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1. Coplanar Circumbinary Planets Can Be Unstable to Large Tilt Oscillations in the Presence of an Inner Polar Planet

   https://doi.org/10.3847/2041-8213/acbcc9  

   Childs, Anna C. ; Martin, Rebecca G. ; Lepp, Stephen ; Lubow, Stephen H. ; Geller, Aaron M. ( March 2023 , The Astrophysical Journal Letters)

   Mutually misaligned circumbinary planets may form in a warped or broken gas disk or from later planet–planet interactions. With numerical simulations and analytic estimates we explore the dynamics of two circumbinary planets with a large mutual inclination. A coplanar inner planet causes prograde apsidal precession of the binary and the stationary inclination for the outer planet is higher for larger outer planet orbital radius. In this case a coplanar outer planet always remains coplanar. On the other hand, a polar inner planet causes retrograde apsidal precession of the binary orbit and the stationary inclination is smaller for larger outer planet orbital radius. For a range of outer planet semimajor axes, an initially coplanar orbit is librating meaning that the outer planet undergoes large tilt oscillations. Circumbinary planets that are highly inclined to the binary are difficult to detect—it is unlikely for a planet to have an inclination below the transit detection limit in the presence of a polar inner planet. These results suggest that there could be a population of circumbinary planets that are undergoing large tilt oscillations.
2. Relativistic Dynamical Stability Criterion of Multiplanet Systems with a Distant Companion

   https://doi.org/10.3847/1538-4357/ac2c70  

   Wei, Lingfeng ; Naoz, Smadar ; Faridani, Thea ; Farr, Will M. ( December 2021 , The Astrophysical Journal)

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

   https://doi.org/10.1051/0004-6361/201935220  

   de Elía, G. C. ; Zanardi, M. ; Dugaro, A. ; Naoz, S. ( July 2019 , Astronomy & Astrophysics)

   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 1more »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 N-body simulations shows that the inverse Lidov-Kozai 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 N-body simulations can be very well explained by the analytical criteria derived in our investigation.« less
4. Eccentric debris belts reveal the dynamical history of the companion exoplanet

   https://doi.org/10.1093/mnras/stac2621  

   Rodet, Laetitia ; Lai, Dong ( September 2022 , Monthly Notices of the Royal Astronomical Society)

   In recent years, a number of eccentric debris belts have been observed in extrasolar systems. The most common explanation for their shape is the presence of a nearby eccentric planetary companion. The gravitational perturbation from such a companion would induce periodic eccentricity variations on the planetesimals in the belt, with a range of precession frequencies. The overall expected shape is an eccentric belt with a finite minimum width. However, several observed eccentric debris discs have been found to exhibit a narrower width than the theoretical expectation. In this paper, we study two mechanisms that can produce this small width: (i) the protoplanetary disc can interact with the planet and/or the planetesimals, slowly driving the eccentricity of the former and damping the eccentricities of the latter; and (ii) the companion planet could have gained its eccentricity stochastically, through planet–planet scatterings. We show that under appropriate conditions, both of these scenarios offer a plausible way to reduce the minimum width of an eccentric belt exterior to a perturbing planet. However, the effects of protoplanetary discs are diminished at large separations (a > 10 au) due to the scarcity of gas and the limited disc lifetime. These findings suggest that one canmore »use the shape and width of debris discs to shed light on the evolution of extrasolar systems, constraining the protoplanetary disc properties and the prevalence of planet–planet scatterings. Further observations of debris-harbouring systems could confirm whether thin debris belts are a common occurrence, or the results of rare initial conditions or evolutionary processes.

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5. Dynamical Mass of the Exoplanet Host Star HR 8799

   https://doi.org/10.3847/1538-3881/ac3bb5  

   Sepulveda, Aldo G. ; Bowler, Brendan P. ( January 2022 , The Astronomical Journal)

   HR 8799 is a young A5/F0 star hosting four directly imaged giant planets at wide separations (∼16–78 au), which are undergoing orbital motion and have been continuously monitored with adaptive optics imaging since their discovery over a decade ago. We present a dynamical mass of HR 8799 using 130 epochs of relative astrometry of its planets, which include both published measurements and new medium-band 3.1μm observations that we acquired with NIRC2 at Keck Observatory. For the purpose of measuring the host-star mass, each orbiting planet is treated as a massless particle and is fit with a Keplerian orbit using Markov chain Monte Carlo. We then use a Bayesian framework to combine each independent total mass measurement into a cumulative dynamical mass using all four planets. The dynamical mass of HR 8799 is${1.47}_{-0.17}^{+0.12}$M_⊙assuming a uniform stellar mass prior, or${1.46}_{-0.15}^{+0.11}$M_⊙with a weakly informative prior based on spectroscopy. There is a strong covariance between the planets’ eccentricities and the total system mass; when the constraint is limited to low-eccentricity solutions ofe< 0.1, which are motivated by dynamical stability, our mass measurement improves to${1.43}_{-0.07}^{+0.06}$M_⊙. Our dynamical mass and other fundamental measured parameters of HRmore »8799 together with Modules for Experiments in Stellar Astrophysics Isochrones and Stellar Tracks grids yields a bulk metallicity most consistent with [Fe/H] ∼ −0.25–0.00 dex and an age of 10–23 Myr for the system. This implies hot-start masses of 2.7–4.9M_Jupfor HR 8799 b and 4.1–7.0M_Jupfor HR 8799 c, d, and e, assuming they formed at the same time as the host star.

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