The Three-dimensional Architecture of the υ Andromedae Planetary System

The υ 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 ~30°, the inner planet's orbital plane has not been detected. We use N-body simulations to search for stable three-planet 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 ~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°. Combined with brightness variations in the combined star/planet light curve ("phase curve"), our results imply that planet b's radius is ~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 10¹⁹ W in the interior of the planet via tidal dissipation, possibly inflating the radius to an amount consistent with phase curve observations.