Details of Modelling the Non-Stationary Thermal Structure of an Axially Symmetric Protoplanetary Disk

In the paper, a model for simulating the non-stationary thermal structure of protoplanetary disk in axial symmetry has been provided. The model has been based on the widely used approach of splitting the radiation field into stellar and intrinsic thermal radiation of the medium. The heating by stellar radiation has been calculated by the ray tracing method while the well-known diffusion approximation with a flux limiter (FLD approach) has been used to treat the thermal radiation. To solve the resulting system of linear equations, a modification to Gauss method has been proposed, which has made it possible to speed up the calculations by a factor of ten compared to the widely adopted GMRES method. This model has been used to calculate the steady-state thermal structure of two disks, including those with the parameters of the EX Lup system. A detailed analysis of the simulation results has been performed. Comparison with the results of more accurate methods has made it possible to identify the main shortcomings of the model related to the ignoring of light scattering and to the diffusion nature of the FLD approximation. It has been shown that the disk thermal structure calculated with the FLD approximation has evolved according to analytical estimates of the characteristic thermal time.