Atomic Physics and the Kramers-Heisenberg Formula for Ly Alpha. Hee-Won Lee Department of Physics and Astrnomy Sejong University January 24, 2019

Transcription

1 Atomic Physics and the Kramers-Heisenberg Formula for Ly Alpha Hee-Won Lee Department of Physics and Astrnomy Sejong University January 24, 2019

2 Contents 1. Introduction Quasar Absorption Systems and Cosmic Reionization 2. Atomic Physics : Kramers-Heisenberg Formula 3. 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 ~ N HI < cm -2 2) Lyman Limit Systems N HI > cm -2 3) Damped Ly alpha Systems N HI > cm -2 4) Metal Systems ~ C, N, O Lines 5) Broad Absorption Line Systems ~ Quasar Wind

4 Quasar Spectra

5 1. Lyman alpha forest may correspond to residual neutral hydrogen forming filametary structures with characteristic length scale of tens of kiloparsecs. 2. Damped Lyman alpha systems are galaxies that lie on the line of sight in front of the quasar Quasar Spectra

6 1. Quasar absorption systems are consistent with fully ionized intergalactic medium in the nearby universe. 2. Gunn-Peterson Troughs in high redshift quasars

7 1. 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 1. Gunn-Peterson Troughs: Due to neutral hydrogen in early universe, blueward of Lyman alpha is heavily absorbed. 2. Accurate atomic physics will be helpful in order to extract useful information from profiles

9 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.

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

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13 Rayleigh Scattering Cross Section For HI col density cm -2 Rayleigh scattering optical depth of unity corresponds to Δv=2x10 4 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/ω Lyα. 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!

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20 Result 2 Blow-up of Red Part Blow-up of Blue Part

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

22 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.

23 Kinematics of a DLA galaxy

24 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?

25 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.

26 Quasar with z= 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.

27 Peebles introduced a heuristic formula.

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31 Cross Section Asymmetry around Ly alpha and beta

32 Cross section asymmetry

33 Asymmetry Profile of DLA

34 Asymmetric Profile of DLA

35 DLAs Observed by Noterdaeme et al. 2015

36 Gunn-Peterson troughs

37 Discussion 1. Asymmetry may be seen in an absorbing system with N HI > 4x10 22 cm May be important in investigating kinematics of DLA s 3. Should continue the study for Ly alpha and Ly beta 4. Can be applied to Gunn-Peterson troughs and Red Ly alpha profiles in the Reionizaiton era