A Dynamical Analysis of the 47 UMa Planetary System

TL;DR

This paper investigates the dynamical stability, resonance states, and potential habitability of the 47 UMa planetary system through numerical, analytical, and hydrodynamical methods, revealing possible resonance capture and constraints on planet inclinations.

Contribution

It provides a comprehensive dynamical analysis of 47 UMa, exploring resonance states, stability constraints, and the effects of protoplanetary disk torques on planetary migration.

Findings

Planets likely participate in a secular resonance or 7:3 mean motion resonance.

Mutual inclination between planets is constrained to 40 degrees or less.

Earth-mass planets can survive in some habitable zone regions, but large terrestrial planet formation is unlikely.

Abstract

The mass and period ratios of the two planets orbiting 47 UMa suggest a possible kinship to the Jupiter-Saturn pair in our solar system. We explore the current dynamical state of the 47 UMa 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. We show that stability considerations restrict the mutual inclination between the two planets to 40 degrees 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 occured. We show that Earth-mass planets can survive for long periods in some regions of the habitable zone of the nominal co-planar 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.