Dynamical Analysis of the Circumprimary Planet in the Eccentric Binary System HD 59686

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-circle dot and the secondary is a star with a minimum mass of m(B) = 0.53 M-circle dot. Additionally, on the basis of precise radial velocity (RV) data, a Jovian planet with a minimum mass of m(p) = 7 M-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 RV 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 degrees. 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 degrees less than or similar to Delta i less than or similar to 180 degrees, the system is fully stable for a large range of orbital solutions.