Aims. To date, more than 600 multi-planetary systems have been discovered. Due to the limitations of the detection methods, our knowledge of the systems is usually far from complete. In particular, for planetary systems discovered with the radial velocity (RV) technique, the inclinations of the orbital planes, and thus the mutual inclinations and planetary masses, are unknown. Our work aims to constrain the spatial configuration of several RV-detected extrasolar systems that are not in a mean-motion resonance.Methods. Through an analytical study based on a first-order secular Hamiltonian expansion and numerical explorations performed with a chaos detector, we identified ranges of values for the orbital inclinations and the mutual inclinations, which ensure the long-term stability of the system. Our results were validated by comparison with n-body simulations, showing the accuracy of our analytical approach up to high mutual inclinations (∼ 70 • -80 • ).Results. We find that, given the current estimations for the parameters of the selected systems, long-term regular evolution of the spatial configurations is observed, for all the systems, i) at low mutual inclinations (typically less than 35 • ) and ii) at higher mutual inclinations, preferentially if the system is in a Lidov-Kozai resonance. Indeed, a rapid destabilisation of highly mutually inclined orbits is commonly observed, due to the significant chaos that develops around the stability islands of the Lidov-Kozai resonance.

Aims. There are a growing number of giant planets discovered moving around one stellar component of a binary star, most of which have very diverse eccentricity. These discoveries raise the question of their formation and long-term evolution because the stellar companion can strongly affect the planet formation process. We aim to study the dynamical influence of a wide binary companion on the evolution of a single giant planet migrating in a protoplanetary disk. Methods. Using a symplectic N-body integrator adapted for binary star systems and modeling the dissipation due to the disk by appropriate formulae emerging from hydrodynamical simulations, we carried out 3200 simulations with different orbital parameters for the planet and different eccentricity and inclination values for the binary companion. The long-term evolution of the planets was followed for 100 Myr and the different dynamical behaviors were unveiled using a quadrupolar Hamiltonian approach. Results. We show that a capture in a Lidov-Kozai resonant state is far from automatic when the binary companion star is highly inclined, since only 36% of the systems end up locked in the resonance at the end of the simulations. Nevertheless, in the presence of a highly inclined binary companion, all the planetary evolutions are strongly influenced by the Lidov-Kozai resonance and the nonresonant evolutions present high eccentricity and inclination variations associated with circulation around the Lidov-Kozai islands.

The discovery of numerous circumprimary planets in the last few years has brought to the fore the question of planet formation in binary systems. The significant dynamical influence, during the protoplanetary disk phase, of a binary companion on a giant planet has previously been highlighted for wide binary stars. In particular, highly inclined binary companion can induce perturbations on the disk and the planets, through the Lidov-Kozai resonance, which could inhibit the formation process. In this work, we aim to study how the disk gravitational potential acting on the planet and the nodal precession induced by the wide binary companion with separation of 1000 AU on the disk act to suppress the Lidov-Kozai perturbations on a migrating giant planet. We derive new approximate formulas for the evolution of the disk’s inclination and longitude of the ascending node, in the case of a rigidly precessing disk with a decreasing mass and perturbed by a wide binary companion, which are suitable for N-body simulations. We carry out 3200 simulations with several eccentricity and inclination values for the binary companion. The gravitational and damping forces exerted by the disk on the planet tend to keep the latter in the midplane of the former, and suppress the effect of the binary companion by preventing the planet from getting locked in the Lidov-Kozai resonance during the disk phase. We also confirm that because of nodal precession induced by the binary, a primordial spin-orbit misalignment could be generated for circumprimary planets with an inclined binary companion.

Aims. The growing population of planets discovered in orbit around one stellar component of a binary star raises the question of the influence of the binary companion on the formation process of planetary systems. The aim of this work is to study the impact of a binary companion on the evolution of two-planet systems during both the type-II migration phase and their long-term evolution after the dissipation of the protoplanetary disk. Methods. We used the symplectic integrator SyMBA, modified to include a wide binary companion. We also included the Type-II migration of giant planets during the protoplanetary disk phase with suitable eccentricity and inclination damping as well as the gravitational potential acting on the planets due to the disk and the nodal precession of the disk induced by the binary companion. We considered various inclinations, eccentricities, and separations of the binary companion. Results. Disk migration allows for the formation of planet pairs in mean-motion resonances despite the presence of the binary companion. When the binary separation is wide (1000 au), the timescale of the perturbations that it raises on the planets is longer than the disk's lifetime and resonant pairs are routinely formed in the 2:1, 5:2, and 3:1 commensurabilities. Provided the planet-planet interaction timescale is smaller than the timescale of binary perturbations, these systems can remain in resonance long after the disk has dissipated. When the binary separation is smaller (250 au), only planets in the 2:1 resonance tend to remain in a resonant state and more chaotic evolutions are observed, as well as more ejections. After those ejections, the remaining planet can become eccentric due to the perturbations from the binary companion in addition, for strongly inclined binary companions, captures in the von Ziepel-Lidov-Kozai resonance can occur. Whereas in systems with two planets, this mechanism is quenched by planet-planet interactions. Our simulations reveal that the interplay between planet-disk, planet-planet, and planet-binary interactions can lead to the formation of resonant pairs of planets which remain stable over timescales much longer than the disk's lifetime.

<p>About half of the Sun-like stars are part of multiple-star systems. To date more than 100 planets are known moving around one stellar component of a binary star (S-type planets), with diverse eccentricities. These discoveries raise the question of their formation and long-term evolution, since the stellar companion can strongly affect the planet formation process. Here we study the dynamical influence of a wide binary companion on the (Type-II) migration of a single giant planet in the protoplanetary disk. Using a modified version of an N-body integrator adapted for binary star systems and adopting eccentricity and inclination damping formulae (derived from hydrodynamical simulations) to properly model the influence of the disk, we carried out more than 3500 numerical simulations with different initial configurations and study the dynamics of the systems up to 100 Myr. Particular attention is paid to the Lidov-Kozai resonance whose role is determinant for the evolution of the giant planet, although initially embedded in the disk, when the stellar companion is highly inclined. We highlight the high probability for the planet of experiencing, during the disk phase, a scattering event or an ejection due to the presence of the binary companion. We also show that a capture of the migrating planet in the Lidov-Kozai resonance is far from being automatic even when the binary companion is highly inclined, since only 10% of the systems actually end up in the resonance. Nevertheless, using a simplified quadrupolar hamiltonian approach, we point out that, for highly inclined binary companions, the dynamical evolutions are strongly affected by the Lidov-Kozai resonance islands, which create the pile-ups observed around – but not centred on – the pericenter values of 90° and 270° in the final distribution of the giant planets. The influence of the self-gravity of the disk on the previous results is finally discussed.</p>