2012 Winner: Stability Analysis of the Companions of Upsilon Andromedae

Project Information
Stability Analysis of the Companions of Upsilon Andromedae
Physical and Biological Sciences
Astrophysics
We present a baseline analysis of the stability of the nominal best-fit Upsilon Andromedae model as presented in McArhur et al. (2010). We find that the nominal two-planet fit for the system becomes violently unstable after 357,000 years after the start of integration. To find a region of stability for the proposed fit, we show that maximum masses required for a stable evolution for 1 Myr begin at 1.645 and 1.206 Jupiter masses for Upsilon Andromedae c and d, respectively, which are much lower than the allowed minimum masses of 1.96 and 4.33 Jupiter masses for the outer two planets. Finally, we test 174 randomly selected configurations within the error range of the model presented in McArthur et al. (2010) and find that all of these configurations resulted in violent instability within 2.1 billion years since the start of integration. In addition to the study of the $upsilon$ Andromedae system that constitutes the primary result of this thesis, we also present a synopsis of preliminary work on dynamical evolution of self-gravitating bodies. To this end, we develop a 4th order Runge-Kutta N-body integrator with energy and angular momentum conservation tracking. Using the integrator, we solve the Pythagorean 3-body problem and test for accuracy of the produced solution using a parallel integration with half the specified time-step.
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Students
  • Irina Goriatcheva (Stevenson)
Mentors