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A method for treating atomic and molecular line opacities in cool stellar atmospheres by a statistical opacity sampling is investigated. Under the usual assumptions of plane-parallel geometry, radiative equilibrium, hydrostatic equilibrium, and LTE, each radiative quantity is computed monochromatically at each chosen frequency and depth without any averaging of the opacity. The number of frequencies needed to allow an accurate integration of the energy flux over a given spectral interval is investigated as a function of depth, including opacity for both CN and C2. This method is extended to the calculation of a model atmosphere of a star, and the effect of the number and placement of frequency points is studied. The method is applied to treating molecular lines of CO, C2, and CN in a cool carbon star. Significant advantages of the opacity sampling method are its flexibility, which permits computation of models having arbitrary variations of chemical composition and of opacity with wavelength and depth, and generalizability to include departures from LTE.
Sneden et al. (1976) studied this question.