Properties of self-excited pulsations in 3D simulations of AGB stars and red supergiants

Context. The characteristic variability of cool giants and supergiants is attributed to a combination of stellar pulsation and large-scale convective flows. Full 3D radiation-hydrodynamical modelling is an essential tool for understanding the nature of these dynamical processes. The parameter space in our 3D model grid of red giants has expanded in recent years. These models can provide many insights on the nature and properties of the pulsations, including the interplay between convection and pulsations.Aims. We treat 3D dynamical models of asymptotic giant branch (AGB) stars and red supergiants (with current masses 1 M-circle dot <= M-* <= 12 M-circle dot) similar to observational data. We aim to explore the relation between stellar parameters and the properties of the self-excited pulsations.Methods. Output from global 'star-in-a-box' models computed with the CO5BOLD radiation-hydrodynamics code were analysed, particularly in regards to the pulsation properties, to find possible correlations with input and emergent stellar parameters. The fast Fourier transform was applied to spherically averaged mass flows to identify possible radial pulsation periods beneath the photosphere of the modelled stars. Stellar parameters were investigated for correlations with the extracted pulsation periods.Results. We find that the pulsation periods varied with the stellar parameters in good agreement with the current expectations. The pulsation periods follow Ritter's period-mean density relation well and our AGB models agree with period-luminosity relations derived from observations. A mass estimate formula was derived from the 3D models, relating the stellar mass to the fundamental mode pulsation period and the stellar radius.Conclusions. While the non-linearity of the interplay between the self-excited pulsations and the self-consistent convection complicates analyses, the resulting correlations are in good agreement with respect to current theoretical and observational understandings.