Statistical and dynamical remastering of classic exoplanet systems

The most powerful constraints on planet formation will come from characterizing the dynamical state of complex multi-planet systems. Unfortunately, with that complexity comes a number of factors that make analyzing these systems a computationally challenging endeavor: the sheer number of model parameters, a wonky shaped posterior distribution, and hundreds to thousands of time series measurements. In this dissertation, I will review our efforts to improve the statistical analyses of radial velocity (RV) data and their applications to some renown, dynamically complex exoplanet system.;In the first project (Chapters 2 and 4), we develop a differential evolution Markov chain Monte Carlo (RUN DMC) algorithm to tackle the aforementioned difficult aspects of data analysis. We test the robustness of the algorithm in regards to the number of modeled planets (model dimensionality) and increasing dynamical strength. We apply RUN DMC to a couple classic multi-planet systems and one highly debated system from radial velocity surveys.;In the second project (Chapter 5), we analyze RV data of 55 Cancri, a wide binary system known to harbor five planetary orbiting the primary. We find the inner-most planet "e" must be coplanar to within 40 degrees of the outer planets, otherwise Kozai-like perturbations will cause the planet to enter the stellar photosphere through its periastron passage. We find the orbits of planets "b" and "c" are apsidally aligned and librating with low to median amplitude (50+/-6 10 degrees), but they are not orbiting in a mean-motion resonance.;In the third project (Chapters 3, 4, 6), we analyze RV data of Gliese 876, a four planet system with three participating in a multi-body resonance, i.e. a Laplace resonance. From a combined observational and statistical analysis computing Bayes factors, we find a four-planet model is favored over one with three-planets. Conditioned on this preferred model, we meaningfully constrain the three-dimensional orbital architecture of all the planets orbiting Gliese 876 based on the radial velocity data alone. By demanding orbital stability, we find the resonant planets have low mutual inclinations phi so they must be roughly coplanar (phicb = 1.41(+/-0.62/0.57) degrees and phibe = 3.87(+/-1.99/1.86 degrees). The three-dimensional Laplace argument librates chaotically with an amplitude of 50.5(+/-7.9/10.0) degrees, indicating significant past disk migration and ensuring long-term stability.;In the final project (Chapter 7), we analyze the RV data for nu Octantis, a closely separated binary with an alleged planet orbiting interior and retrograde to the binary. Preliminary results place very tight constraints on the planet-binary mutual inclination but no model is dynamically stable beyond 105 years.;These empirically derived models motivate the need for more sophisticated algorithms to analyze exoplanet data and will provide new challenges for planet formation models.