Close-in planets evolve under extreme conditions, raising questions about their origins and current nature. Two predominant mechanisms are orbital migration, which brings them close to their star, and atmospheric escape under the resulting increased irradiation. Yet, their relative roles remain unclear because we lack models that couple the two mechanisms with high precision on secular timescales. To address this need, we developed the JADE code, which simulates the secular atmospheric and dynamical evolution of a planet around its star, and can include the perturbation induced by a distant third body. On the dynamical side, the 3D evolution of the orbit is modeled under stellar and planetary tidal forces, a relativistic correction, and the action of the distant perturber. On the atmospheric side, the vertical structure of the atmosphere is integrated over time based on its thermodynamical properties, inner heating, and the evolving stellar irradiation, which results, in particular, in photo-evaporation. The JADE code is benchmarked on GJ436 b, prototype of evaporating giants on eccentric, misaligned orbits at the edge of the hot Neptunes desert. We confirm that its orbital architecture is well explained by Kozai migration and unveil a strong interplay between its atmospheric and orbital evolution. During the resonance phase, the atmosphere pulsates in tune with the Kozai cycles, which leads to stronger tides and an earlier migration. This triggers a strong evaporation several Gyr after the planet formed, refining the paradigm that mass loss is dominant in the early age of close-in planets. This suggests that the edge of the desert could be formed of warm Neptunes whose evaporation was delayed by migration. It strengthens the importance of coupling atmospheric and dynamical evolution over secular timescales, which the JADE code will allow simulating for a wide range of systems.
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