Agol, EricGordon, Tyler A.2023-09-272023-09-272023-09-272023Gordon_washington_0250E_26232.pdfhttp://hdl.handle.net/1773/50682Thesis (Ph.D.)--University of Washington, 2023In recent decades the observation of planetary transits has emerged as the most successful method of exoplanet detection and characterization. Transits give us access to regions of parameter space that are inaccessible to RV and direct imaging -- notably low-mass planets in the habitable zones of dwarf stars are best observed via their transits. Followup observations of planetary transits can, in principle, constrain molecular signatures in rocky exoplanet atmospheres via transit transmission spectroscopy, measure the densities of planets via transit timing effects, and even potentially reveal the presence of exomoon companions. Despite the success of the transit method, challenges remain with regards to objects with shallow and/or infrequent transits. In this dissertation I detail some of those challenges and describe the progress that I have made towards mitigating them. Along the way I will describe a number of projects on subjects ranging from the characterization of stellar variability to modeling planetary interiors, all of which relate back to the basic theme of characterizing small, rocky transiting exoplanets. In Chapter 2 I review Gaussian process methods for modeling stellar variability, and demonstrate the utility of these methods by applying a one-dimensional GP model to measure stellar rotation periods in the K2 sample. In Chapter 3 I will extend this one-dimensional GP model to two dimensions in order to capture the wavelength-dependence of starspots and granulation. I then apply this model to simulated transit observations in order to demonstrate improved inference over the one-dimensional case. In Chapter 4 I summarize some additional applications of the Gaussian process framework including Fisher Information analysis, outlier detection and modeling, and non-stationary Gaussian processes. In Chapter 5 I review the subject of transiting exomoons and detail the development of an exomoon transit model that is intended to be combined with the stellar variability model from Chapter 2 in order to enable the detection of transiting exomoons. Finally, in chapter 6 I describe the prospects for exomoon detection in the near future with JWST.application/pdfen-USCC BY-SAAstrobiologyExomoonsExoplanetsGaussian ProcessesStellar VariabilityTransitsAstronomyAstrophysicsAstronomyThesis