The Spin-Orbit Evolution of GJ 667C System: The Effect of Composition and Other Planet's Perturbations

Potentially habitable planets within the habitable zone of M-dwarfs are affected by tidal interaction. We studied the tidal evolution in GJ 667C using a numerical code we call TIDEV. We reviewed the problem of the dynamical evolution focusing on the effects that a rheological treatment, different compositions and the inclusion of orbital perturbations, have on the spin-down time and the probability to be trapped in a low spin-orbit resonance. Composition have a strong effect on the spin-down time, changing, 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 to reach a low resonance value (3:2) for the configuration of 6 planets. Capture probabilities are affected when assuming different compositions and eccentricities 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 noth- ing on spin-down times. The implications of the eccentricity variations and actual habitability of the GJ 667C system are discussed.