Rayleigh and Raman scattering cross-sections and phase matrices of the ground-state hydrogen atom, and their astrophysical implications

TL;DR

This paper derives explicit formulas for Rayleigh and Raman scattering of hydrogen, showing how Raman scattering can produce broad emission features that mimic astrophysical phenomena, and discusses how to distinguish these effects observationally.

Contribution

It provides new analytical expressions for hydrogen scattering phase matrices and explores their astrophysical implications, especially in line broadening and polarization.

Findings

Raman scattering can produce broad emission features mimicking Doppler-broadened lines.

The phase matrix of Raman s-branch scattering matches Thomson scattering.

D-branch Raman scattering results in depolarized features.

Abstract

We present explicit expressions for Rayleigh and Raman scattering cross-sections and phase matrices of the ground $1s$ state hydrogen atom based on the Kramers-Heisenberg dispersion formula. The Rayleigh scattering leaves the hydrogen atom in the ground-state while the Raman scattering leaves the hydrogen atom in either $ns$ ($n\geq2$; $s$-branch) or $nd$ ($n\geq3$; $d$-branch) excited state, and the Raman scattering converts incident ultraviolet (UV) photons around the Lyman resonance lines into optical-infrared (IR) photons. We show that this Raman wavelength conversion of incident flat UV continuum in dense hydrogen gas with a column density of $N_{\text{H}} > 10^{21}~\text{cm}^{-2}$ can produce broad emission features centred at Balmer, Paschen, and higher-level lines, which would mimic Doppler-broadened hydrogen lines with the velocity width of $\gtrsim 1,000~\text{km}~\text{s}^{-1}$ that could be misinterpreted as signatures of Active Galactic Nuclei, supernovae, or fast stellar winds. We show that the phase matrix of the Rayleigh and Raman $s$-branch scatterings is identical to that of the Thomson scattering while the Raman $d$-branch scattering is more isotropic, thus the Paschen and higher-level Raman features are depolarized compared to the Balmer features due to the flux contribution from the Raman $d$-branch. We argue that observations of the line widths, line flux ratios, and linear polarization of multiple optical/IR hydrogen lines are crucial to discriminate between the Raman-scattered broad emission features and Doppler-broadened emission lines.