Highly eccentric orbits are one of the major surprises of exoplanets relative to the solar system and indicate rich and tumultuous dynamical histories. One system of particular interest is Kepler1656, which hosts a subJovian planet with an eccentricity of 0.8. Sufficiently eccentric orbits will shrink in the semimajor axis due to tidal dissipation of orbital energy during periastron passage. Here our goal was to assess whether Kepler1656b is currently undergoing such higheccentricity migration, and to further understand the system’s origins and architecture. We confirm a second planet in the system with
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Abstract M _{c}= 0.40 ± 0.09M _{jup}and P_{c}= 1919 ± 27 days. We simulated the dynamical evolution of planet b in the presence of planet c and find a variety of possible outcomes for the system, such as tidal migration and engulfment. The system is consistent with an in situ dynamical origin of planet b followed by subsequent eccentric Kozai–Lidov perturbations that excite Kepler1656b’s eccentricity gently, i.e., without initiating tidal migration. Thus, despite its high eccentricity, we find no evidence that planet b is or has migrated through the higheccentricity channel. Finally, we predict the outer orbit to be mutually inclined in a nearly perpendicular configuration with respect to the inner planet orbit based on the outcomes of our simulations and make observable predictions for the inner planet’s spin–orbit angle. Our methodology can be applied to other eccentric or tidally locked planets to constrain their origins, orbital configurations, and properties of a potential companion. 
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.more » « less

Abstract The recent discoveries of WD J091405.30+191412.25 (WD J0914 hereafter), a white dwarf (WD) likely accreting material from an icegiant planet, and WD 1856+534 b (WD 1856 b hereafter), a Jupitersized planet transiting a WD, are the first direct evidence of giant planets orbiting WDs. However, for both systems, the observations indicate that the planets’ current orbital distances would have put them inside the stellar envelope during the redgiant phase, implying that the planets must have migrated to their current orbits after their host stars became WDs. Furthermore, WD J0914 is a very hot WD with a short cooling time that indicates a fast migration mechanism. Here, we demonstrate that the Eccentric Kozai–Lidov Mechanism, combined with stellar evolution and tidal effects, can naturally produce the observed orbital configurations, assuming that the WDs have distant stellar companions. Indeed, WD 1856 is part of a stellar triple system, being a distant companion to a stellar binary. We provide constraints for the orbital and physical characteristics for the potential stellar companion of WD J0914 and determine the initial orbital parameters of the WD 1856 system.more » « less

null (Ed.)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.more » « less

ABSTRACT The binary star Par 1802 in the Orion Nebula presents an interesting puzzle in the field of stellar dynamics and evolution. Binary systems such as Par 1802 are thought to form from the same natal material and thus the stellar members are expected to have very similar physical attributes. However, Par 1802’s stars have significantly different temperatures despite their identical (within $3\, {\rm per\, cent}$) masses of about 0.39 M⊙. The leading proofofconcept idea is that a third companion gravitationally induced the two stars to orbit closer than their Roche limit, which facilitated heating through tidal effects. Here we expand on this idea and study the threebody dynamical evolution of such a system, including tidal and premainsequence evolution. We also include tidal heating and mass transfer at the onset of Roche limit crossing. We show, as a proofofconcept, that mass transfer combined with tidal heating can naturally explain the observed temperature discrepancy. We also predict the orbital configuration of the possible tertiary companion. Finally, we suggest that the dynamical evolution of such a system has pervasive consequences. We expect an abundance of systems to undergo mass transfer during their premainsequence time, which can cause temperature differences.more » « less

ABSTRACT At least $70\, {\rm per\, cent}$ of massive OBAtype stars reside in binary or higher order systems. The dynamical evolution of these systems can lend insight into the origins of extreme phenomena such as Xray binaries and gravitational wave sources. In one such dynamical process, the Eccentric Kozai–Lidov (EKL) mechanism, a third companion star alters the secular evolution of a binary system. For dynamical stability, these triple systems must have a hierarchical configuration. We explore the effects of a distant third companion’s gravitational perturbations on a massive binary’s orbital configuration before significant stellar evolution has taken place (≤10 Myr). We include tidal dissipation and general relativistic precession. With large (38 000 total) Monte Carlo realizations of massive hierarchical triples, we characterize imprints of the birth conditions on the final orbital distributions. Specifically, we find that the final eccentricity distribution over the range of 0.1–0.7 is an excellent indicator of its birth distribution. Furthermore, we find that the period distributions have a similar mapping for wide orbits. Finally, we demonstrate that the observed period distribution for approximately 10Myrold massive stars is consistent with EKL evolution.more » « less

Aims. We analyze the behavior of the argument of pericenter ω 2 of an outer particle in the elliptical restricted threebody problem, focusing on the ω 2 resonance or inverse LidovKozai 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 Nbody 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 between 0.25 and 0.40825, (d ω 2 /d τ ) quad can be vanished for any particle for a suitable selection of pairs (Ω 2 , i 2 ). Our analysis of the Nbody simulations shows that the inverse LidovKozai resonance is possible for small, moderate, and high values of e 1 . Moreover, such a resonance produces distinctive features in the evolution of a particle in the (Ω 2 , i 2 ) plane. In fact, if ω 2 librates and Ω 2 circulates, the extremes of i 2 at Ω 2 = 90° and 270° do not reach the same value, while if ω 2 and Ω 2 librate, the evolutionary trajectory of the particle in the (Ω 2 , i 2 ) plane shows evidence of an asymmetry with respect to i 2 = 90°. The evolution of ω 2 associated with the outer particles of the Nbody simulations can be very well explained by the analytical criteria derived in our investigation.more » « less