Long-Term Stability of Planets in the $\alpha$ Centauri System

TL;DR

This study investigates the long-term stability of small planets in the Alpha Centauri system, identifying stable orbital regions and the influence of resonances and dynamical mechanisms over billion-year timescales.

Contribution

It provides detailed analysis of stable orbital zones in Alpha Centauri, confirming previous qualitative results and highlighting the effects of resonances and the Lidov-Kozai mechanism.

Findings

Stable regions are larger for retrograde orbits.

Mean motion resonances affect orbital stability boundaries.

Lidov-Kozai mechanism influences long-term orbital dynamics.

Abstract

We evaluate the extent of the regions within the $\alpha$ Centauri AB star system where small planets are able to orbit for billion-year timescales, and we calculate the positions on the sky plane where planets on stable orbits about either stellar component may appear. We confirm the qualitative results of Wiegert and Holman (AJ 113, 1445, 1997) regarding the approximate size of the regions of stable orbits, which are larger for retrograde orbits relative to the binary than for prograde orbits. Additionally, we find that mean motion resonances with the binary orbit leave an imprint on the limits of orbital stability, and the effects of the Lidov-Kozai mechanism are also readily apparent.