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 computin g a detailed line-blanketed hydrostatic model atmosphere. However, the computing time increases approximately linearly with the number of fr equency points. For computationally more complex and time-consuming pr oblems, such as dust driven winds or pulsating AGB stars, it is theref ore often not feasible to solve the radiative transfer problem for mor e than a single (i.e. mean or constant opacity) or a very modest numbe r of frequencies. This paper analyzes how to optimize the selection of frequency points in particular when solving the radiative transfer pr oblem at a very small number of points. We compute opacity sampled hyd rostatic model atmospheres based on a large number of opacity sampling frequency points (of the order of 10.000), and successively reduce th e number of frequencies in order to quantify the statistical error in the model structure introduced by a too coarse sampling. The results a re compared to hydrostatic model atmospheres obtained by using other o pacity approximations (Rosseland mean, straight means, constant opacit y). 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 recommendati ons on how to choose the frequencies optimally.