Astrometric Modeling of Exoplanetary Orbits: Validation of an Integrated Bayesian Framework

Over the last three decades, the detection and characterization of planets orbiting stars outside our own Solar System has become an important field of astronomy, allowing us to place our own planet into broader scientific context, and enabling searches for habitable planets and life beyond Earth. The most important parameter which characterizes any exoplanet is its mass, which cannot be truly determined by radial velocity measurements if the planet is not transiting. Indeed, the radial velocity technique provides only the minimum mass. In order to constrain the inclination of a non-transiting planet and therefore attain its true mass, astrometry is used in tandem with Doppler measurements. The astrometric technique measures the motions of celestial bodies in the plane of the sky. In the context of exoplanets, the deviation of a star from its predicted linear path in the sky due to the presence of a disturbing gravitational force can be identified and used to characterize this perturbing companion. The discovery and analysis of exoplanets using astrometry is possible with the high-resolution astrometry of the ESA’s Hipparcos and Gaia missions. These missions established the absolute celestial reference frame and have collectively characterized the five-parameter astrometric solution for billions of stars. The anticipated fourth-generation Gaia data release is expected to further refine and extend this catalog. Using the data from both Hipparcos and Gaia to establish the long-term systemic proper motion of a star, we can compare this value to the short-term proper motion observed by Gaia to identify the proper motion anomaly caused by perturbing orbital companions for baselines of up to ~24 years. This technique allows for the exploration and characterization of a wide range of planets not easily studied through other methods. With the upcoming release of Gaia DR4, we expect new measurements of higher precision and longer baselines which will increase the ability of the astrometric technique to constrain orbital parameters. Consequently, astrometry is poised to become a much more relevant discovery and constraint technique for exoplanets in coming years. This thesis presents the construction and validation of an orbital fitting framework combining the proper motion anomaly technique into a native radial velocity fitting software in order to constrain all Keplerian elements of a planetary candidate. This framework uses the astrometric software package orbitize! in conjunction with the multi-method orbital-fitting package PyORBIT. This framework was validated through the analysis of seven planetary candidates whose mass parameters had been previously constrained through astrometric techniques by Kiefer et al. (2021) and Piccinini et al. (2026). Each resulting orbital model was evaluated for self-consistency, accuracy, and agreement to literature values. We report that this framework correctly integrates both codes' radial velocity likelihoods, producing consistent and generally well-converged constraints on the period, eccentricity, radial velocity semi-amplitude, argument of periastron, time of periastron, and minimum mass across all targets in the sample. The inclination was not confidently constrained by the PMA signal for any target in this sample. Disentanglement of the mass-inclination degeneracy and subsequent calculations of the true companion mass were therefore not achieved, due to the limitations of the astrometric technique on companions in the planetary mass regime. Nevertheless, we obtained upper limit for the mass of the objects, confirming their planetary nature. This framework can be confirmed as a viable method for constraining orbital parameters using radial velocity and shows promise for future use on targets with stronger astrometric signals. With the release of higher precision data across a longer temporal baseline from Gaia DR4, this framework may be utilized for full characterization of exoplanets.