Asymmetric Deviation of the Scattering Cross Section around Lyα by Atomic Hydrogen

We investigate the asymmetry of the scattering cross section of radiation around Lyα by atomic hydrogen, which may be applied to analyses of scattering media with high column neutral hydrogen densities including damped Lyα 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 ∆ω/ωLyα, where ωLyα is the angular frequency of the Lyα transition and ∆ω is the deviation of incident radiation from ωLyα. To the first order of ∆ω/ωLyα, we obtain σ(ω) = σT (0.5f12ωLyα/∆ω) (1 − 1.79∆ω/ωLyα), where σT is the Thomson scattering cross section and f12 = 0.4162 is the oscillator strength for the Lyα transition. With this deviation, the line center of the damped wing profile apparently shifts blueward of the true Lyα line center. In the case of a damped Lyα system with a H I column density 5× 10 cm, the apparent line center shift relative to the true center amounts to 0.2 Å resulting in an underestimation of redshift by ∆z ∼ 10. A measurable underestimation by an amount of ∆z ∼ 10 is expected for absorbing systems with NHI ≥ 4× 10 22 cm.