 Award ID(s):
 1739160
 Publication Date:
 NSFPAR ID:
 10137095
 Journal Name:
 Astronomy & Astrophysics
 Volume:
 627
 Page Range or eLocationID:
 A17
 ISSN:
 00046361
 Sponsoring Org:
 National Science Foundation
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ABSTRACT We study the stationary points of the hierarchical three body problem in the planetary limit (m1, m2 ≪ m0) at both the quadrupole and octupole orders. We demonstrate that the extension to octupole order preserves the principal stationary points of the quadrupole solution in the limit of small outer eccentricity e2 but that new families of stable fixed points occur in both prograde and retrograde cases. The most important new equilibria are those that branch off from the quadrupolar solutions and extend to large e2. The apsidal alignment of these families is a function of mass and inner planet eccentricity, and is determined by the relative directions of precession of ω1 and ω2 at the quadrupole level. These new equilibria are also the most resilient to the destabilizing effects of relativistic precession. We find additional equilibria that enable libration of the inner planet argument of pericentre in the limit of radial orbits and recover the nonlinear analogue of the Laplace–Lagrange solutions in the coplanar limit. Finally, we show that the chaotic diffusion and orbital flips identified with the eccentric Kozai–Lidov mechanism and its variants can be understood in terms of the stationary points discussed here.

Abstract Multiplanetary systems are prevalent in our Galaxy. The longterm stability of such systems may be disrupted if a distant inclined companion excites the eccentricity and inclination of the inner planets via the eccentric Kozai–Lidov mechanism. However, the star–planet and the planet–planet interactions can help stabilize the system. In this work, we extend the previous stability criterion that only considered the companion–planet and planet–planet interactions by also accounting for shortrange forces or effects, specifically, relativistic precession induced by the host star. A general analytical stability criterion is developed for planetary systems with N inner planets and a relatively distant inclined perturber by comparing precession rates of relevant dynamical effects. Furthermore, we demonstrate as examples that in systems with two and three inner planets, the analytical criterion is consistent with numerical simulations using a combination of Gauss’s averaging method and direct N body integration. Finally, the criterion is applied to observed systems, constraining the orbital parameter space of a possible undiscovered companion. This new stability criterion extends the parameter space in which an inclined companion of multiplanet systems can inhabit.

ABSTRACT Exoplanetary observations reveal that the occurrence rate of hot Jupiters is correlated with star clustering. In star clusters, interactions between planetary systems and close flyby stars can significantly change the architecture of primordially coplanar, circular planetary systems. Flybys can impact hot Jupiter formation via activation of higheccentricity excitation mechanisms such as the Zeipel–Lidov–Kozai (ZLK) effect and planet–planet scattering. Previous studies have shown that, for a twoplanet system, close flybys, especially at high incidence angles, can efficiently activate the ZLK mechanism, thus triggering higheccentricity tidal migration and ultimately form hot Jupiters. Here, we extend our previous study with a multiplanet (triple) system. We perform highprecision, highaccuracy fewbody simulations of stellar flybys and subsequent planetary migration within the perturbed planetary systems using the code spacehub. Our simulations demonstrate that a single close flyby on a multiplanet system can activate secular chaos and ultimately lead to hot Jupiter formation via higheccentricity migration. We find that the hot Jupiter formation rate per system increases with both the size of the planetary system and the mass of the outer planet, and we quantify the relative formation fractions for a range of parameters. Hot Jupiters formed via secular chaos are expected to be accompanied bymore »

Aims. The orbit of the outer satellite Alexhelios of (216) Kleopatra is already constrained by adaptiveoptics astrometry obtained with the VLT/SPHERE instrument. However, there is also a preceding occultation event in 1980 attributed to this satellite. Here, we try to link all observations, spanning 1980–2018, because the nominal orbit exhibits an unexplained shift by + 60° in the true longitude. Methods. Using both a periodogram analysis and an ℓ = 10 multipole model suitable for the motion of mutually interacting moons about the irregular body, we confirmed that it is not possible to adjust the respective osculating period P 2 . Instead, we were forced to use a model with tidal dissipation (and increasing orbital periods) to explain the shift. We also analysed light curves spanning 1977–2021, and searched for the expected spin deceleration of Kleopatra. Results. According to our bestfit model, the observed period rate is Ṗ 2 = (1.8 ± 0.1) × 10 −8 d d −1 and the corresponding timelag Δ t 2 = 42 s of tides, for the assumed value of the Love number k 2 = 0.3. This is the first detection of tidal evolution for moons orbiting 100 km asteroids. The corresponding dissipationmore »

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