Obliquities of stars from the study of transiting exoplanets and eclipsing binaries

In this thesis I study stellar obliquities across a range of companion masses, and in new regimes, that aims at constraining theories of planet formation and evolution. I begin in Chapter 1 with an introduction to the state of the field of extrasolar planets, key discoveries that have motivated previous studies on the misalignments between planetary orbits and stellar spins, and highlight the gaps in our knowledge where this thesis aims to make an impact. In Chapter 2, I outline the models and tools that underpin the analysis of transit light curves and high-resolution spectra in subsequent chapters. In Chapter 3, I apply these tools to the discovery of binary systems of various mass ratios. Two such systems are rare brown dwarfs whose discoveries help calibrate models of sub-stellar evolution, and the connection to giant planet formation and evolution. In Chapters 4-6, I present new measurements of stellar obliquities across a range of companion masses. In Chapter 4 I consider two systems hosting small planets. I demonstrate a misalignment the stellar spin and the orbit of a planet twice the size of Earth. This discovery is consistent with some disc-free migration scenarios, and provides the first observational evidence of its kind that super-Earths may form far from their star. In Chapter 5, I consider a sample of 13 giant planets orbiting cool stars in weak-tide regimes. I show that their host stars display a variety of obliquities, contrary to similar planets orbiting closer to their star. Such an effect is consistent with the expectation from tidal evolution, but has not yet been tested on this scale. In Chapter 6, I study the spin angular momentum of the primary component of a binary star hosting a circumbinary planet. I demonstrate that the star is aligned with the binary and planet orbit, providing an important constraint on the formation of binary stars and circumbinary planets. Finally, in Chapter 7, I conclude and offer some thoughts on future prospects.