2009MNRAS.400.2153L

Using a Monte Carlo technique, we compute the profiles and linear polarization of Raman-scattered Heii λ6545 in young planetary nebulae. We assume that the Heii emission region is a rotating ring surrounded by a cylindrical neutral shell. We also assume that the Heii emission line is characterized by the rotation speed of the emission ring convolved with the turbulent speed, whereas the scattering region is allowed to expand or rotate with respect to the central star. We provide fitting formulae for the total and Raman scattering cross-sections around Lyβ up to the first order of λ - λ₀ with λ₀being the wavelength of Heii λ1025. For small velocity scales associated with the emission region, the linear degree of polarization as a function of wavelength bends convex upwards for a rotating scattering region, whereas an opposite behaviour is obtained for an expanding scattering region. For large turbulent and bulk velocity scales of the emission region, the linear degree of polarization decreases almost linearly for both models. The redwards decrease of the linear degree of polarization is a result of the increase of the Raman scattering optical depth towards the resonance of atomic hydrogen. The slope of the linear degree of polarization can be a useful diagnostic to find the Hi column density near N_Hi= 10²⁰/cm2. We propose that linear spectropolarimetry of Raman-scattered Heii may put strong constraints on N_Hi to lift the degeneracy problem in the line profile involving the covering factor and N_Hi.