The Stability of the Suggested Planet in the nu Octantis System: A Numerical and Statistical Study

TL;DR

This study investigates the potential stability of a proposed planet in the nu Octantis system, concluding it is likely stable only in a retrograde orbit based on numerical and statistical analyses of observational data.

Contribution

It extends previous work by incorporating observational uncertainties and additional mathematical methods to assess the planet's orbital stability.

Findings

The planet is likely stable in a retrograde orbit.

Prograde orbit stability is virtually impossible.

The results align with observational data and uncertainties.

Abstract

We provide a detailed theoretical study aimed at the observational finding about the nu Octantis binary system that indicates the possible existence of a Jupiter-type planet in this system. If a prograde planetary orbit is assumed, it has earlier been argued that the planet, if existing, should be located outside the zone of orbital stability. However, a previous study by Eberle & Cuntz (2010) [ApJ 721, L168] concludes that the planet is most likely stable if assumed to be in a retrograde orbit with respect to the secondary system component. In the present work, we significantly augment this study by taking into account the observationally deduced uncertainty ranges of the orbital parameters for the stellar components and the suggested planet. Furthermore, our study employs additional mathematical methods, which include monitoring the Jacobi constant, the zero velocity function, and the maximum Lyapunov exponent. We again find that the suggested planet is indeed possible if assumed to be in a retrograde orbit, but it is virtually impossible if assumed in a prograde orbit. Its existence is found to be consistent with the deduced system parameters of the binary components and of the suggested planet, including the associated uncertainty bars given by observations.