Asymmetric Deviation of the Scattering Cross Section around Ly$\alpha$ by Atomic Hydrogen

Abstract

We investigate the asymmetry of the scattering cross section of radiation around Ly$\alpha$ by atomic hydrogen, which may be applied to analyses of scattering media with high column neutral hydrogen densities including damped Ly$\alpha$ absorption systems of quasars. The exact scattering cross section is given by the Kramers-Heisenberg formula obtained from the fully quantum mechanical second-order time dependent theory, where, in the case of hydrogen, each matrix element is given in a closed analytical form. The asymmetric deviation of the scattering cross section from the Lorentzian near the line center is computed by expanding the Kramers-Heisenberg formula in terms of $\Delta \omega /{\omega }_{Ly\alpha }$,where ${\omega }_{Ly\alpha }$ is the angular frequency of the Ly$\alpha$ transition and $\Delta \omega$ is the deviation of incident radiation from ${\omega }_{Ly\alpha }$. To the first order of $\Delta \omega /{\omega }_{Ly\alpha }$, we obtain $\sigma (\omega )={\sigma }_T(0.5f_{12}{\omega }_{Ly\alpha }/\Delta \omega {)}^2(1-1.79\Delta \omega /{\omega }_{Ly\alpha })$, where ${\sigma }_T$ is the Thomson scattering cross section and $f_{12}=0.4162$ is the oscillator strength for the Ly$\alpha$ transition. With this deviation, the line center of the damped wing profile apparently shifts blueward of the true Ly$\alpha$ line center. In the case of a dampedLy$\alpha$ system with a H I column density $5\times 10^{21}\mathrm{c}{\mathrm{m}}^{-2}$, the apparent line center shift relative to the true center amounts to $0.2\mathring{\mathrm{A}}$ resulting in an underestimation of redshift by $\Delta z\sim 10^{-4}$. A measurable underestimation by an amount of $\Delta z\sim 10^{-3}$ is expected for absorbing systems with $N_{HI}\ge 4\times 10^{22}\mathrm{c}{\mathrm{m}}^{-2}$.

13 pages, 3 figures, ApJ in press

References in corpus (8)

• Evidence for Reionization at z ~ 6: Detection of a Gunn-Peterson Trough in a z=6.28 Quasar
• A Survey of z>5.7 Quasars in the Sloan Digital Sky Survey II: Discovery of Three Additional Quasars at z>6
• Reionization of the Intergalactic Medium and the Damping Wing of the Gunn-Peterson Trough
• On the Kinematics of the Damped Lyman Alpha Protogalaxies
• Discovery of Damped Lyman-Alpha Systems at Redshifts Less Than 1.65 and Results on their Incidence and Cosmological Mass Density
• Protogalactic Disk Models of Damped Lya Kinematics
• The Temperature and Opacity of Atomic Hydrogen in Spiral Galaxies
• Discovery of z=0.0912 and z=0.2212 Damped Lyman-alpha Absorption Line Systems Toward the Quasar OI 363: Limits on the Nature of Damped Lyman-alpha Galaxies

Cited by in corpus (5)

• The Physics of the Intergalactic Medium
• Deep Learning of Quasar Spectra to Discover and Characterize Damped Lya Systems
• Quasars as probes of cosmological reionization
• Asymmetric Absorption Profiles of Lyα and Lyβ in Damped Lyman Alpha Systems
• Centre Shift of the Raman Scattered He II $\lambda$ 4850 in the Symbiotic Star V1016 Cygni