Title: On the Detection and Characterization of Exomoons Through Survey and Targeted Observations
Description: Exomoons remain amongst the most elusive targets in observational astronomy. Nevertheless, these worlds stand to provide an unprecedented window into the formation and evolution of planetary systems. If the Solar System is any guide, we can expect exomoons will be geologically active and diverse, with the potential for hosting volatiles, atmospheres, and even life. Moreover, a thorough understanding of the population and occurrence rates of exomoons will help to place our own Solar System in a galactic context, speaking to the commonality of our own history. And though there are a variety of known pathways for moon formation, the discovery of exomoons may yet reveal heretofore unanticipated system architectures and defy easy explanation, thereby enriching our theoretical understanding of system formation. In this Dissertation I present a population study of exomoons in the Kepler data, finding an apparent dearth of Galilean-analog satellites orbiting planets between 0.1 and 1 AU. I then present evidence for a large exomoon orbiting Kepler-1625b -- potentially the first ever discovery of a transiting exomoon -- as suggested by a joint analysis of Kepler and Hubble Space Telescope data.

The following chapter further investigates a number of alternative hypotheses relating to the candidate moon, though the conclusion that an exomoon best explains the data in hand remains unchanged. Finally, I present the results of an effort to identify candidate exomoon signals in the Kepler data by developing a convolutional neural network trained on O(10⁵) Kepler light curves injected with simulated planet and moon transit signals. The most promising exomoon candidates identified by the neural network are examined in detail, undergoing a full photodynamical model fit and Bayesian model selection. I conclude by discussing the outlook for the moon search, highlighting strategies for future work and myriad unanswered questions that should be pursued in the coming years.