The Three-Dimensional Architecture Of The Upsilon Andromedae Planetary System

The upsilon Andromedae system is the first exoplanetary system to have the relative inclination of two planets' orbital planes directly measured, and therefore offers our first window into the three-dimensional configurations of planetary systems. We present, for the first time, full three-dimensional, dynamically stable configurations for the three planets of the system consistent with all observational constraints. While the outer two planets, c and d, are inclined by similar to 30 degrees the inner planet's orbital plane has not been detected. We use N-body simulations to search for stable threeplanet configurations that are consistent with the combined radial velocity and astrometric solution. We find that only 10 trials out of 1000 are robustly stable on 100 Myr timescales, or similar to 8 billion orbits of planet b. Planet b's orbit must lie near the invariable plane of planets c and d, but can be either prograde or retrograde. These solutions predict that b's mass is in the range of 2-9 M-Jup and has an inclination angle from the sky plane of less than 25 degrees Combined with brightness variations in the combined star/planet light curve ("phase curve"), our results imply that planet b's radius is similar to 1.8 R-jup, relatively large for a planet of its age. However, the eccentricity of b in several of our stable solutions reaches >0.1, generating upward of 10(19) W in the interior of the planet via tidal dissipation, possibly inflating the radius to an amount consistent with phase curve observations.