The Shapes of Planet Transits and Planetary Systems

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

Collaboration Between Content Experts and Assessment Specialists: Using a Validity Argument Framework to Develop a College Mathematics Assessment

Developing a new assessment requires the expertise of both content experts and assessment specialists. Using the example of an assessment developed for Ontario’s Colleges Mathematics Assessment Program (CMAP), this article (1) describes the decisions that must be made in developing a new assessment, (2) explores the complementary contributions of content experts and assessment specialists, and (3) illustrates how the use of a validity argument framework can support collaboration in assessment development. The authors conclude that the validity argument framework facilitated effective collaboration between content experts and assessment specialists, and suggest that this approach may help other collaborators pursue transparent and effective assessment development