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Asymmetric Absorption Profiles of Lyα and Lyβ in Damped Lyman Alpha Systems

Damped Lyα systems (DLAs) observed in the quasar spectra are characterized by a high neutral hydrogen column density $N_{HI}>2\times 10^{20}{\rm\ cm^{-2}}$. 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 Lyα and Lyβ as a function of the neutral hydrogen column density $N_{HI}$. In terms of $Δλ\equivλ-λ_α$ we expand the Kramers-Heisenberg formula around Lyα to find $σ(λ)\simeq (0.5 f_{12})^2σ_{T}(Δλ/λ_α)^{-2}[1+3.792 (Δλ/λ_α)]$, where $f_{12}$ and $σ_T$ are the oscillator strength of Ly$α$ and the Thomson scattering cross section, respectively. In terms of $Δλ_2\equivλ-λ_β$ in the vicinity of Lyβ, the total scattering cross section, given as the sum of cross sections for Rayleigh and Raman scattering, is shown to be $σ(λ)\simeq σ_T(0.5f_{13})^2(1+R_0) (Δλ_2/λ_β)^{-2}[1-24.68(Δλ_2/λ_β)]$ with $f_{13}$ and the factor $R_0=0.1342$ being the oscillator strength for Lyβ and the ratio of Raman cross section to Rayleigh cross section, respectively. A redward asymmetry develops around Lyα whereas a blue asymmetry is obtained for Lyβ. The absorption center shifts are found to be almost proportional to the neutral hydrogen column density.