The stability of the suggested planet in the ν Octantis system: a numerical and statistical study

Abstract

We provide a detailed theoretical study aimed at the observational finding about the ν 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 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.

Testing a hypothesis of the ν Octantis planetary system

“…Smooth, coloured curves are for formal 1,2,3σ levels of the best-fit model marked with a star symbol. ously, we found stable solutions only as retrograde orbits, actually in accord with the original hypothesis in (Eberle & Cuntz 2010) and later investigated by Quarles et al (2012). This is illustrated in Fig.…”

“…Earlier, Eberle & Cuntz (2010) following the stability studies of the restricted three body problem by Jefferys (1974) found that a retrograde orbit of the planet lies in much wider stable zone than the direct configuration. In a new work, Quarles et al (2012) investigate this model, extending the set of orbital configurations, through a numerical study in the framework of the elliptic, restricted three-body problem.…”

Line-depth-ratio temperatures for the close binary ν Octantis: new evidence supporting the conjectured circumstellar retrograde planet

“…The controversial geometry of ν Oct has been investigated with increasing depth beginning with Eberle & Cuntz (2010) and subsequently by Quarles, Cuntz & Musielak (2012) and Goździewski et al (2013). Goździewski et al explored the system in considerable detail and found that stable solutions consistent with the Ramm et al results existed but were confined to tiny regions of the phase space.…”

The three-body problem

“…This posed a problem for the confirmation of the exoplanet. However, if one considers an exoplanet in retrograde orbit relative to the orbiting binary, then enlarged regions of stability arise, which would be consistent with the putative exoplanet [Eberle and Cuntz, 2010b, Quarles et al, 2012a, Goździewski et al, 2013. The restricted three-body problem has also been applied to P-type or circumbinary exoplanets.…”