A photometric-only measurements of stellar obliquities for tens of thousands of stars and exoplanetary system using a machine-learning approach

A key aspect in our understanding of planet formation and the architecture of planetry systems is the orbital inclinations of exoplanets and their relation to the stellar spin. However, stellar obliquities are difficult to measure, and typically require both photometric and spectroscopic data. Although thousands of exoplanets have been discovered and characterized to various degrees, The stellar obliquity have been measured only for a few tens of exoplanetary systems. Nevertheless, the photometric data of stars affected by the existence of sun-spots holds valuable information. These data have been used to measure the stellar spins of tens of thousands of stars, through the identification of quasi-periodicity. However, these data also hold information of the stellar obliquity. We have developed a novel machine-learning assisted measurement and analysis of stellar obliquity using only photometric data. We show that this method provide good measurement of the obliquities on mock data, and apply it to the photometric data of Kepler. We are now able, for the first time, to measure the obliquities of tens of thousands of stars, including thousands of exoplanetary systems, allowing us to provide a detailed characterization of obliquities in exoplanetary systems and their dependence on the stellar and planetary system properties. We will present our method and our results, and discuss the newly found distributions and their implications for our understanding of planet formation and the architecture of planetary systems.