Evolution of rotating stars with PARSEC: implementation and comparison with observations

The goal of this thesis is to study the effects of stellar rotation onto the evolution of stars.o this purpose, I have dedicated a good part of my PhD to study and implement the main rotation effects on our stellar evolutionary code parsec (PAdova tRieste Stellar Evolutionary Code). The first project in which I was involved was to investigate the possible concurrence between the convective core overshooting phenomenon and the rotation in intermediate-mass stars. For such study, I analyzed a sample of double-line eclipsing binaries (DLEBs, with very well determined masses radii and metallicities) by means of a Bayesian method and the new parsec v2.0 rotating tracks. This study allowed me to calibrate the overshooting efficiency in the code and to conclude that a constant efficiency of overshooting in concurrence with a star-to-star variation of the rotational mixing might be crucial in the interpretation of intermediate-mass stars observations. The second project consisted of a study of the effects of rotation in the stellar photometry. As the rotation grows the star becomes more and more oblate, this induces a thermal imbalance between the poles and the equator that is known as the Von Zeipel effect. Rotating stars do not have a constant effective temperature along the surface and for higher rotational velocity such difference increases. Since the temperature is proportional to the emitted flux, a fast-rotating star will look very different if observed at the pole or at the equator (this is also called gravity darkening). In this work, we developed a tool to compute the rotating isochrones with the gravity darkening. This work is fundamental to interpret the observed stellar clusters CMD and their features that are emerging thanks to the recent excellent photometry provided by the extit{Hubble Space Telescope} (HST). These two projects have been fundamental steps in the building of a new collection of tools to study stellar clusters populations. My third project was the first attempt to use these tools to analyze the Large Magellanic Cloud (LMC) stellar cluster NGC~1866. Instead of looking at individual features in the CMD, like the split main sequence (MS), eMSTO, and evolved stars, we seek to reinterpret the entire available data, in particular exploiting Cepheids that have accurate pulsational mass determinations. I found that four Cepheids out of five, belong to a young (of $ 176 pm 5$~Myr) and slowly rotating (omegai~$ < 0.3$) population, while the fifth belongs to an older population (of $ 288 pm 20$~Myr) of rapidly rotating stars (omegai~$ sim 0.9$). Later, I fitted the observed CMD of the cluster with isochrones with selected ages and initial rotations obtained from the Cepheids analysis and corrected with the gravity darkening effect. I found that the two isochrones well fit the split-MS and the cluster turn-off. This study goes in the direction to confirm that some young clusters like NGC~1866 harbour multiple populations, but gives also hints on its formation.