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GJ 436b is a Neptune-size planet with 23.2 Earth masses in an ellipticalorbit of period 2.64 days and eccentricity 0.16. With a typical tidaldissipation factor (Q' ~ 10^6) as that of a giant planet with convectiveenvelope, its orbital circularization timescale under internal tidaldissipation is around 1 Gyr, at least two times less than the stellar age (>3Gyr). A plausible mechanism is that the eccentricity of GJ 436b is modulated bya planetary companion due to their mutual perturbation. Here we investigatethis possibility from the dynamical viewpoint. A general method is given topredict the possible locations of the dynamically coupled companions, includingin nearby/distance non-resonant or mean motion resonance orbits with the firstplanet. Applying the method to GJ 436 system, we find it is very unlikely thatthe eccentricity of GJ 436b is maintained at the present location by anearby/distance companion through secular perturbation or mean motionresonance. In fact, in all these simulated cases, GJ 436b will undergoeccentricity damp and orbital decay, leaving the present location within thestellar age. However, these results do not rule out the possible existence ofplanet companions in nearby/distance orbits, although they are not able tomaintain the eccentricity of GJ 436b.

Eccentricity modulation of a close-in planet by a companion - application to GJ 436 system