Abstract
Aims. The detection of the first exoplanet around a solar-type star revealed the existence of close-in planets. Several of these close-in planets are part of multi-planet systems. For systems detected via the radial velocity (RV) method, we lack information on the mutual inclination of the orbital planes. The aim of this work is to study the long-term stability of RV-detected two-planet systems with close-in planets and identify possible three-dimensional configurations for these systems that are compatible with observations. To do so, we focused on the protective mechanism of the Lidov-Kozai (LK) secular resonance and studied the effects of general relativity (GR) on long-term evolution. Methods. By means of an analytical study based on a high-order secular Hamiltonian expansion in the eccentricities and inclinations, we first identified ranges of values for the orbital and mutual inclinations that are compatible with the presence of the LK resonance in the purely gravitational case. Then, adding the secular contribution of the relativistic corrections exerted by the central star on the inner planet, namely the advance of its pericenter precession, we analysed the outcomes of the two sets of simulations. We compared our results to analytical estimates to determine the importance of GR effects. Results. We find that for the majority of the systems considered, GR strongly affects the dynamics of the system and, most of the time, voids the LK resonance, as observed for GJ 649, GJ 832, HD 187123, HD 190360, HD 217107, and HD 47186. The long-term stability of these systems is then possible whatever the mutual inclination of the orbits. On the contrary, for GJ 682, HD 11964, HD 147018, and HD 9446, the LK resonant region in the parameter space of the orbital and mutual inclinations is left (almost) unchanged when GR effects are considered, and consequently their long-term stability is only possible if the mutual inclination of the orbits is low or if the systems are in the LK regime with a high mutual inclination.
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