[Paper Review] Radiative Transfer with Finite Elements II. Ly-alpha Line Transfer in Moving Media

E. Meinkoehn, Sabine Richling|ArXiv.org|Jun 26, 2002

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy15 references17 citations

TL;DR

This paper presents a 3D finite element method for solving Lyα line transfer in moving, inhomogeneous media with adaptive unstructured grids and first-order frequency discretization. It demonstrates that velocity fields like inflow, outflow, and rotation produce distinct double-peaked line profiles and characteristic patterns in 2D spectra—triangular for inflow/outflow and shear-like for rotation—enabling source identification in high-redshift galaxies with optical depths up to 10⁴.

ABSTRACT

A finite element method for solving the resonance line transfer problem in moving media is presented. The algorithm works in three spatial dimensions on unstructured grids which are adaptively refined by means of an a posteriori error indicator. Frequency discretization is implemented via a first-order Euler scheme. We discuss the resulting matrix structure for coherent isotropic scattering and complete redistribution. The solution is performed using an iterative procedure, where monochromatic radiative transfer problems are successively solved. The present implementation is applicable for arbitrary model configurations with an optical depth up to 10^(3-4). Results of Ly-alpha line transfer calculations for a spherically symmetric model, a disk-like configuration, and a halo containing three source regions are discussed. We find the characteristic double-peaked Ly-alpha line profile for all models with an optical depth > 1. In general, the blue peak of the profile is enhanced for models with infall motion and the red peak for models with outflow motion. Both velocity fields produce a triangular shape in the two-dimensional Ly-alpha spectra, whereas rotation creates a shear pattern. Frequency-resolved Ly-alpha images may help to find the number and position of multiple Ly-alpha sources located in a single halo. A qualitative comparison with observations of extended Ly-alpha halos associated with high redshift galaxies shows that even models with lower hydrogen column densities than required from profile fitting yield results which reproduce many features in the observed line profiles and two-dimensional spectra.

Motivation & Objective

• To develop a numerical method for 3D resonance line transfer in moving media with arbitrary geometry and velocity fields.
• To model Lyα emission in optically thick (τ ≤ 10⁴) configurations typical of high-redshift galaxies.
• To investigate how kinematics and geometry affect line profiles, frequency-resolved images, and 2D spectra.
• To enable identification of multiple Lyα sources via frequency-resolved imaging and spectral diagnostics.

Proposed method

• Uses a finite element method on unstructured 3D grids with adaptive refinement based on a posteriori error indicators.
• Implements frequency discretization via a first-order Euler scheme to handle Doppler shifts and scattering in moving media.
• Solves the radiative transfer equation in the comoving frame, including coherent and complete redistribution scattering.
• Applies an iterative solver to monochromatic problems, treating frequency dependence through successive frequency slices.
• Models extinction and scattering coefficients spatially dependent, with velocity fields defined via the Doppler operator.
• Uses the full 6D intensity field (x, n, ν) to capture angular and spectral transfer in three dimensions.

Experimental results

Research questions

• RQ1 How do global inflow and outflow motions affect the shape and asymmetry of Lyα line profiles in 3D media?
• RQ2 What spectral patterns emerge in 2D Lyα spectra for rotating versus radially moving media?
• RQ3 Can frequency-resolved Lyα images distinguish multiple sources in a single halo with complex kinematics?
• RQ4 How do optical depth and viewing angle influence the observed flux and spectral features in clumpy, asymmetric configurations?
• RQ5 To what extent can 3D radiative transfer modeling reproduce observed extended Lyα halos with lower-than-expected column densities?

Key findings

• All models with optical depth τ ≥ 1 produce the characteristic double-peaked Lyα line profile with a central absorption trough due to resonant scattering.
• Infall motion enhances the blue peak, while outflow motion enhances the red peak, breaking spectral symmetry.
• Global inflow or outflow produces a triangular pattern in 2D spectra, whereas rotation leads to a shear or banana-shaped emission pattern.
• Frequency-resolved Lyα images can help identify the number and positions of multiple sources in a single halo, especially when combined with 2D spectra.
• Even models with lower hydrogen column densities than required by profile fitting reproduce key features of observed high-redshift Lyα halos, including line profiles and 2D spectra.