Fear the Shadows of the Giants: On Secular Perturbations in Circumstellar Habitable Zones of Double Stars

After the detection of extrasolar planets in binary- and multiple-star systems, questions arose about their dynamics and habitability. In this study we investigate a five-dimensional parameter space for wide binary stars with a massive planet beyond the habitable zone (HZ). Our aim is to reveal those orbital and physical parameter combinations that expose bodies in the primary star's HZ to secular perturbations. Building on an established semianalytical model, we combine two separate analytical models into a new one to treat the restricted four-body problem. We apply this new Combined Analytical Model (CAM) to different synthetic systems and systematically map the occurrence of secular resonances (SRs). These maps are then visualized as two-dimensional sections of the parameter space. The CAM model has a median error below 3% relative to numerical reference simulations. We also derive a simplified CAM that performs well for hierarchical systems with moderate to large separations between the bodies. Our results show that SRs appear in the HZ even for large secondary-star distances (up to >1000 au) if either (i) the planet's distance is larger than Jupiter's or (ii) its mass is about Saturn's or lower. Changes in the secondary star's eccentricity by stellar flybys or galactic tides can push a formerly dynamically quiet HZ to a high-eccentricity state. Based on these results, we provide the easy-to-use online tool "SHaDoS" that evaluates the CAM for a given user input and traces the locations of SRs in the HZ in two-dimensional parameter space plots.