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The close-in planet orbiting GJ 436 presents a puzzling orbital eccentricityconsidering its very short orbital period. Given the age of the system, thisplanet should have been tidally circularized a long time ago. Many attempts toexplain this were proposed in recent years, either involving abnormally weaktides, or the perturbing action of a distant companion. We address here thelatter issue based on Kozai migration. We propose that GJ 436b was formerlylocated further away from the star and that it underwent a migration induced bya massive, inclined perturber via Kozai mechanism. In this context, theperturbations by the companion trigger high amplitude variations to GJ 436bthat cause tides to act at periastron. Then the orbit tidally shrinks to reachits present day location. We numerically integrate the 3-body system includingtides and General Relativity correction. We first show that starting from thepresent-day location of GJ 436b inevitably leads to damping the Kozaioscillations and to rapidly circularizing the planet. Conversely, starting from5-10 times further away allows the onset of Kozai cycles. The tides act in peakeccentricity phases and reduce the semi-major axis of the planet. The netresult is an evolution characterized by two phases: a first one with Kozaicycles and a slowly shrinking semi-major axis, and a second one once the planetgets out of the Kozai resonance characterized by a more rapid decrease. Thetimescale of this process appears in most cases much longer than the standardcircularization time of the planet by a factor larger than 50. This model canprovide a solution to the eccentricity paradox of GJ 436b. Depending on thevarious orbital configurations, it can take several Gyrs to GJ 436b to achievea full orbital decrease and circularization. According to this scenario, wecould be witnessing today the second phase of the scenario where the semi-majoraxis is already reduced while the eccentricity is still significant. We thenexplore the parameter space and derive in which conditions this model can berealistic given the age of the system. This yields constraints on thecharacteristics of the putative companion.

Dynamical evolution of the Gliese 436 planetary system - Kozai migration as a potential source for Gliese 436b's eccentricity