treatment of scattering around H I Lyman lines (trac #257)

reported by: @CloudyLex

Asymmetric Absorption Profiles of Ly? and Ly? in Damped Lyman Alpha Systems

Hee-Won Lee
(Submitted on 2 Jun 2013)
Damped Ly\alpha\ systems (DLAs) observed in the quasar spectra are characterized by a 
high neutral hydrogen column density $N_{HI}>2\times 10^{20}{\
m\ cm^{-2}}$. The 
absorption wing profiles are often fitted using the Voigt function due to the fact that the 
scattering cross section near resonant line center is approximately described by the 
Lorentzian function. Since a hydrogen atom has infinitely many $p$ states that participate
 in the electric dipole interaction, the cross section starts to deviate from the Lorentzian in 
an asymmetric way in the line wing regions. We investigate this asymmetry in the 
absorption line profiles around Ly\alpha\ and Ly\beta\ as a function of the neutral 
hydrogen column density $N_{HI}$. In terms of $\Delta\lambda\equiv\lambda-
\lambda_\alpha$ we expand the Kramers-Heisenberg formula around Ly\alpha\ to find 
$\sigma(\lambda)\simeq (0.5 f_{12})^2\sigma_{T}(\Delta\lambda/\lambda_\alpha)^{-2}
[1+3.792 (\Delta\lambda/\lambda_\alpha)]$, where $f_{12}$ and $\sigma_T$ are the 
oscillator strength of Ly$\alpha$ and the Thomson scattering cross section, respectively. In
 terms of $\Delta\lambda_2\equiv\lambda-\lambda_\beta$ in the vicinity of Ly\beta, the 
total scattering cross section, given as the sum of cross sections for Rayleigh and Raman 
scattering, is shown to be $\sigma(\lambda)\simeq \sigma_T(0.5f_{13})^2(1+R_0) 
(\Delta\lambda_2/\lambda_\beta)^{-2}[1-24.68(\Delta\lambda_2/\lambda_\beta)]$ with 
$f_{13}$ and the factor $R_0=0.1342$ being the oscillator strength for Ly\beta\ and the 
ratio of Raman cross section to Rayleigh cross section, respectively. A redward asymmetry 
develops around Ly\alpha\ whereas a blue asymmetry is obtained for Ly\beta. The 
absorption center shifts are found to be almost proportional to the neutral hydrogen 
column density.

Comments:   30 pages, 8 figures, 3 tables, accpeted for publication in ApJ
Subjects:   Cosmology and Extragalactic Astrophysics (astro-ph.CO)
Cite as:    arXiv:1306.0181 [astro-ph.CO]
    (or arXiv:1306.0181v1 [astro-ph.CO] for this version)

Submission history
From: Hee-Won Lee [view email] 
[v1] Sun, 2 Jun 2013 07:37:59 GMT (69kb)

Migrated from https://www.nublado.org/ticket/257

{
    "status": "new",
    "changetime": "2019-02-04T13:07:06Z",
    "_ts": "1549285626580696",
    "description": "{{{\nAsymmetric Absorption Profiles of Ly? and Ly? in Damped Lyman Alpha Systems\n\nHee-Won Lee\n(Submitted on 2 Jun 2013)\nDamped Ly\\alpha\\ systems (DLAs) observed in the quasar spectra are characterized by a \nhigh neutral hydrogen column density $N_{HI}>2\\times 10^{20}{\\\nm\\ cm^{-2}}$. The \nabsorption wing profiles are often fitted using the Voigt function due to the fact that the \nscattering cross section near resonant line center is approximately described by the \nLorentzian function. Since a hydrogen atom has infinitely many $p$ states that participate\n in the electric dipole interaction, the cross section starts to deviate from the Lorentzian in \nan asymmetric way in the line wing regions. We investigate this asymmetry in the \nabsorption line profiles around Ly\\alpha\\ and Ly\\beta\\ as a function of the neutral \nhydrogen column density $N_{HI}$. In terms of $\\Delta\\lambda\\equiv\\lambda-\n\\lambda_\\alpha$ we expand the Kramers-Heisenberg formula around Ly\\alpha\\ to find \n$\\sigma(\\lambda)\\simeq (0.5 f_{12})^2\\sigma_{T}(\\Delta\\lambda/\\lambda_\\alpha)^{-2}\n[1+3.792 (\\Delta\\lambda/\\lambda_\\alpha)]$, where $f_{12}$ and $\\sigma_T$ are the \noscillator strength of Ly$\\alpha$ and the Thomson scattering cross section, respectively. In\n terms of $\\Delta\\lambda_2\\equiv\\lambda-\\lambda_\\beta$ in the vicinity of Ly\\beta, the \ntotal scattering cross section, given as the sum of cross sections for Rayleigh and Raman \nscattering, is shown to be $\\sigma(\\lambda)\\simeq \\sigma_T(0.5f_{13})^2(1+R_0) \n(\\Delta\\lambda_2/\\lambda_\\beta)^{-2}[1-24.68(\\Delta\\lambda_2/\\lambda_\\beta)]$ with \n$f_{13}$ and the factor $R_0=0.1342$ being the oscillator strength for Ly\\beta\\ and the \nratio of Raman cross section to Rayleigh cross section, respectively. A redward asymmetry \ndevelops around Ly\\alpha\\ whereas a blue asymmetry is obtained for Ly\\beta. The \nabsorption center shifts are found to be almost proportional to the neutral hydrogen \ncolumn density.\n\nComments:\t30 pages, 8 figures, 3 tables, accpeted for publication in ApJ\nSubjects:\tCosmology and Extragalactic Astrophysics (astro-ph.CO)\nCite as:\tarXiv:1306.0181 [astro-ph.CO]\n \t(or arXiv:1306.0181v1 [astro-ph.CO] for this version)\n\nSubmission history\nFrom: Hee-Won Lee [view email] \n[v1] Sun, 2 Jun 2013 07:37:59 GMT (69kb)\n}}}",
    "reporter": "gary",
    "cc": "",
    "resolution": "",
    "time": "2013-06-05T00:10:42Z",
    "component": "radiative transfer",
    "summary": "treatment of scattering around H I Lyman lines",
    "priority": "good to do",
    "keywords": "",
    "version": "trunk",
    "milestone": "no milestone",
    "owner": "nobody",
    "type": "enhancement"
}

cloudy-astrophysics / bug-tracker-migration-test

treatment of scattering around H I Lyman lines (trac #257) #259