Granulation signatures in 3D hydrodynamical simulations: Evaluating background model performance using a Bayesian nested sampling framework

Context. Understanding the granulation background signal is vital when interpreting the asteroseismic diagnostics of solar-like oscillators. Various descriptions exist throughout literature for modelling the surface manifestation of convection, with the choice of description affecting our interpretations. Aims. We aim to evaluate the performance of and preference for various granulation background models for a suite of 3D hydrodynamical simulations of convection across the Hertzsprung-Russell diagram, thereby expanding the number of simulations and coverage of parameter space for which such investigations have been made. Methods. We took a statistical approach by considering the granulation signatures in power density spectra of 3D hydrodynamical simulations, in which no biases or systematics of observational origin are present. To properly contrast the performance of the background models, we developed a Bayesian nested sampling framework for model inference and comparison. This framework was subsequently extended to real stellar data using the solar analogue KIC 8006161 (Doris) and the Sun. Results. We find that multi-component models are consistently preferred over a single-component model, with each tested multicomponent model demonstrating merit in specific cases. This occurs for simulations with no magnetic activity, ruling out stellar faculae as the sole source of the second granulation component. Similar to a previous study, we find that a hybrid model with a single overall amplitude and two characteristic frequencies performs well for numerous simulations. Additionally, a tentative third granulation component beyond the value of νmax is seen for some simulations, but its potential presence in observations requires further study. Conclusions. Studying the granulation signatures in these simulations paves the way for studying real stars with accurate granulation models. This deeper understanding of the granulation signal may lead to complementary methods to existing algorithms for determining stellar parameters, with the goal of providing an independent radius estimate for stars where oscillations are not observable.