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

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-Waller 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 >= 2; s-branch) or nd (n >= 3; 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-H > 10(21) 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 greater than or similar to 1000 km 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.