2025 Theses Doctoral

From Wobbles to Worlds: Developing a Framework for Detecting Unseen Planets and Moons

Yahalomi, Daniel Alexander

Over the past three decades, advances in observational techniques, computational and statistical methods, and dynamical modeling have collectively transformed our ability to characterize and understand the architectures of planetary systems. Transit timing variations (TTVs) are observational manifestations of wobbles in the orbits of transiting planets that are caused by the gravitational influence of perturbing bodies in the system. Each individual TTV signal yields multi-modal, degenerate constraints on the surrounding worlds in the planetary system - they are whispers of what lies beyond. But together, these whispers become a chorus, one previously untapped to pull away the veil of the planetary architectures. TTVs are ubiquitous in exoplanet transit datasets, with 𝘒𝘦𝘱𝘭𝘦𝘳 alone containing nearly 2,000 periodic TTVs. However, these TTVs are often ambiguous from a model selection perspective, as it is difficult to determine the physical cause of a TTV, be it another planet, a moon, or stellar activity. Currently, careful considerations must be taken, on a case-by-case basis, using computationally expensive N-body simulations, in order to determine the cause of an observed TTV signal.

This dissertation presents work towards the development of TTV model selection techniques. It begins with the presentation of the 𝚍𝚎𝚖𝚘𝚌𝚛𝚊𝚝𝚒𝚌 𝚍𝚎𝚝𝚛𝚎𝚗𝚍𝚎𝚛 a novel ensemble-based approach to detrending stellar time-series photometry. This critical addition to the TTV analysis toolkit is an open-source code made available to the community.

Next, we present findings of a case study of the most ``exomoon corridor''-like TTV signal: Kepler-1513, from which a new planetary perturber interloper was uncovered. Then via numerical simulations, we introduce an approach for modeling single-planet TTVs in the low-eccentricity regime, by splitting the orbital period space into a number of uniform prior bins over which there aren't perturbing planet period degeneracies. We demonstrate, analytically, how one can explain these numerical simulations using first-order near mean-motion resonance super-periods, the synodic period, and their aliases -- the expected dominant TTV periods in the low-eccentricity regime. Using a Bayesian framework, we then present a method for determining the optimal solution between TTVs induced by a perturbing planet and TTVs induced by a moon.

We then present a deep dive into our discovery of the ``exoplanet edge'' -- the finding that perturbing planets are not expected to induce a dominant TTV with an observable period less than half their own orbital period. This ``exoplanet edge'' is the manifestation of an observational alias and a rotating tidal distortion effect. The presence of an anomalous dominant TTV period, in a two-planet system, that falls below the exoplanet edge would suggest the presence of additional mass in the system, besides the two known exoplanets. We identify 13 two-planet systems in Kepler data that display anomalously fast TTVs, and discuss several possible explanations for additional mass in the system. Then we present injection recovery simulations of next generation radial velocity and astrometric searches for Solar System analogs. Finally, we conclude by discussing future work that can stem from the work presented in this dissertation.