Recommendations for Monte Carlo nucleosynthesis sampling

Context. Recent reaction rate evaluations include reaction rate uncertainties that have been determined in a statistically meaningful manner. Furthermore, reaction rate probability density distributions have been determined and published in the form of lognormal parameters with the specific goal of pursuing Monte Carlo nucleosynthesis studies. Aims. A variety of methods is available for randomly sampling over reaction rate probability densities. The aim of this work is to investigate these methods and determine the most accurate method for estimating elemental abundance uncertainties. Methods. Experimental Monte Carlo reaction rates are first computed for the 22Ne + α, 20Ne(p, γ)21Na, 25Mg(p, γ)26Al, and 18F(p, α)15O reactions, which are used to calculate reference nucleosynthesis yields for 16 nuclei affected by nucleosynthesis in massive stars and classical novae. Five different methods of randomly sampling over these reaction rate probability distributions are then developed, tested, and compared with the reference nucleosynthesis yields. Results. Given that the reaction rate probability density distributions can be described accurately with a lognormal distribution, Monte Carlo nucleosynthesis variations arising from the parametrised estimates for the reaction rate variations agree remarkably well with those obtained from the true rate samples. Most significantly, the most simple parametrisation agrees within just a few percent, meaning that Monte Carlo nucleosynthesis studies can be performed reliably using lognormal parametrisations of reaction rate probability density functions