New models of pulsating red giant stars: application to Long-Period Variables in the Large Magellanic Cloud

Stars of low and intermediate mass (0.9 ≲ M/M ⊙ ≲ 8) develop an electron-degenerate CO core after the core He-burning phase, and experience the thermally pulsing asymptotic giant branch phase (TP-AGB) as they approach the end of their evolution. Although very short lived, TP-AGB stars are of paramount importance in the study of stellar populations and galaxy evolution. In fact, being intrinsically very bright, they provide a significant contribution to the total luminosity of single stellar populations, and galaxies in general. Most of their radiation is emitted at infrared wavelengths, a spectral range where extinction by dust is small. They are thus very useful as tracers of intermediate age stars, and are often used to characterise stellar populations in external galaxies. The characteristic spectral signatures of TP-AGB stars have been observed even at high redshift, and they are in general visible even at large distances. Additionally, variable TP-AGB stars follow a well defined period-luminosity relation in the near infrared, which makes them a promising distance indicator. TP-AGB stars play a prominent role in the chemical enrichment of galaxies. Repeated third dredge-up events are efficient in bringing nucleosynthesis products (He, C, N, s-process elements) to the stellar surface, which low temperature favours the formation of molecular species. Stellar pulsations induce shock waves that compress the atmosphere and allow for the condensation of dust grains. Being highly opaque, dust is pushed outwards in the interstellar medium by radiation pressure, dragging the enriched gas with itself. The chain of events just described represents a clear example of the various physical processes, poorly understood and heavily entangled, involved in TP-AGB evolution. As a result, in spite of its crucial role across astrophysics, the TP-AGB is one of the least understood phases of stellar evolution. Its modelling is affected by large uncertainties that propagate in the field of extragalactic astronomy, degrading the predicting power of current population synthesis models of galaxies. The present PhD thesis is the result of three years of work within the ERC project STARKEY, which major goal is exactly to provide a physically-sound calibration of the TP-AGB phase as a function of age and metallicity. This is pursued by requiring models to simultaneously reproduce different observables of resolved TP-AGB stellar populations in star clusters and nearby galaxies. The project adopts an all-round theoretical approach that takes into account several, strongly interconnected, key physical processes (convective mixing, stellar winds, dust formation, and stellar pulsation). These calibrated models are used to generate new well-tested grids of stellar tracks, isochrones, chemical yelds of gas and dust, stellar spectra, pulsation models, all made available to the scientific community. The specific subject of the present work is the study of stellar pulsations on the TP-AGB, and was performed by computing a large grid of new pulsation models. Updated models of luminous red giant variables have long been missing from the scientific literature, and a set of models systematically accounting for the variety of properties of TP-AGB stars has never been published. A critical shortcoming of previous models, with the relevant exception of a few selected studies, is that they do not account for surface chemical enrichment. Carbon stars, produced by the dredge-up of carbon, have characteristic spectral features that are dramatically different than those of their O-rich counterpart. This is a consequence of altered molecular equilibria, and the corresponding drastic change in the main sources of molecular opacity. Atmospheric opacities determine stellar radii, thus affecting the pulsation period. It is therefore clear that they need to be consistent with the detailed chemical mixture predicted by evolutionary models. Part of this work was devoted to the inclusion of updated opacities in the modelling of pulsation, a significant improvement with respect to past studies, which generally employed opacity data computed for standard scaled-solar mixtures. As already mentioned, pulsation on the TP-AGB is essential to the enrichment of the interstellar medium. More generally, it is crucial for mass-loss, dust formation, and ultimately evolution. But of course, pulsating red giant stars are important for a number of other reasons. The most luminous ones, the large-amplitude Mira variables, have long been known to follow a period-luminosity (PL) relation that is very clear in the near-infrared bands, and represents a very promising distance indicator (see, e.g., Whitelock, 2013; Huang et al., 2018), especially in view of the forthcoming missions such as JWST. The discovery, during the last two decades, of multiple PL relations in the long-period variables (LPVs) of the Large Magellanic Cloud (Wood et al., 1999) re-ignited the interest for such stars. The different PL relations, or sequences, are assumed to be due to different pulsation modes, which are characterised by distinct period and excitation properties depending on the stellar properties and evolutionary stages. Therefore, observed periods provide an additional constraint, together with other observables, to be matched by theoretical models, allowing us to refine our knowledge of stellar structure and evolution. Observed periods represent also a powerful tool to estimate global parameters such as stellar masses and radii. However, to fully exploit the potential of LPVs, a knowledge of the exact pulsation modes corresponding to each sequence is required. This aim has been pursued by numerous studies in the past decades, with the unfortunate result that two interpretations emerged, both based on valid arguments, but providing mode assignments in contrast with each other. Again, this disagreement is largely due to the use of pulsation models unable to represent the variety of the AGB population of the Magellanic Clouds. In the present work, we present a new, large grid of linear, radial, non-adiabatic pulsation models, with updated opacity data for CNO-varied metal mixtures. The grid covers a wide range of the space of stellar parameters characterising the TP-AGB phase, in terms of total mass, core mass, luminosity, effective temperature, and chemical composition. Models include periods and amplitude growth rates for five radial pulsation modes, from the fundamental to the fourth overtone. Growth rates allow us to predict to a reasonably good accuracy the excitation/stability degree of individual modes, and provide information on their expected observability. The structure of the grid in terms of its defining parameters is based on detailed TP-AGB evolutionary tracks, but the computation of pulsation models is decoupled from evolutionary models. This way, pulsation models are compatible with virtually any output from evolutionary and population synthesis codes, and are going to be made publicly available, filling a long-existing gap. The grid of pulsation models has been implemented in the STARKEY framework to be tested against observations. Our approach involves the simulation of the pulsation properties of a synthetic population of luminous red giant stars. Such a simulation was computed to reproduce the observed photometric and variability properties of AGB stars in the Large Magellanic Cloud (Trabucchi et al., 2017). The results have shown a good degree of agreement between models and observations, and allowed us to provide a new interpretation of the observed PL sequences, essentially solving the past tensions and bringing the previous interpretations into alignment. Our result provides additional information about the open topic of long secondary periods in red giant variables. Moreover, it supports the idea of a connection between faint LPVs and solar-like oscillations in less evolved red giants (see, e.g., Mosser et al., 2013, and references therein), the implications of which would open new frontiers in the study of stellar oscillations. The comparison with observations confirmed that the new models are able to predict pulsation periods of all observed modes with good accuracy. Remarkably, theoretical growth rates are able to account for the observed distribution of overtone modes amplitudes, in spite of the uncertainties in the treatment of the interaction between convection and pulsation. On the other hand, growth rates of the fundamental mode are still affected by large uncertainties, as they are not able to reproduce the observed instability strip. Further studies are required to address in more detail the excitation of pulsation in luminous red giants, with special attention for the fundamental mode. Additional future developments include the use of non-linear models to: (1) constrain models by reproducing observed variability amplitudes, (2) investigate the conditions under which linear models are not appropriate to describe pulsation periods, and (3) provide, for those cases, suitable period corrections as a function of global stellar parameters.