Application of the Titius–Bode Rule to the 55 Cancri System: Tentative Prediction of a Possibly Habitable Planet

Abstract

Abstract Following the notion that the Titius–Bode rule (TBR) may also be applicable to some extrasolar planetary systems, although this number could be relatively small, it is applied to 55 Cancri, which is a G-type main-sequence star currently known to host five planets. Following a concise computational process, we tentatively identified four new hypothetical planetary positions, given as 0.081, 0.41, 1.51, and 2.95 AU from the star. The likelihood that these positions are occupied by real existing planets is significantly enhanced for the positions of 1.51 and 2.95 AU in view of previous simulations on planet formation and planetary orbital stability. For example, Raymond, Barnes, and Gorelick (2008, ApJ, 689, 478) argued that additional planets would be possible between 55 Cnc f and 55 Cnc d, which would include planets situated at 1.51 and 2.95 AU. If two additional planets are assumed to exist between 55 Cnc f and 55 Cnc d, the deduced domains of stability would be given as 1.3–1.6 and 2.2–3.3 AU. The possible planet near 1.5 AU appears to be located at the outskirts of the stellar habitable zone, which is, however, notably affected by the stellar parameters as well as the adopted model of circumstellar habitability. We also computed the distance of the next possible outer planet in the 55 Cnc system, which, if existing, is predicted to be located between 10.9 and 12.2 AU, which is consistent with orbital stability constraints. The inherent statistical significance of the TBR was evaluated following a method by Lynch (2003, MNRAS, 341, 1174). Yet it is up to future planetary search missions to verify or falsify the applicability of the TBR to the 55 Cnc system, and to obtain information on additional planets, if existing.