Dynamical influence of a wide binary companion on giant planet migration

<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>

Inverse Lidov-Kozai resonance for an outer test particle due to an eccentric perturber

Aims. We analyze the behavior of the argument of pericenter ω2 of an outer particle in the elliptical restricted three-body problem, focusing on the ω2 resonance or inverse Lidov-Kozai resonance. Methods. First, we calculated the contribution of the terms of quadrupole, octupole, and hexadecapolar order of the secular approximation of the potential to the outer particle’s ω2 precession rate (dω2∕dτ). Then, we derived analytical criteria that determine the vanishing of the ω2 quadrupole precession rate (dω2/dτ)quad for different values of the inner perturber’s eccentricity e1. Finally, we used such analytical considerations and described the behavior of ω2 of outer particles extracted from N-body simulations developed in a previous work. Results. Our analytical study indicates that the values of the inclination i2 and the ascending node longitude Ω2 associated with the outer particle that vanish (dω2/dτ)quad strongly depend on the eccentricity e1 of the inner perturber. In fact, if e1 < 0.25 (>0.40825), (dω2/dτ)quad is only vanished for particles whose Ω2 circulates (librates). For e1 between 0.25 and 0.40825, (dω2/dτ)quad can be vanished for any particle for a suitable selection of pairs (Ω2, i2). Our analysis of the N-body simulations shows that the inverse Lidov-Kozai resonance is possible for small, moderate, and high values of e1. Moreover, such a resonance produces distinctive features in the evolution of a particle in the (Ω2, i2) plane. In fact, if ω2 librates and Ω2 circulates, the extremes of i2 at Ω2 = 90° and 270° do not reach the same value, while if ω2 and Ω2 librate, the evolutionary trajectory of the particle in the (Ω2, i2) plane shows evidence of an asymmetry with respect to i2 = 90°. The evolution of ω2 associated with the outer particles of the N-body simulations can be very well explained by the analytical criteria derived in our investigation.

The 3D secular dynamics of radial-velocity-detected planetary systems

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. The extent of the Lidov-Kozai resonant region is discussed for ten planetary systems (HD 11506, HD 12661, HD 134987, HD 142, HD 154857, HD 164922, HD 169830, HD 207832, HD 4732, and HD 74156).

Controlling the Eccentricity of Polar Lunar Orbits with Low-Thrust Propulsion

It is well known that lunar satellites in polar orbits suffer a high increase on the eccentricity due to the gravitational perturbation of the Earth. That effect is a natural consequence of the Lidov-Kozai resonance. The final fate of such satellites is the collision with the Moon. Therefore, the control of the orbital eccentricity leads to the control of the satellite's lifetime. In the present work we study this problem and introduce an approach in order to keep the orbital eccentricity of the satellite at low values. The whole work was made considering two systems: the 3-body problem, Moon-Earth-satellite, and the 4-body problem, Moon-Earth-Sun-satellite. First, we simulated the systems considering a satellite with initial eccentricity equals to 0.0001 and a range of initial altitudes between 100 km and 5000 km. In such simulations we followed the evolution of the satellite's eccentricity. We also obtained an empirical expression for the length of time needed to occur the collision with the Moon as a function of the initial altitude. The results found for the 3-body model were not significantly different from those found for the 4-body model. Secondly, using low-thrust propulsion, we introduced a correction of the eccentricity every time it reached the value 0.05. These simulations were made considering a set of different thrust values, from 0.1 N up to 0.4 N which can be obtained by using Hall Plasma Thrusters. In each run we measured the length of time, needed to correct the eccentricity value (frome=0.04toe=0.05). From these results we obtained empirical expressions of this time as a function of the initial altitude and as a function of the thrust value.