Processing and analysis of the cycle shape in hydrodynamic pulsation models: application to Long-Period Variables

Low- to intermediate-mass stars experience the Asymptotic Giant Branch (AGB) phase in their late evolution, during which they display periodic variability due to pulsation. Not only this provides a powerful observable with applications in distance and age determinations, but it also represents a crucial link between structure of the stellar interior and the dust-driven stellar winds that enrich the interstellar medium with stellar nucleosynthesis products while causing the end of stellar evolution. Modeling the pulsation of AGB stars is therefore of critical importance for several astrophysical applications. Recent results indicate that hydrodynamic pulsation codes are necessary to capture the nonlinear dynamical feedback of pulsation on the stellar structure, which in turn controls the pulsation period. As the output from such codes consists in bulky synthetic time series, a dedicated processing is required. The main difficulty in doing so stems from the emergence of multiperiodicity, the potential interference between distinct periodic signals, and the possible occurrence of a long-term oscillatory behavior of thermal origin superimposed to the dynamic oscillation. The purpose of this work is to identify a valid approach to encode the information contained in the time series into a compact form, pursuing an optimal trade off between accuracy and manageability. The core of this task involves the development of a Fourier decomposition algorithm capable of handling the variety of time series resulting from the exploration of the space of AGB stellar parameters, as well as auxiliary tools. Once applied to a selected sample of hydrodynamic models, the processing algorithm reveal results consistent with the physical understanding of pulsation, and are overall in agreement with observations. The results of this thesis represent a proof of concept and a solid basis for a framework aimed at efficiently delivering theoretical pulsation models to the astronomical community.