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 non-linear 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.
Inverse Lidov-Kozai resonance for an outer test particle due to an eccentric perturber
Aims. We analyze the behavior of the argument of pericenter ω 2 of an outer particle in the elliptical restricted three-body problem, focusing on the ω 2 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 ω 2 precession rate (d ω 2 ∕d τ ). Then, we derived analytical criteria that determine the vanishing of the ω 2 quadrupole precession rate (d ω 2 /d τ ) quad for different values of the inner perturber’s eccentricity e 1 . Finally, we used such analytical considerations and described the behavior of ω 2 of outer particles extracted from N-body simulations developed in a previous work. Results. Our analytical study indicates that the values of the inclination i 2 and the ascending node longitude Ω 2 associated with the outer particle that vanish (d ω 2 /d τ ) quad strongly depend on the eccentricity e 1 of the inner perturber. In fact, if e 1 < 0.25 (>0.40825), (d ω 2 /d τ ) quad is only vanished for particles whose Ω 2 circulates (librates). For e 1 more »
- Award ID(s):
- 1739160
- Publication Date:
- NSF-PAR ID:
- 10137095
- Journal Name:
- Astronomy & Astrophysics
- Volume:
- 627
- Page Range or eLocation-ID:
- A17
- ISSN:
- 0004-6361
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Multiplanetary systems are prevalent in our Galaxy. The long-term 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 short-range 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 high-eccentricity excitation mechanisms such as the Zeipel–Lidov–Kozai (ZLK) effect and planet–planet scattering. Previous studies have shown that, for a two-planet system, close flybys, especially at high incidence angles, can efficiently activate the ZLK mechanism, thus triggering high-eccentricity tidal migration and ultimately form hot Jupiters. Here, we extend our previous study with a multiplanet (triple) system. We perform high-precision, high-accuracy few-body 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 high-eccentricity 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 adaptive-optics 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 best-fit model, the observed period rate is Ṗ 2 = (1.8 ± 0.1) × 10 −8 d d −1 and the corresponding time-lag 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 »
-
ABSTRACT Mergers of binaries comprising compact objects can give rise to explosive transient events, heralding the birth of exotic objects that cannot be formed through single-star evolution. Using a large number of direct N-body simulations, we explore the possibility that a white dwarf (WD) is dynamically driven to tidal disruption by a stellar-mass black hole (BH) as a consequence of the joint effects of gravitational wave (GW) emission and Lidov–Kozai oscillations imposed by the tidal field of an outer tertiary companion orbiting the inner BH–WD binary. We explore the sensitivity of our results to the distributions of natal kick velocities imparted to the BH and WD upon formation, adiabatic mass loss, semimajor axes and eccentricities of the triples, and stellar-mass ratios. We find rates of WD–tidal disruption events (TDEs) in the range 1.2 × 10−3 − 1.4 Gpc−3 yr−1 for z ≤ 0.1, rarer than stellar TDEs in triples by a factor of ∼3–30. The uncertainty in the TDE rates may be greatly reduced in the future using GW observations of Galactic binaries and triples with LISA. WD–TDEs may give rise to high-energy X-ray or gamma-ray transients of duration similar to long gamma-ray bursts but lacking the signatures of a core-collapse supernova,more »
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Publisher's Version of Record
- https://doi.org/10.1051/0004-6361/201935220
