A Dynamical Analysis of the 47 Ursae Majoris Planetary System

Abstract

Thirteen years of Doppler velocity measurements have revealed the presence of two planets orbiting the star 47 Ursae Majoris on low-eccentricity orbits. A two-Keplerian fit to the radial velocity data suggests that the inner planet has a period Pb = 1089.0 ± 2.9 days and a nominal [sin(i) = 1] mass M sin i = 2.54 MJup, while the outer planet has a period Pc = 2594 ± 90 days and a mass M sin i = 0.76 MJup. These mass and period ratios suggest a possible kinship to the Jupiter-Saturn pair in our own solar system. We explore the current dynamical state of this system with numerical integrations, and compare the results with analytic secular theory. We find that the planets in the system are likely participating in a secular resonance in which the difference in the longitudes of pericenter librates around zero. Alternately, it is possible that the system is participating in the 7 : 3 mean motion resonance (in which case apsidal alignment does not occur). Using a self-consistent fitting procedure in conjunction with numerical integrations, we show that stability considerations restrict the mutual inclination between the two planets to ~40° or less, and that this result is relatively insensitive to the total mass of the two planets. We present hydrodynamical simulations which measure the torques exerted on the planets by a hypothesized external protoplanetary disk. We show that planetary migration in response to torques from the disk may have led to capture of the system into a 7 : 3 mean-motion resonance, although it is unclear how the eccentricities of the planets would have been damped after capture occurred. We show that Earth-mass planets can survive for long periods in some regions of the habitable zone of the nominal coplanar system. A set of planetary accretion calculations, however, shows that it is unlikely that large terrestrial planets can form in the 47 UMa habitable zone.