A tunable Monte Carlo method for mixing correlated-k opacities

Context . Mixed-gas opacities are critical for radiative transfer in stellar and substellar atmospheres. Several approaches exist to obtain net k-coefficients for arbitrary mixtures, each trading accuracy against computational cost. Aims . I introduce a tunable polynomial (or spline) reconstruction and sampling (PRAS) method to compute randomly overlapped opacities within a wavelength band. Methods . For each species and band, PRAS fits the opacity cumulative distribution function (CDF) with a polynomial or spline and then performs a Monte Carlo convolution to form the mixed distribution. The quality of the CDF fit and the total number of random samples used in the Monte Carlo integration scheme control the trade-off between accuracy and computational speed. Results . The PRAS method is typically as accurate as, or more accurate than, other methods at recovering individual pre-mixed (PM) k-coefficients under the random overlap assumption. In an exoplanet atmosphere outgoing spectral flux comparison test, even with a small number of samples (250), PRAS is at most within ≲20% of the PM reference and typically within ≈5% of the random overlap with resorting and rebinning (RORR) method. In the vertical flux and heating rate tests, PRAS produces results similar to those of RORR and improves upon the adaptive equivalent extinction (AEE) method. Conclusions . In the limit of exact CDF representation and infinite samples, PRAS converges to the exact, convolved randomly overlapped opacity distribution. Given its accuracy and scalability to larger quadrature sets at cost comparable to RORR, PRAS is a practical alternative for retrievals and post-processing applications.