We use numerical integrations to investigate the dynamical evolution of resonant Trojan and quasi-satellite companions during the late stages of migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. Our migration simulations begin with Jupiter and Saturn on orbits already well separated from their mutual 2:1 mean-motion resonance. Neptune and Uranus are decoupled from each other and have orbital eccentricities damped to near their current values. From this point we adopt a planet migration model in which the migration speed decreases exponentially with a characteristic timescale tau (the e-folding time). We perform a series of numerical simulations, each involving the migrating giant planets plus test particle Trojans and quasi-satellites. We find that the libration frequencies of Trojans are similar to those of quasi-satellites. This similarity enables a dynamical exchange of objects back and forth between the Trojan and quasi-satellite resonances during planetary migration. Furthermore, under the influence of these secondary resonances quasi-satellites can have their libration amplitudes enlarged until they undergo a close-encounter with their host planet and escape from the resonance. High-resolution simulations of this escape process reveal that ~80% of Jovian quasi-satellites experience one or more close-encounters within Jupiter's Hill radius (R_H) as they are forced out of the quasi-satellite resonance. As many as ~20% come within R_H/4 and ~2.5% come within R_H/10. Close-encounters of escaping quasi-satellites occur near or even below the 2-body escape velocity from the host planet.
The orbital distribution of trans-Neptunian objects provides strong evidence for the radial migration of Neptune. The outer planets' orbits are thought to have become unstable during the early stages with Jupiter having scattering encounters with a Neptune-class planet. As a consequence, Jupiter jumped inward by a fraction of an au, as required from inner solar system constraints, and obtained its current orbital eccentricity. The timing of these events is often linked to the lunar Late Heavy Bombardment that ended ~700 Myr after the dispersal of the protosolar nebula (t_0). Here we show inste…
Pebble accretion is an efficient mechanism able to build up the core of the giant planets within the lifetime of the protoplanetary disc gas-phase. The core grows via this process until the protoplanet reaches its pebble isolation mass and starts to accrete gas. During the growth, the protoplanet undergoes a rapid, large-scale, inward migration due to the interactions with the gaseous protoplanetary disc. In our work, we investigate how this early migration would have affected the minor body populations in our solar system. In particular, we focus on the Jupiter Trojans and the Hildas asteroid…
Close encounters (CEs) between celestial objects may exert significant influence on their orbits. The influence will be even enhanced when two groups of celestial objects are confined in stable orbital configurations, e.g. in adjacent mean motion resonances (MMRs). Plutinos and Neptune Trojans, trapped in the 2:3 and 1:1 MMRs with Neptune respectively, are such examples. %Meanwhile, many objects among these two groups have peculiar orbits, seemingly as the vestige of CEs. As the first part of our investigation, this paper provides a detailed description of CEs between Plutinos and Trojans and …
We aim to locate the stability region for Uranus Trojans (UT hereafter) and find out the dynamical mechanisms responsible for the structures in the phase space. Using the spectral number as the stability indicator, we construct the dynamical maps on the (a0, i0) plane. The proper frequencies of UTs are determined precisely so that we can depict the resonance web via a semi-analytical method. Two main stability regions are found, one each for the low-inclination (0-14deg) and high-inclination regime (32-59deg). There is also an instability strip in each of them, at 9deg and 51deg respectively. …
Context. More than 10000 Jupiter Trojans have been detected so far. They are moving around the L4 and L5 triangular Lagrangian points of the Sun-Jupiter system and their distributions can provide important clues to the early evolution of the Solar System. Aims. The number asymmetry of the L4 and L5 Jupiter Trojans is a longstanding problem. We aim to test a new mechanism in order to explain this anomalous feature by invoking the jumping-Jupiter scenario. Methods. First, we introduce the orbital evolution of Jupiter caused by the giant planet instability in the early Solar System. In this scena…
The stability of satellites in the solar system is affected by the so-called evection resonance. The moons of Saturn, in particular, exhibit a complex dynamical architecture in which co-orbital configurations occur, especially close to the planet where this resonance is present. We address the dynamics of the evection resonance, with particular focus on the Saturn system, and compare the known behavior of the resonance for a single moon to that of a pair of moons in co-orbital trojan configuration. We developed an analytic expansion of the averaged Hamiltonian of a trojan pair of bodies, inclu…
The Trojan clouds contain a surprisingly diverse population of objects. It is only by understanding this diversity can we unravel their history. The more objects Lucy visits the better we can constrain the formation and evolution of the giant planets. While Lucy will visit four Trojans in the L$_4$ cloud, its trajectory only passes one known Trojan system, the PM binary, in L$_5$. There is ample time in the Lucy timeline to possibly add additional L$_5$ targets, thereby maximizing the mission's science return. In the next decade, the 8.4-m Large Synoptic Survey Telescope (LSST), is expected to…
The Lucy Mission accomplishes its science during a series of five flyby encounters with seven Trojan asteroid targets. This mission architecture drives a concept of operations design that maximizes science return, provides redundancy in observations where possible, features autonomous fault protection and utilizes onboard target tracking near closest approach. These design considerations reduce risk during the relatively short time-critical periods when science data is collected. The payload suite consists of a color camera and infrared imaging spectrometer, a high-resolution panchromatic imag…
Jupiter Trojan asteroids are located around L4 and L5 Lagrangian points on relatively stable orbits, in 1:1 MMR with Jupiter. However, not all of them lie in orbits that remain stable over the age of the Solar System. Unstable zones allow some Trojans to escape in time scales shorter than the Solar System age. This may contribute to populate other small body populations. In this paper, we study this process by performing long-term numerical simulations of the observed Trojans, focusing on the trajectories of those that leave the resonance. The orbits of current Trojans are taken as initial con…
The Trojan asteroids of Jupiter and Neptune are likely to have been captured from original heliocentric orbits in the dynamically excited ("hot") population of the Kuiper belt. However, it has long been known that the optical color distributions of the Jovian Trojans and the hot population are not alike. This difference has been reconciled with the capture hypothesis by assuming that the Trojans were resurfaced (for example, by sublimation of near-surface volatiles) upon inward migration from the Kuiper belt (where blackbody temperatures are $\sim$40 K) to Jupiter's orbit ($\sim$125 K). Here, …
We describe the discovery of a satellite of the Trojan asteroid (3548) Eurybates in images obtained with the Hubble Space Telescope. The satellite was detected on three separate epochs, two in September 2018 and one in January 2020. The satellite has a brightness in all three epochs consistent with an effective diameter of d2 =1.2+/-0.4 km. The projected separation from Eurybates was s~1700-2300 km and varied in position, consistent with a large range of possible orbits. Eurybates is a target of the Lucy Discovery mission and the early detection of a satellite provides an opportunity for a sig…
One outstanding problem in extrasolar planet studies is why no co-orbital exoplanets have been found, despite numerous searches among the many known planetary systems, many of them in other mean-motion resonances. Here we examine the hypothesis that dissipation of energy by tides in Trojan planets is preventing their survival. The Appendix of this paper generalizes the conventional theory of tides to include tidal forces independent of dissipation, as well as the effects of one body on tides raised by another. The main text applies this theory to a model system consisting of a primary of stell…
Neptunian Trojans (NTs), trans-Neptunian objects in 1:1 mean-motion resonance with Neptune, are generally thought to have been captured from the original trans-Neptunian protoplanetary disk into co-orbital resonance with the ice giant during its outward migration. It is possible, therefore, that the colour distribution of NTs is a constraint on the location of any colour transition zones that may have been present in the disk. In support of this possible test, we obtained $g$, $r$, and $i$-band observations of 18 NTs, more than doubling the sample of NTs with known visible colours to 31 object…
Hot Jupiters (HJs) are short-period giant planets that are observed around ~ 1% of solar-type field stars. One possible formation scenario for HJs is high-eccentricity (high-e) migration, in which the planet forms at much larger radii, is excited to high eccentricity by some mechanism, and migrates to its current orbit due to tidal dissipation occurring near periapsis. We consider high-e migration in dense stellar systems such as the cores of globular clusters (GCs), in which encounters with passing stars can excite planets to the high eccentricities needed to initiate migration. We study this…
Trojans are defined as objects that share the orbit of a planet at the stable Lagrangian points $L_4$ and $L_5$. In the Solar System, these bodies show a broad size distribution ranging from micrometer($μ$m) to centimeter(cm) particles (Trojan dust) and up to kilometer (km) rocks (Trojan asteroids). It has also been theorized that earth-like Trojans may be formed in extra-solar systems. The Trojan formation mechanism is still under debate, especially theories involving the effects of dissipative forces from a viscous gaseous environment. We perform hydro-simulations to follow the evolution of …
A recent examination of K2 lightcurves indicates that ~15% of Jupiter Trojans have very slow rotation (spin periods Ps>100 h). Here we consider the possibility that these bodies formed as equal-size binaries in the massive outer disk at ~20-30 au. Prior to their implantation as Jupiter Trojans, tight binaries tidally evolved toward a synchronous state with Ps~Pb, where Pb is the binary orbit period. They may have been subsequently dissociated by impacts and planetary encounters with at least one binary component retaining its slow rotation. Surviving binaries on Trojan orbits would continue to…
Where Do Hot Jupiters Come From? Revisiting Tidal Disruption and Ejection in High-Eccentricity Migration
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；CSST Science Center for the Guangdong-HongKong-Macau Great Bay Area, Sun Yat-sen University（中山大学中国空间站科学中心粤港澳大湾区分中心）
The process of planet conglomeration, which primarily unfolds in a geometrically thin disk of gas and dust, is often accompanied by dynamical excitation of the forming planets and planetesimals. The ensuing orbital crossing can lead to large-scale collisional fragmentation, populating the system with icy and rocky debris. In a gaseous nebula, such leftover solid matter tends to spiral down towards the host star due to aerodynamic drag. Along the way, the inward drifting debris can encounter planets and gravitationally couple to them via mean-motion resonances, sapping them of their orbital ene…
Several properties of the Solar System, including the wide radial spacing of the giant planets, can be explained if planets radially migrated by exchanging orbital energy and momentum with outer disk planetesimals. Neptune's planetesimal-driven migration, in particular, has a strong advocate in the dynamical structure of the Kuiper belt. A dynamical instability is thought to have occurred during the early stages with Jupiter having close encounters with a Neptune-class planet. As a result of the encounters, Jupiter acquired its current orbital eccentricity and jumped inward by a fraction of an…
During their formation, emerging protoplanets tidally interact with their natal disks. Proto-gas-giant planets, with Hills radius larger than the disk thickness, open gaps and quench gas flow in the vicinity of their orbits. It is usually assumed that their type II migration is coupled to the viscous evolution of the disk. Although this hypothesis provides an explanation for the origin of close-in planets, it also encounter predicament on the retention of long-period orbits for most gas giant planets. Moreover, numerical simulations indicate that planets migrations are not solely determined by…
The obliquity of a planet is the tilt between its equator and its orbital plane. Giant planets are expected to form with near-zero obliquities. After its formation, some dynamical mechanism must therefore have tilted Saturn up to its current obliquity of 26.7°. This event is traditionally thought to have happened more than 4 Gyrs ago during the late planetary migration because of the crossing of a resonance between the spin-axis precession of Saturn and the nodal orbital precession mode of Neptune. Here, we show that the fast tidal migration of Titan measured by Lainey et al. (2020) is incompa…
Capture and escape from the 2:1 resonance between Ariel and Umbriel in a fast-migration scenario of the Uranian system
University of Pisa（比萨大学）；Anton Pannekoek Institute for Astronomy, University of Amsterdam（阿姆斯特丹大学安东·范·列文虎克天文学研究所）；Université PSL, Sorbonne Université, Université de Lille（巴黎文理研究大学、索邦大学、里尔大学）
Despite the existence of co-orbital bodies in the solar system, and the prediction of the formation of co-orbital planets by planetary system formation models, no co-orbital exoplanets (also called trojans) have been detected thus far. In this paper we investigate how a pair of co-orbital exoplanets would fare during their migration in a protoplanetary disc. To this end, we computed a stability criterion of the Lagrangian equilibria L4 and L5 under generic dissipation and slow mass evolution. Depending on the strength and shape of these perturbations, the system can either evolve towards the L…
The orbital distribution of transneptunian objects (TNOs) in the distant Kuiper Belt (with semimajor axes beyond the 2:1 resonance, roughly $a$=50-100 au) provides constraints on the dynamical history of the outer solar system. Recent studies show two striking features of this region: 1) a very large population of objects in distant mean-motion resonances with Neptune, and 2) the existence of a substantial detached population (non-resonant objects largely decoupled from Neptune). Neptune migration models are able to implant some resonant and detached objects during the planet migration era, bu…
Convergent migration involving multiple planets embedded in a viscous protoplanetary disc is expected to produce a chain of planets in mean motion resonances, but the multiplanet systems observed by the Kepler spacecraft are generally not in resonance. We demonstrate that under equivalent conditions, where in a viscous disc convergent migration will form a long-term stable system of planets in a chain of mean motion resonances, migration in an inviscid disc often produces a system which is highly dynamically unstable. In particular, if planets are massive enough to significantly perturb the di…
Recent studies suggest that ultra-short period planets (USPs), Earth-sized planets with sub-day periods, constitute a statistically distinct sub-sample of {\it Kepler} planets: USPs have smaller radii ($1-1.4R_\oplus$) and larger mutual inclinations with neighboring planets than nominal {\it Kepler} planets, and their period distribution is steeper than longer-period planets. We study a "low-eccentricity" migration scenario for the formation of USPs, in which a low-mass planet with initial period of a few days maintains a small but finite eccentricity due to secular forcings from exterior comp…
We present radiation hydrodynamic simulations in which binary planets form by close encounters in a system of several super-Earth embryos. The embryos are embedded in a protoplanetary disk consisting of gas and pebbles and evolve in a region where the disk structure supports convergent migration due to Type I torques. As the embryos accrete pebbles, they become heated and thus affected by the thermal torque (Benítez-Llambay et al. 2015) and the hot-trail effect (Chrenko et al. 2017) which excites orbital eccentricities. Motivated by findings of Eklund & Masset (2017), we assume the hot-trail e…
