The 3-dimensional architecture of the Upsilon Andromedae planetary system

TL;DR

This study constructs the first full 3D, dynamically stable models of the Upsilon Andromedae planetary system consistent with observations, revealing the possible inclinations, masses, and orbital configurations of its three planets.

Contribution

It provides the first comprehensive 3D dynamical models of the system, integrating radial velocity and astrometric data to constrain planetary inclinations and stability.

Findings

Only 10 out of 1000 configurations are stable for 100 million years.

Planet b's orbit is near the invariable plane of c and d, with possible prograde or retrograde motion.

Planet b's radius is estimated at about 1.8 Jupiter radii, with eccentricity potentially causing radius inflation.

Abstract

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 3-dimensional configurations of planetary systems. We present, for the first time, full 3-dimensional, dynamically stable configurations for the 3 planets of the system consistent with all observational constraints. While the outer 2 planets, c and d, are inclined by about 30 degrees, the inner planet's orbital plane has not been detected. We use N-body simulations to search for stable 3-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 about 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 b's mass is in the range 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 about 1.8 $R_{Jup}$, relatively large for a planet of its age. However, the eccentricity of b in several of our stable solutions reaches values greater than 0.1, generating upwards of $10^{19}$ watts in the interior of the planet via tidal dissipation, possibly inflating the radius to an amount consistent with phase curve observations.