A Model for Astrometric Detection and Characterization of Multi-Exoplanet Systems

Abstract

In this thesis, we develop an approximate linear model of stellar motion in multiplanet systems as an aid to observers using the astrometric method to detect and characterize exoplanets. Recent and near-term advances in satellite and groundbased instruments are on the threshold of achieving sufficient (⇠10 micro-arcsecond) angular accuracies to allow astronomers to measure and analyze the transverse motion of stars about the common barycenter in single- and multi-planet systems due to the gravitational influence of companion planets. Given the emerging statistics of extrasolar planetary systems and the long observation periods required to assess exoplanet influences, astronomers should find an approximate technique for preliminary estimates of multiple planet numbers, masses and orbital parameters useful in determining the most likely stellar systems for follow-up studies. In this paper, we briefly review the history of astrometry and discuss its advantages and limitations in exoplanet research. In addition, we define the principal astrometric signature and describe the main variables affecting it, highlighting astrometry’s complementary role to radial velocity and photometric transit exoplanet detection techniques. We develop and test a Python computer code using actual data and projections of the Sun’s motion due to the influence of the four gas giants in the solar system. We then apply this model to over 50 hypothetical massive two- and three-exoplanet systems to discover useful general patterns by employing a heuristic examination of key aspects of the host star’s motion over long observation intervals. Finally, we modify the code by incorporating an inverse least-squares fit program to assess its efficiency in identifying the main characteristics of multi-planet systems based on observational records over 5-, 10- and 20-year periods for a variety of actual and hypothetical exoplanetary systems. We also explore the method’s sensitivity to measurement frequencies, intervals and errors.