Numerical methods for radiative transfer in circumstellar environnements

Overview & Synopsis

The study of the radiative transfer problem is crucial for the characterisation of circumstellar environments. Radiative processes play a major role in the determination of physical observables of these astrophysical objects, such as the temperature, abundances, velocity fields, etc. The description of the frequency dependent and multi-dimensional radiation field is both a theoretical and numerical challenge, especially in the presence of scattering. The development of approximate descriptions and/or numerical methods is necessary in order to efficiently and accurately describe the radiation. This thesis investigate one approximate and one numerical method for solving the radiative transfer equation, coupled with the radiative equilibrium equation, in axis-symmetric circumstellar envelope of dust.We first considered one of these approximate descriptions, the Flux-Limited Diffusion (FLD) which recasts the radiative transfer equation into a non-linear diffusion equation, asymptotically exact in both optically-thin and thick regimes. One important aspect for the accuracy of the method lies in the derivation of appropriate boundary conditions. We derived non-linear mixed boundary conditions aimed to be accurate enough in all optical regimes. We implemented in a code the FLD approximation together with our derived boundary conditions and tested their accuracy by comparing our results (temperature profiles and spectral energy distributions) with benchmarks from literature, for spherically-symmetric and for axis-symmetric configurations. Our results showed a very good agreement for the spherically symmetric case, enabling astrophysical applications for objects compatible with this symmetry. For the axis-symmetric case, the agreement is not as good and is the result of the limitations of FLD approximation itself. In all cases, we show that the boundary conditions we derived correctly describe the mean specific radiation field at all the boundaries of circumstellar envelope.Second, we investigated the Discontinuous Galerkin finite element method (DG-FEM) applied to the radiative transfer equation in spherical coordinates. The method make use of elements and flux integrals along their boundaries, insuring local conservation. However, as opposed to the classical finite-element methods, the reconstructed solution is discontinuous across the element edges. A useful feature of the method is the possibility for the user to control the order of the method, allowing to resolve strong spatial and angular gradients with a limited number of points. This feature is particularly appealing in radiative transfer where we often are limited by computer memory. We implemented the method in a code that compute the specific intensity, the temperature structure and the emissivity, allowing to compute images and SED's from ray tracing techniques. We tested its accuracy by comparing our results with the previously mentioned benchmarks. Our results shows a very good agreement, for all the tested cases, and show that the method can be used for further astrophysical applications.