Context. Recently, using the light-travel time effect, planets and substellar companions have been proposed to orbit around binary star systems (also known as circumbinary companions) as a result of variations in timing of the observed eclipses. For the majority of these systems the proposed orbital architecture features a crossing of the orbital configurations as a result of high eccentricities for one or both of the companions. For such systems, strong mutual gravitational interactions are expected, resulting in catastrophic orbital instabilities, or collisions between the proposed components, on very short timescales.
Aims. We re-examine the primary and secondary eclipse timings of the short-period and semi-detached binary RZ Draconis (RZ Dra). The proposed companions were reported to have masses of around ≃ 0.07 and ≃ 0.18 M⊙ with the inner companion on an orbit with moderate eccentricity (0.46), whose apocenter distance crosses the orbit of the outer companion. We show that the companions proposed previously follow highly unstable orbits. In an attempt to find a stable system we searched the underlying χ2 parameter space for a best-fit model and carried out an orbit-stability study to test possible best-fit models. If the binary period changes are truly due to additional massive companions in a hierarchical configuration, they must follow stable orbits.
Methods. For numerical orbital stability calculations we used well established orbit integration routines. Computations were carried out using a large-scale multi-CPU computing environment. Our data analysis of times of primary and secondary eclipse is based on the Levenberg-Marquardt least-squares minimization algorithm using the two-body Keplerian light-travel time effect model.
Results. Despite the wide variety of potential models tested for the RZ Dra system in this work, we found very few models that were stable for even one million years, with the vast majority of systems tested falling apart on timescales of just hundreds of years. It seems therefore likely that the observed timing variations are not solely the result of massive, unseen companions.
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