3D continuum radiative transfer - A new adaptive grid construction algorithm based on the Monte Carlo method

Aims. The continuum radiative transfer is a common problem in Astrophysics, that must be solved to describe the physics and interpret the observations of objects embedded ( for instance) in a dusty medium ( e. g. evolved stars, young stellar objects,...). Extreme high angular resolution observations reveal in general complex geometries ( e. g. mediums with clumps of matter, warps...). It is thus necessary to solve the radiative transfer problem making no simplifying assumptions on the geometry, i.e. resolve the full spatial three dimensional problem. Methods. We use the flexible Monte Carlo ( MC) method to solve the continuum radiative transfer problem. We focus on the computation of the temperature structure of a dusty medium and the construction of the grid that samples this structure. We propose to use a natural by-product of the MC method, the locations of the photon package absorptions in the medium, to build an adaptive grid to reach the finest resolution in the regions of interest. Results. We present the details of the new algorithm used for the construction of the grid. We also propose modifications to a widely used MC propagation framework. The reliability of our method is numerically tested against well established numerical results in one and two dimensions. In order to illustrate the capabilities of our three dimensional methods, we examine the observational evidence for the presence of warps in circumstellar discs.