1. Atomic Physics of Lyman Alpha And Intergalactic Medium
Hee-Won Lee
Department of Astrnomy and Space Science, Sejong University
September 21, 2012

2. Contents Introduction – Quasar Absorption System, Cosmic Reionization
Atomic Physics : Kramers-Heisenberg Formula
Applications
3.1 Asymmetry in DLA profiles
3.2 Exact analysis of Gunn-Peterson Troughs
3.3 Polarized Lyman Alpha
4. Discussion

3. Introduction Quasar Absorption Systems
1) Ly alpha Forest ~ NHI < 1017 cm-2
2) Lyman Limit Systems NHI > 1017 cm-2
3) Damped Ly alpha Systems NHI > cm-2
4) Metal Systems ~ C, N, O Lines
5) Broad Absorption Line Systems ~ Quasar Wind

4. Quasar Spectra

5. Quasar Spectra
Lyman alpha forest may correspond to residual neutral hydrogen forming filametary structures with characteristic length scale of tens of kiloparsecs.
Damped Lyman alpha systems are galaxies that lie on the line of sight in front of the quasar

6. Cosmic Reionizaation
Quasar absorption systems are consistent with fully ionized intergalactic medium in the nearby universe.
Gunn-Peterson Troughs in high redshift quasars

7. Cosmic Reionization and Population III Objects
First stars and galaxies emit strong UV radiation.
2. More and more part of intergalactic medium gets ionized.
3. First stars are believed to be very massive due to lack of coolants during their star formation.

8. Gunn-Peterson Troughs
Gunn-Peterson Troughs: Due to neutral hydrogen in early universe, blueward of Lyman alpha is heavily absorbed.
Accurate atomic physics will be helpful in order to extract useful information from profiles

9. Atomic Physics of Hydrogen: Interaction with radiation
1. Matrix elements of dipole operator weighted by energy comprise the probability amplitude.
2. In the case of hydrogen, all the matrix elements are known analytically.
3. Exact atomic physical knowledge can be applied to interpret observational data.

10. Matrix Elements

11. Matrix Elements for Continuum States
Analytic continuation into complex plane in order to obtain the wavefunction for continuum states.

12. Dalgarno-Lewis Method and Exact Low Energy Expansion

13. Rayleigh Scattering Cross Section
For HI col density 1022 cm-2
Rayleigh scattering optical depth of unity corresponds to Δv=2x104 km/s.
This is comparable to the velocity scale of Broad Emission Line Region in Active Galactic Nuclei.
In the case of DLA, a careful treatment is necessary!

14. Images of DLA

15. HST Wide Field Camera 2 sub-pixelised image of a region 43 arcsec by 17 arcsec around the quasar PKS (marked Q), showing the three galaxies S1, S2, S3. The upper panel is a weighted average of the data for the three filters, from all 30 orbits. The lower panel is the same image convolved with a Gaussian profile of sigma=1.3 sub-pixel. An inset panel shows a small region to the S of the quasar after subtraction of the quasar image, revealing the image of S1.

16. Voigt Profile Fitting Analysis
1. Voigt function is given by convolution of a Gaussian and a Lorentzian.
2. A Lorentzian function represents a natural profile near a resonance transition in the rest frame of the atom.
3. A real atom has infinietely many levels, so that a natural profile deviates from a Lorentzian far away from a resonance

17. Analysis Faithful to Atomic Physics
1. No atom is not a two-level system. Need to consider the contribution from other levels.
2. This leads to cross section that deviates from the simple Lorentzian.
3. One can expand the Kramers-Heisenberg formula in terms of Δω/ωLyα. The leading term is Lorentzian, but the next term provides redward deviation of cross section.
4. This effect is important in high column system including DLAs.

18. Cross section blueward of line center is smaller that redward in the first order approximation!

19. Result 2
Blow-up of Red Part
Blow-up of Blue Part

20. Result 3
The line center of of damped wing profile appears redward of true Ly a center.
2. For NHI= cm-2, the apparent shift is 0.2 .
3. For NHI= cm-2 the apparent shift is 1 , which is quite measurable.

21. Result 1 실선: K-H Formula 점선: Voigt Fit
Transmission coefficient for N_HI=5X1021 cm-2.
Dotted lines are shifted from the atomic line center by an amount Angstrom.

22. Kinematics of
a DLA galaxy

23. Scattering Cross Section near Ly beta
In a similar way we may expand K-H formula in the vicinity of Ly beta.
We also have to consider additional scattering channel that gives rise to H alpha emission.
More significant deviation from Lorentzian.
Do we have Damped Lyman Beta systems?

24. Neutral Fraction in High z Intergalactic Medium
Hard to quantify because Ly alpha is very optically thick.
Only a little amount of neutral hydrogen is sufficient to suppress blueward of Lyman alpha.
Require knowledge detailed information about kinematics, photoionization process with the availability of high S/N, high resolution spectra.

25. Quasar with z=7.085
1. The luminous quasar ionizes its neighboring space (proximity effect) .
2. Fractional transmission implies the absorption of damping wing of Lyman alpha.
3. The universe at z~7 is partially neutral.

26. Gunn-Peterson Profile
Peebles introduced a heuristic formula.

27. Radiative Transfer of Resonance Line Photons
Transfer of resonance line photon is summarized by diffusion in real and frequency space.
A large number of local resonance scattering
Diffusion in frequency space results in line photon out of resonance
Long excursion of wing photons
Escape or re-entry of resonance

28. Monte Carlo Procedure Three kinds of scattering for Lyman alpha:
Resonance scattering with 1/2(s)-1/2(p)
Resonance scattering with
1/2(s)-3/2(p)
3. Wing scattering (off resonance scattering)

29. Subaru Image and Spectrum of LAE galaxy (z=5.69)

30. Radiative Transfer of Resonance Line Photons
Escape is affected significantly by the kinematics of the medium.
If the medium is expanding, then blue photons cannot escape from the region due to resonance scattering by receding atoms.
Multiple peaks are obtained due to bouncing photons

31. Polarization of Scatterd Ly alpha
Resonance scattering with 1s1/2-2p1/2
- No polarization
Resonance scattering with 1s1/2-2p3/2
- Max. Polarization 3/7
Wing scattering (or Rayleigh scattering)
- Max. Polarization 1
2p1/2
1s1/2

32. Polarized Lyman alpha Hayes et al, 2011, Nature
Polarimetry of Lyman alpha of LAB1

33. Polarized Lyman alpha
The polarized fraction (P) increases to ~20 per cent at a radius of 45 kpc, forming an almost complete polarized ring.
The detection of polarized radiation is inconsistent with the in situ production of Ly-alpha photons.
Photons are produced in the galaxies hosted within the nebula, and re-scattered by neutral hydrogen.

34. Polarization of Thomson Scattered Radiation in a Plane-Parallel Medium
Classic Work by Chandrasekhar
When tau -> infinity, P ->11.7 % in the direction perpendicular to the slab normal
In the presence of absorptive processes (bound-free or dust), the polarization weakens.

35. Polarized Ly alpha emergent from a thick slab

36. Polarized Lyman alpha emergent from thick slabs

37. Discussion
Asymmetry may be seen in an absorbing system with NHI > 4x1022 cm-2
May be important in investigating kinematics of DLA’s
Should continue the study for Ly alpha and Ly beta
Can be applied to Rayleigh scattering processes