Exciting Mutual Inclination in Planetary Systems with a Distant Stellar Companion: The Case of Kepler-108

We study the excitation of mutual inclination between planetary orbits by a novel secular-orbital resonance in multi-planet systems perturbed by binary companions, which we call “ivection.” The ivection resonance happens when the nodal precession rate of the planet matches a multiple of the orbital frequency of the binary, and its physical nature is similar to the previously studied evection resonance. Capture into an ivection resonance requires encountering the resonance with slowly increasing nodal precession rate, and it can excite the mutual inclination of the planets without affecting their eccentricities. We discuss the possible outcomes of ivection resonance capture, and we use simulations to illustrate that it is a promising mechanism for producing the mutual inclination in systems where planets have significant mutual inclination but modest eccentricity, such as Kepler-108. We also find an apparent deficit of multi-planet systems that would have a nodal precession period comparable to the binary orbital period, suggesting that ivection resonance may inhibit formation of or destablize multi-planet systems with an external binary companion.

The Lynden-Bell bar formation mechanism in simple and realistic galactic models

ABSTRACT Using the canonical Hamilton–Jacobi approach we study the Lynden-Bell concept of bar formation based on the idea of orbital trapping parallel to the long or short axes of the oval potential distortion. The concept considered a single parameter – a sign of the derivative of the precession rate over angular momentum, determining the orientation of the trapped orbits. We derived a perturbation Hamiltonian that includes two more parameters characterizing the background disc and the perturbation, which are just as important as the earlier known one. This allows us to link the concept with the matrix approach in linear perturbation theory, the theory of weak bars, and explain some features of the non-linear secular evolution observed in N-body simulations.

Cassini state of Galilean Moons: Influence of a subsurface ocean

<p>Large moons such as the Galilean satellites are thought to be in an equilibrium rotation state, called a Cassini state (Peale, 1969). This state is characterized by a synchronous rotation and a precession rate of the rotation axis that is equal to the precession rate of the normal to its orbit. It also implies that the spin axis, the normal to the orbit and the normal to the Laplace plane are coplanar with a (nearly) constant obliquity.</p><p>For rigid bodies, up to 4 possible Cassini states exist, but not all of them are stable. It is generally assumed that the Galilean satellites are in Cassini State I for which the obliquity is close to zero (see e.g. Baland et al. 2012). However, it is also theoretically possible that these satellites occupy or occupied another Cassini state.</p><p>We here investigate how the interior structure, and in particular the presence of a subsurface ocean, influences the existence and stability of the different possible Cassini states.</p><p><em>References :</em></p><p>Baland, R.M., Yseboodt, M. and Van Hoolst, T. (2012). Obliquity of the Galilean satellites: The influence of a global internal liquid layer. Icarus 220, 435-448.</p><p>Peale, S. (1969). Generalized Cassini’s laws. Astron. J. 74 (3), 483-489.</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.