Title: The Shapes of Planet Transits and Planetary Systems
Description: In this Thesis, I explore transiting exoplanets: what we can learn from modeling their light curves, and what we can learn from their arrangement in planetary systems. I begin in Chapter 1 by briefly reviewing the history of transit modeling, from the earliest theoretical models of eclipsing binary stars to the models in current widespread use to model exoplanet transits. In Chapter 2, I model the transits of a sample of Kepler exoplanets with strong prior eccentricity constraints in order to derive correspondingly strong constraints on the density of their host stars, and find that the density constraints I derive are as precise as density constraints from asteroseismology if the transits are observed at high signal-to-noise. In Chapter 3, I apply the same methodology in reverse: using prior knowledge of the stellar density based on Gaia parallax measurements, I model the transits of twelve singly-transiting planets observed by K2 and derive constraints on their periods. In Chapter 4, I consider the general problem of deducing the shape of a transiting object from its light curve alone, which I term ``shadow imaging;'' I explore the mathematical degeneracies of the problem and construct shadow images to explain Dips 5 and 8 of Boyajian's Star.

I next turn to multi-planet systems: in Chapter 5, I investigate the underlying multiplicity distribution of planetary systems orbiting FGK dwarfs observed by Kepler. I find that we can explain the multiplicities of these systems with a single Zipfian multiplicity distribution, without invoking a dichotomous population. In Chapter 6, I consider the arrangement of planets in those systems, and use neural networks inspired by models used for part-of-speech tagging in computational linguistics to model the relationship between exoplanets and their surrounding "context," i.e. their host star and sibling planets. I find that our trained regression model is able to predict the period and radius of an exoplanet to a factor of two better than a naive model which only takes into account basic dynamical stability. I also find that our trained classification model identifies consistent classes of planets in the period-radius plane, and that it is rare for multi-planet systems to contain a neighboring pair of planets from non-contiguous classes.

In Chapter 7, I summarize these results and briefly discuss avenues for future work, including the application of our methods to planets and planetary systems discovered by TESS.