Thesis (Ph.D.)--University of Washington, 2020The majority of main sequence (MS) and pre-MS (PMS) stars reside in binaries or hierarchical multiples (Abt 1979; Duchêne & Kraus 2013). Understanding planetary processes and regimes of habitability in a general framework requires statistical studies of planets around all modes of stellar multiplicity. This thesis aims to constrain the demographics of planets orbiting binary stars (circumbinary planets; CBPs), using an independent, automated detection pipeline analysis. To do this, I exploit high cadence & high precision photometry and the transiting geometry to measure physical properties of eclipsing binaries (EBs) and detect CBPs around them. In particular, I create a modular eclipsing binary modeling code which leverages stellar evolution models with time-series, multi-band, and positional photometry to extract full system parameters, including stellar mass. This technique enables mass estimation for large ensembles of EBs, accurate to within 10% for detached MS systems, and I apply it to assemble a Bayesian catalogue of 728 fully characterized Kepler EBs. Next, I develop a hybrid transit detection method that is robust to large transit timing and duration variations associated with transiting CBPs. It corrects for large scale variations induced by binary reflex motion using a physical CBP model, and subsequently employs the Quasi-periodic Automated Transit Search algorithm (QATS; Carter & Agol 2013) to empirically treat additional aperiodicities, due to model inaccuracies and assumptions. This dual accounting for quasi-periodicity improves CBP detection significance, by greater than a factor of 2 from previous efforts. Finally, I apply a CBP transit search on the Kepler EB subsample with full system solutions, and detect 8 robust candidates (corresponding to previously by-eye discovered CBPs) and 4 marginal candidates. Reconciling the detected CBP candidates with a thorough audit of detection and selection biases, I infer population-level trends for CBPs and contextualize my findings with complementary detection results, formation theories, as well as important directions for the future
