of detailed balance (Milne equations). ionization recombination

  19. Regimes of Ionization • High density: each process and its inverse occurs. • Collisional ionization equilibrium (CIE): every excitation followed by radiative decay. • Non-equilibrium ionization (NIE): sudden heating causes the electron temperature to be hot compared to the ionization state. • Photoionization: strong radiation field causes the ionization state to be much higher than the electron temperature.

  20. Regimes of Ionization • High density: • Photoionization:

  21. Regimes of Ionization • Collisional ionization equilibrium (CIE): The X-ray emitting plasma, with n<1 cm3, is certainly diffuse enough to be in the CIE limit.

  22. Regimes of Ionization • Non-equilibrium ionization (NIE):

  23. CIE: The Coronal Model • Plasma is optically thin. • Most ions are in their ground states. • Radiative losses are balanced by mechanical heating. • Plasma electrons and ions are Maxwellian with a single temperature • Gas assumed to be in a steady state.

  24. Solving Ionization Balance:Coronal Approximation Steady state Most ions are in the ground state Ionization balance only depends on temperature (to first order).

  25. Temperature & Ionization States • An ion of a given species will be most common when the temperature is close to the ionization energy. Mewe (1997)

  26. Line Transition Rates Line emissivity • See Mewe (1997) for discussion of the rates and cross-sections - that’s where the work is!

  27. Line Transition Rates radiation recombination collisional de-excitation excitation • See Mewe (1997) for discussion of the rates and cross-sections - that’s where the work is! ionization ionization collisional de-excitation radiation excitation

  28. Line Transition Rates:Coronal Approximation steady state Collisional excitation is the only way into an excited state Radiation is the only way out

  29. Coronal Line Emission • Of course, all those terms we ignore are interesting for identifying, e.g., density effects.

  30. Energy Levels: What Lines Will We See? • Solutions to the non-relativistic Shrodinger equation are Laguerre polynomials, with: • Principle quantum number n • Angular momentum l≤n-1 • Spin m = (-l, +l) • Quantum numbers m, l are degenerate in energy in this approximation.

  31. Fine Structure Relativistic equation Spin-orbit coupling Fine structure energy levels • Considering relativistic effects and spin-orbit coupling breaks the degeneracy in l, m. • We use the quantum numbers n, l, s, j (=l+s).

  32. Spectroscopic Notation • To start, assume all electrons (except maybe the outer one) are in the ground state. • We denote the electronic state by: |L-S| < J < L+S n1l1…nili2S+1LJ configuration of each electron total orbital angular momentum S,P,D,F,G,H… electron spin one electron: S=1/2 two electrons: S=0,1

  33. 2p 2P3/2 2s 2S1/2 2p 2P1/2 1s 2S1/2 One Electron Atom E Doublets

  34. 1s2p 1P1 1s2s 3S1 1s2s 1S0 1s21S0 Two Electron Atom 1s2p 3P0,1,2 E Singlets Triplets

  35. Selection Rules for Radiation • Can also be understood based on the conservation of angular momenum, since photons have spin 1. • Can be derived using time-dependent perturbation theory, or equivalently considering the mean position of an electron:

  36. 2p 2P3/2 2s 2S1/2 2p 2P1/2 1s 2S1/2 One Electron Atom Dl=1 Dm=-1,1 E Dl=0 Dm=-1,0,1 Dl=1 Dm=-1,0,1

  37. 2p 2P3/2 2s 2S1/2 E1 2p 2P1/2 2g/M1 E1 1s 2S1/2 One Electron Atom E

  38. 1s2p 1P1 1s2s 3S1 1s2s 1S0 1s21S0 Two Electron Atom 1s2p 3P2 E1 E M2 1 0 E1 2g 2g M1 Transition rules depend on the strength of the LS coupling. Those above are for strong coupling, as appropriate for high-Z metal ions.

  39. 1s2p 1P1 1s2s 3S1 1s2p 3P2 1s2s 1S0 1 0 w y+x z 1s21S0 Two Electron Atom 2g continuum w: resonance y+x: intecombination z: forbidden

  40. 1s2p 1P1 1s2s 3S1 2p 2P3/2 3p 2P3/2 1s2p 3P2 1s2s 1S0 1/2 1/2 2s 2S1/2 1 0 b R I F a 1s21S0 R He-like H-like F 1s 2S1/2 a Photoelectric edge b I Energy Lines from H- & He-like Ions

  41. The X-ray Spectrum We see He-like and H-like ion lines. At CCD resolution, the He-like triplets are blended.

  42. Diagnostics: Temperature • Continuum shape. • Ratio of lines from ions of the same element. • Lines from same ion.

  43. Diagnostics: Abundance • Compare lines from different atoms. • Compare line strength to continuum.

  44. R I F He-like Diagnostics: Density • Density-sensitive lines (ne>108 cm-3). • Emission measure.

  45. “spectator” e- Diagnostics: Ionization Balance • Compare continuum temperature to charge distribution. • Fluorescence or satellite lines from Li-like ions.

  46. 5 pc Chandra Observations of the Galactic Center

  47. 5 pc Arches & Quintuplet: ~10 pc North Neutral Fe Filaments Sgr A East Sgr A* Outflow

  48. Chandra Observations of the Galactic Center

  49. 5 pc Arches & Quintuplet: ~10 pc North IRS 16 & Sgr A* • kT = 0.8 keV • L = 20 pc • Worb = (6 105 y)-1 The soft plasma is quite young.

  50. Properties of the Galactic Center Diffuse X-ray Emitting Plasma

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