On the Validity of the "Hill Radius Criterion" for the Ejection of Planets from Stellar Habitable Zones

We challenge the customary assumption that the entering of an Earth-mass planet into the Hill radius (or multiples of the Hill radius) of a giant planet is a valid criterion for its ejection from the star-planet system. This assumption has widely been used in previous studies, especially those with an astrobiological focus. As intriguing examples, we explore the dynamics of the systems HD 20782 and HD 188015. Each system possesses a giant planet that remains in or crosses into the stellar habitable zone, thus effectively thwarting the possibility of habitable terrestrial planets. In the case of HD 188015, the orbit of the giant planet is almost circular, whereas in the case of HD 20782, it is extremely elliptical. Although it is found that Earth-mass planets are eventually ejected from the habitable zones of these systems, the "Hill Radius Criterion" is identified as invalid for the prediction of when the ejection is actually occurring.