Spin-orbit evolution of the GJ 667C system: the effect of composition and other planets' perturbations

Potentially habitable planets within the habitable zone of M dwarfs are affected by tidal interaction. We studied tidal evolution in GJ 667C using a numerical code we call TIDEV. We reviewed the problem of dynamical evolution, focusing on the effects of a rheological treatment, different compositions and the inclusion of orbital perturbations on the spin-down time and the probability of becoming trapped in a low spin-orbit resonance. The composition has a noticeable effect on the spin-down time, which changes, in some cases, by almost a factor of 2 with respect to the value estimated for a reference Earth-like model. We calculated the time required to reach a low resonance value (3:2) for a configuration of six planets. Capture probabilities are affected when assuming different compositions and eccentricity variations. We chose planets b and c to evaluate the probabilities of capture in resonances below 5:2 for two compositions: Earth-like and Waterworld planets. We found that perturbations, although having a secular effect on eccentricities, have a low impact on capture probabilities and no effect on spin-down times. The implications of the eccentricity variations and actual habitability of the GJ 667C system are discussed.