Asymmetric Absorption Profiles of Ly\alpha\ and Ly\beta\ in Damped Lyman Alpha Systems

TL;DR

This paper analyzes the asymmetric absorption profiles of Lyα and Lyβ lines in damped Lyman-alpha systems, revealing how quantum mechanical effects cause deviations from Lorentzian shapes and induce asymmetries depending on hydrogen column density.

Contribution

It provides a detailed quantum mechanical derivation of the asymmetry in Lyα and Lyβ absorption profiles, extending the understanding beyond the traditional Lorentzian approximation.

Findings

Lyα shows redward asymmetry in absorption profiles.

Lyβ exhibits blueward asymmetry.

Absorption center shifts are proportional to hydrogen column density.

Abstract

Damped Ly\alpha\ systems (DLAs) observed in the quasar spectra are characterized by a high neutral hydrogen column density $N_{HI}>2\times 10^{20}{\rm\ cm^{-2}}$. 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 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.