Resulting temperature distribution (top) and relative difference (bottom) of the 1D model discussed in Sect. 3.1 with different temporal step widths At for the time-dependent (dashed) and stationary (solid) method. The number of photon packages per step is set to 10³, the total number of photon packages used for the stationary simulation is 10⁸, respectively. Lines for radii larger than 20 AU are overlapping and are therefore not shown.