# Dynamical analysis of the circumprimary planet in the eccentric binary system HD59686

## TL;DR

This paper conducts a comprehensive dynamical analysis of the HD59686 binary star system with a planet, exploring orbital stability and configurations through simulations and data fitting.

## Contribution

It provides the first detailed stability analysis of the HD59686 system, identifying stable orbital configurations including coplanar and retrograde arrangements.

## Key findings

- Stable solutions exist for coplanar, aligned orbits with secular apsidal alignment.
- Retrograde and highly inclined orbits can also be stable over long timescales.
- Narrow stable regions are identified for specific orbital parameters.

## Abstract

We present a detailed orbital and stability analysis of the HD~59686 binary-star planet system. HD~59686 is a single-lined moderately close ($a_{B} = 13.6\,$AU) eccentric ($e_{B} = 0.73$) binary, where the primary is an evolved K giant with mass $M = 1.9 M_{\odot}$ and the secondary is a star with a minimum mass of $m_{B} = 0.53 M_{\odot}$. Additionally, on the basis of precise radial velocity (RV) data a Jovian planet with a minimum mass of $m_p = 7 M_{\mathrm{Jup}}$, orbiting the primary on a nearly circular S-type orbit with $e_p = 0.05$ and $a_p = 1.09\,$AU, has recently been announced. We investigate large sets of orbital fits consistent with HD 59686's radial velocity data by applying bootstrap and systematic grid-search techniques coupled with self-consistent dynamical fitting. We perform long-term dynamical integrations of these fits to constrain the permitted orbital configurations. We find that if the binary and the planet in this system have prograde and aligned coplanar orbits, there are narrow regions of stable orbital solutions locked in a secular apsidal alignment with the angle between the periapses, $\Delta \omega$, librating about $0^\circ$. We also test a large number of mutually inclined dynamical models in an attempt to constrain the three-dimensional orbital architecture. We find that for nearly coplanar and retrograde orbits with mutual inclination $145^\circ \lesssim \Delta i \leq 180^\circ$, the system is fully stable for a large range of orbital solutions.