| Abstract
| - Context. The close-in planet orbiting GJ 436 presents a puzzling orbital eccentricity (e ≃ 0.14) considering its very short orbital period. Given the age of the system, this planet should have been tidally circularized a long time ago. Many attempts to explain this were proposed in recent years, either involving abnormally weak tides, or the perturbing action of a distant companion. Aims. In this paper, we address the latter issue based on Kozai migration. We propose that GJ 436b was formerly located further away from the star and that it underwent a migration induced by a massive, inclined perturber via Kozai mechanism. In this context, the perturbations by the companion trigger high-amplitude variations to GJ 436b that cause tides to act at periastron. Then the orbit tidally shrinks to reach its present day location. Methods. We numerically integrate the 3-body system including tides and general relativity correction. We use a modified symplectic integrator as well as a fully averaged integrator. The former is slower but accurate to any order in semi-major axis ratio, while the latter is first truncated to some order (4th) in semi-major axis ratio before averaging. Results. We first show that starting from the present-day location of GJ 436b inevitably leads to damping the Kozai oscillations and to rapidly circularizing the planet. Conversely, starting from 5-10 times further away allows the onset of Kozai cycles. The tides act in peak eccentricity phases and reduce the semi-major axis of the planet. The net result is a two-fold evolution, characterized by two phases: a first one with Kozai cycles and a slowly shrinking semi-major axis, and a second one once the planet gets out of the Kozai resonance characterized by a more rapid decrease. The timescale of this process appears in most cases much longer than the standard circularization time of the planet by a factor of 50 or above. Conclusions. This model can provide a solution to the eccentricity paradox of GJ 436b. Depending on the various orbital configurations (mass and location o the perturber, mutual inclination, etc.), it can take several Gyr to GJ 436b to achieve a full orbital decrease and circularization. According to this scenario, we could be witnessing today the second phase of the scenario, where the semi-major, axis is already reduced while the eccentricity is still significant. We then explore the parameter space and derive in which conditions this model can be realistic given the age of the system. This yields constraints on the characteristics of the putative companion.
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