Asteroseismology in the Kepler era and from ground-based observations

In this dissertation we present and investigate the new results attained in the field of Asteroseismology, a branch of stellar physics that aims at deriving the fundamental stellar properties and at describing the internal structure of the stars by means of the oscillations observed at their surface. The stochastically excited and intrinsically damped acoustic modes, also known as solar-like oscillations, represent the main class of pulsations discussed in this thesis. The document is sectioned into four parts, with the last one including a complementary material for the reader. Part I deals with ground-based observations of solar-like oscillations detected through the measurement of Doppler shifts in star's spectra. Here, Chapter 1 provides a comprehensive introduction to Asteroseismology, together with an intuitive description of the equations and tools used for asteroseismic analysis of stars. Chapter 2 is dedicated to a detailed study of the solar-like subgiant stars beta Aquilae and mu Herculis, which were observed by means of the SARG spectrograph operating @TNG. This is done by exploiting the classical Fourier analysis of radial velocity time-series. In addition, we stress that the research leading to these results included the use of time-series derived by means of the iSONG code, the new software to be used within the SONG project for stellar oscillations. Part II gives a particular focus to the space-based NASA's Kepler Mission, whose high-precision photometric observations represent the main source of data used for the research presented here. An overview of the NASA's Kepler Mission is given in Chapter 3, together with a brief presentation of some achievements derived for large ensemble of stars observed with Kepler. The results discussed in this chapter were derived by means of the ORK pipeline developed @OACT. Chapter 4 instead, is related to a thorough investigation of the ensemble seismic properties of a sample of red giant stars belonging to the open clusters NGC 6791, NGC 6811, and NGC 6819 observed by Kepler. The excellent quality of the 19 months-long observations carried out by Kepler made this analysis possible. Last but not least, Part III debates with the use of Bayesian methods applied to \kepler light curves for studying both the seismic properties of solar-like oscillations and the stellar differential rotation in active stars. In particular, an exhaustive introduction to the Bayesian concept of probability, to the main tools of Bayesian statistics, and to the numerical solutions of interest are provided in Chapter 5. To follow, Chapter 6 describes a detailed Bayesian inference and model comparison applied to the scaling relations adopted for predicting the amplitudes of solar-like oscillations in stars spanning from main sequence to the late red giant phase of the stellar evolution. Finally, Chapter 7 is related to a detailed study of the differential rotation in the Kepler targets KIC 7985370 and KIC 7765135, two young and active Sun-like stars that show an evident photometric modulation caused by star spots at their surfaces. The appendices are listed in Part IV. Appendix A describes in more detail the AARG code used to derive the results discussed in Chapter 4. The entire set of measurements derived by means of the AARG code is available in Appendix B. Appendices C and D instead, deal with a description about some numerical methods used for the Bayesian analysis presented in Chapter 6 and about the theory of Principal Component Analysis, respectively