Context. Some post-common-envelope binaries (PCEBs) are binary stars with short periods that exhibit significant period variations over long observational time spans. These eclipse timing variations (ETVs) are most likely to be accounted for by the presence of an unseen massive companion, potentially of planetary or substellar nature, and the light-travel time (LTT) effect. The existence of such companions challenges our current understanding of planetary formation and stellar evolution.
Aims: In this study, our main objective is to describe the diversity of compatible nontransit companions around PCEBs and explore the robustness of the solutions by employing tools for uncertainty estimation. We select the controversial data of the QS Vir binary star, which previous studies have suggested hosts a planet.
Methods: We employ a minimizing strategy, using genetic algorithms to explore the global parameter space followed by refinement of the solution using the simplex method. We evaluate errors through the classical Markov chain Monte Carlo (MCMC) approach and discuss the error range for parameters, considering the 1σ values obtained from the minimization.
Results: Our results highlight the strong dependence of ETV models for close binaries on the dataset used, which leads to relatively loose constraints on the parameters of the unseen companion. We find that the shape of the O - C curve is influenced by the dataset employed. We propose an alternative method to evaluate errors on the orbital fits based on a grid search surrounding the best-fit values, obtaining a wider range of plausible solutions that are compatible with goodness-of-fit statistics. We also analyze how the parameter solutions are affected by the choice of the dataset, and find that this system continuously changes the compatible solutions as new data are obtained from eclipses.
Conclusions: The best-fit parameters for QS Vir correspond to a low-mass stellar companion (57.71 M_jup ranging from ~40 to ~64 M_jup) on an eccentric orbit (e = 0.91_−0.17^+0.07) with a variety of potential periods (P = 16.69_−0.42^+0.47 yr.). Most solutions within 1σ exhibit regular orbits, despite their high eccentricity. Additional observations are required to accurately determine the period and other parameters of the unseen companion. In this context, we propose that a fourth body should not be modeled to fit the data, unless new observations considerably modify the computed orbital parameters. This methodology can be applied to other evolved binary stars suspected of hosting companions.