Can GJ 876 host four planets in resonance?

TL;DR

This study analyzes the dynamical stability of the GJ 876 planetary system, concluding it is most likely dynamically full with no additional stable interior planets, and discusses implications for its formation.

Contribution

The paper introduces a numerical scheme for efficiently exploring orbital stability regions and applies it to GJ 876 to assess the possibility of additional planets.

Findings

The 15-day orbit is unstable over long timescales.

GJ 876 is most likely dynamically full with no stable interior planets.

Potential stability regions exist outside the known planetary orbits.

Abstract

Prior to the detection of its outermost Uranus-mass object, it had been suggested that GJ 876 could host an Earth-sized planet in a 15-day orbit. Observation, however, did not support this idea, but instead revealed evidence for the existence of a larger body in a $\sim$125-day orbit, near a three-body resonance with the two giant planets of this system. In this paper, we present a detailed analysis of the dynamics of the four-planet system of GJ 876, and examine the possibility of the existence of other planetary objects interior to its outermost body. We have developed a numerical scheme that enables us to search the orbital parameter-space very effectively and, in a short time, identify regions where an object may be stable. We present details of this integration method and discuss its application to the GJ 876 four-planet system. The results of our initial analysis suggested possible stable orbits at regions exterior to the orbit of the outermost planet and also indicated that an island of stability may exist in and around the 15-day orbit. However, examining the long-term stability of an object in that region by direct integration revealed that the 15-day orbit becomes unstable and that the system of GJ 876 is most likely dynamically full. We present the results of our study and discuss their implications for the formation and final orbital architecture of this system.