Optimizing the opacity sampling method

Modern computers allow solutions of the radiative transfer problem at a large number of frequencies during the iterative process of computing a detailed line-blanketed hydrostatic model atmosphere. However, the computing time increases approximately linearly with the number of frequency points. For computationally more complex and time-consuming problems, such as dust driven winds or pulsating AGB stars, it is therefore often not feasible to solve the radiative transfer problem for more than a single (i.e. mean or constant opacity) or a very modest number of frequencies. This paper analyzes how to optimize the selection of frequency points in particular when solving the radiative transfer problem at a very small number of points. We compute opacity sampled hydrostatic model atmospheres based on a large number of opacity sampling frequency points (of the order of 10.000), and successively reduce the number of frequencies in order to quantify the statistical error in the model structure introduced by a too coarse sampling. The results are compared to hydrostatic model atmospheres obtained by using other opacity approximations (Rosseland mean, straight means, constant opacity). We conclude that a considerable improvement in the accuracy of the model structure over such approximations can be achieved with a very modest number (20 - 50) of sampling frequencies, and give recommendations on how to choose the frequencies optimally.