Unveiling hidden companions in post-common-envelope binaries: A robust strategy and uncertainty exploration

Some post-common-envelope binaries 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. 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. 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 MCMC approach and discuss the error range for parameters. 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. 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 ($e=0.91^{+0.07}_{-0.17}$) with a variety of potential periods ($P = 16.69 ^{+0.47}_{-0.42}$ yr.)