The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type mean-motion resonances. Both the sequence of 2:1 eccentricity resonances that the system is driven through by continued migration and the possibility of a subsequent capture into the 4:2 inclination resonances are sensitive to the migration rate within the range expected for type II migration. If the migration rate is fast, the resonant pair can evolve into a family of 2:1 eccentricity resonances different from those found by Lee (2004). This new family has outer orbital eccentricity e_2 > 0.4-0.5, asymmetric librations of both eccentricity resonance variables, and orbits that intersect if they are exactly coplanar. Although this family exists for an inner-to-outer planet mass ratio m_1/m_2 > 0.2, it is possible to evolve into this family by fast migration only for m_1/m_2 > 2. Thommes and Lissauer (2003) have found that a capture into the 4:2 inclination resonances is possible only for m_1/m_2 < 2. We show that this capture is also possible for m_1/m_2 > 2 if the migration rate is slightly slower than that adopted by Thommes and Lissauer. There is significant theoretical uncertainty in both the sign and the magnitude of the net effect of planet-disk interaction on the orbital eccentricity of a planet. If the eccentricity is damped on a timescale comparable to or shorter than the migration timescale, e_2 may not be able to reach the values needed to enter either the new 2:1 eccentricity resonances or the 4:2 inclination resonances. Thus, if future observations of extrasolar planetary systems were to reveal certain combinations of mass ratio and resonant configuration, they would place a constraint on the strength of eccentricity damping during migration, as well as on the migration rate itself.
We study the evolution of the eccentricity and inclination of protoplanetary embryos and low-mass protoplanets (from a fraction of an Earth mass to a few Earth masses) embedded in a protoplanetary disc, by means of three dimensional hydrodynamics calculations with radiative transfer in the diffusion limit. When the protoplanets radiate in the surrounding disc the energy released by the accretion of solids, their eccentricity and inclination experience a growth toward values which depend on the luminosity to mass ratio of the planet, which are comparable to the disc's aspect ratio and which are…
Transiting Extrasolar Planet with a Companion: Effects of Orbital Eccentricity and Inclination
在早期的出版物[Sato and Asada，PASJ，61，L29（2009）]中开始的继续工作，我们考虑了光变曲线受轨道倾角和轨道偏心率的影响，该轨道围绕凌日系外行星（在行星-卫星系统或假设的真双星中）。我们表明，半长轴，偏心率和倾角的一个“月亮”围绕主行星的轨道可以确定由过境方法单独。为此目的，我们提出了一个配方的参数确定在一个小偏心率近似以及在确切的形式。因此，半长轴可以用亮度变化、渡越时间和光变曲线的间隔等可观测量来表示。我们还讨论了一个狭窄的参数区域，产生一个太阳系外的卫星相互过境。
We explore planetary migration scenarios for formation of high inclination Neptune Trojans (NTs) and how they are affected by the planetary migration of Neptune and Uranus. If Neptune and Uranus's eccentricity and inclination were damped during planetary migration, then their eccentricities and inclinations were higher prior and during migration than their current values. Using test particle integrations we study the stability of primordial NTs, objects that were initially Trojans with Neptune prior to migration. We also study Trans-Neptunian objects captured into resonance with Neptune and be…
Five Long-period Extrasolar Planets in Eccentric orbits from the Magellan Planet Search Program
麦哲伦速度巡天发现了五颗围绕G和K矮星运行的新行星。这些伴星是木星质量的行星，在偏心（e \geq 0.24）的中长期轨道上运行。HD 86226b围绕着一颗金属丰度为G2的矮星。行星的MP sin i质量为1.5 MJUP，半长轴为2.6 AU，离心率为0.73。HD 129445b围绕着一颗富含金属的G6矮星运行。该行星的最小质量为MP sin i =1.6 MJUP，半长轴为2.9 AU，离心率为0.70。HD 164604b围绕一颗K2矮星运行。MP sin i质量为2.7 MJUP，半长轴为1.3 AU，偏心率为0.24。HD 175167b是一颗富含金属的G5恒星。MP sin i质量为7.8 MJUP，半长轴为2.4 AU，偏心率为0.54。HD 152079b围绕一颗G6矮星运行。行星的MP sin i质量为3 MJUP，半长轴为3.2 AU，离心率为0.60。
By means of three dimensional, high resolution hydrodynamical simulations we study the orbital evolution of weakly eccentric or inclined low-mass protoplanets embedded in gaseous discs subject to thermal diffusion. We consider both non-luminous planets, and planets that also experience the radiative feedback from their own luminosity. We compare our results to previous analytical work, and find that thermal forces (the contribution to the disc's force arising from thermal effects) match those predicted by linear theory within $\sim 20$%. When the planet's luminosity exceeds a threshold found t…
Structures observed in debris disks may be caused by gravitational interaction with planetary or stellar companions. These perturbed disks are often thought to indicate the presence of planets and offer insights into the properties of both the disk and the perturbing planets. Gaps in debris disks may indicate a planet physically present within the gap, but such gaps can also occur away from the planet's orbit at mean-motion resonances (MMRs), and this is the focus of our interest here. We extend our study of planet-disk interaction through MMRs, presented in an earlier paper, to systems in whi…
The focus of this paper is on inclination-only dependent lunisolar resonances, which shape the dynamics of a MEO (Medium Earth Orbit) object over secular time scales (i.e. several decades). Following the formalism of arXiv:2107.14507, we discuss an analytical model yielding the correct form of the separatrices of each one of the major lunisolar resonances in the "action" space $(i, e)$ (inclination, eccentricity) for any given semi-major axis $a$. We then highlight how our method is able to predict and explain the main structures found numerically in Fast Lyapunov Indicator (FLI) cartography. …
The minor planets on orbits that are dynamically stable in Neptune's 1:1 resonance on Gyr timescales were likely emplaced by Neptune's outward migration. We explore the intrinsic libration amplitude, eccentricity, and inclination distribution of Neptune's stable Trojans, using the detections and survey efficiency of the Outer Solar System Origins Survey (OSSOS) and Pan-STARRS1. We find that the libration amplitude of the stable Neptunian Trojan population can be well modeled as a Rayleigh distribution with a libration amplitude width $σ_{A_phi}$ of 15$^\circ$. When taken as a whole, the Neptun…
Recent SPH simulations by Martin et al. (2014) suggest a circumstellar gaseous disk may exhibit coherent eccentricity-inclination oscillations due to the tidal forcing of an inclined binary companion, in a manner that resembles Lidov-Kozai oscillations in hierarchical triple systems. We carry out linear stability analysis for the eccentricity growth of circumstellar disks in binaries, including the effects of gas pressure and viscosity and secular (orbital-averaged) tidal force from the inclined companion. We find that the growth of disk eccentricity depends on the dimensionless ratio ($S$) be…
Using linear perturbation theory, we evaluate the time-dependent force exerted on an eccentric and inclined low-mass planet embedded in a gaseous protoplanetary disc with finite thermal diffusivity $χ$. We assume the eccentricity and inclination to be small compared to the size of the thermal lobes $λ\sim(χ/Ω)^{1/2}$, itself generally much smaller than the scalelength of pressure $H$. When the planet is non-luminous, we find that its eccentricity and inclination are vigorously damped by the disc, over a timescale shorter by a factor $H/λ$ than the damping timescale in adiabatic discs. On the c…
The behavior of an interior test particle in the secular 3-body problem has been studied extensively. A well-known feature is the Lidov-Kozai resonance in which the test particle's argument of periapse librates about $\pm 90^\circ$ and large oscillations in eccentricity and inclination are possible. Less explored is the inverse problem: the dynamics of an exterior test particle and an interior perturber. We survey numerically the inverse secular problem, expanding the potential to hexadecapolar order and correcting an error in the published expansion. Four secular resonances are uncovered that…
The angular momentum deficit (AMD) of a planetary system is a measure of its orbital excitation and a predictor of long-term stability. We adopt the AMD-stability criteria to constrain the orbital architectures for exoplanetary systems. Previously, He, Ford, & Ragozzine (2019) (arXiv:1907.07773v2) showed through forward modelling (SysSim) that the observed multiplicity distribution can be well reproduced by two populations consisting of a low and a high mutual inclination component. Here, we show that a broad distribution of mutual inclinations arising from systems at the AMD-stability limit c…
The young star PDS110 in the Ori OB1a association underwent two similar eclipses in 2008 and 2011, each of which lasted for a period of at least 25 days. One plausible explanation for these events is that the star was eclipsed by an unseen giant planet (named PDS110b) circled by a ring system that fills a large fraction of its Hill sphere. Through thousands of numerical simulations of the three-body problem, we constrain the mass and eccentricity of this planet as well the size and inclination of its ring, parameters that are not well determined by the observational data alone. We carried out …
Recent studies have proposed that most warm Jupiters (WJs, giant planets with semi-major axes in the range of 0.1-1 AU) probably form in-situ, or arrive in their observed orbits through disk migration. However, both in-situ formation and disk migration, in their simplest flavors, predict WJs to be in low-eccentricity orbits, in contradiction with many observed WJs that are moderately eccentric (e=0.2-0.7). This paper examines the possibility that the WJ eccentricities are raised by secular interactions with exterior giant planet companions, following in-situ formation or migration on a circula…
The classical disturbing function of the three-body problem widely used in planetary dynamics studies is an expansion of the gravitational interaction of the three-body problem with respect to zero eccentricity and zero inclination. This restricts its validity to nearly coplanar orbits. Motivated by the dynamical study of asteroids, Centaurs and transneptunian objects with arbitrary inclinations, we derive a series expansion of the gravitational interaction with respect to an arbitrary reference inclination that generalises our work on the polar and retrograde disturbing functions. The new dis…
The orbit of Mercury has large values of eccentricity and inclination that cannot be easily explained if this planet formed on a circular and coplanar orbit. Here, we study the evolution of Mercury's orbit during the instability related to the migration of the giant planets in the framework of the jumping Jupiter model. We found that some instability models are able to produce the correct values of Mercury's eccentricity and inclination, provided that relativistic effects are included in the precession of Mercury's perihelion. The orbital excitation is driven by the fast change of the normal o…
Planet-planet scattering best explains the eccentricity distribution of extrasolar giant planets. Past literature showed that the orbits of planets evolve due to planet-planet scattering. This work studies the spin evolution of planets in planet-planet scattering in 2-planet systems. Spin can evolve dramatically due to spin-orbit coupling made possible by the evolving spin and orbital precession during the planet-planet scattering phase. The main source of torque to planet spin is the stellar torque, and the total planet-plane torque contribution is negligible. As a consequence of the evolutio…
Scattering outcomes of close-in planets: constraints on planet migration
许多靠近轨道的系外行星被观测到具有相对较高的离心率和较大的恒星偏心率。我们通过研究两个和三个气体巨行星在近轨道（0.05 AU < a < 0.15 AU）的系统中大量轨道积分的动力学结果，探索了这些结果来自行星-行星散射的可能性。我们发现，在这些轨道分离，不稳定的系统开始与低偏心率和相互倾斜（$e\lesssim0.1$，$i\lesssim0.1$）通常会导致行星-行星碰撞的碰撞产物是一个行星在一个低偏心率，低倾角的轨道。这一结果与观察结果不一致。我们的结论是，偏心率和倾斜激发行星行星散射必须先迁移到短周期轨道的行星。这一结果限制了行星迁移的理论：半长轴必须缩小1-2个数量级，而不影响偏心率和倾角。
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…
A commonly noted feature of the population of multi-planet extrasolar systems is the rarity of planet pairs in low-order mean-motion resonances. We revisit the physics of resonance capture via convergent disk-driven migration. We point out that for planet spacings typical of stable configurations for Kepler systems, the planets can routinely maintain a small but nonzero eccentricity due to gravitational perturbations from their neighbors. Together with the upper limit on the migration rate needed for capture, the finite eccentricity can make resonance capture difficult or impossible in Sun-lik…
Applying the technique of dynamical maps we study the orbital stability of test particles in the Solar System in the space (a,e,i) defined by 0.1<a<38 au, 0<e<0.9 and 0<i<180 identifying the unstable and stable regions. We find stable niches where small bodies can survive even for very high eccentricities. Mean motion resonances play a fundamental role providing stability against the planetary perturbations specially for high inclination orbits. A stability stripe around i=150 is present all along the Solar System. We found that the population of objects with semimajor axes between 10 and 30 a…
Eccentricity and Inclination Excitation of Stellar Orbits around merging Black-Hole Binaries
School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University（南京大学现代天体学与天体物理教育部重点实验室）
We present the detection of a Warm Neptune orbiting the M-dwarf Gl378, using radial velocity measurements obtained with the SOPHIE spectrograph at the Observatoire de Haute-Provence. The star was observed in the context of the SOPHIE exoplanets consortium's subprogramme dedicated to finding planets around M-dwarfs. Gl378 is an M1 star, of solar metallicity, at a distance of 14.96 pc. The single planet detected, Gl378 b, has a minimum mass of 13.02 $\rm M_{Earth}$ and an orbital period of 3.82 days, which place it at the lower boundary of the Hot Neptune desert. As one of only a few such planet…
We report the detection of two exoplanets and a further tentative candidate around the M-dwarf stars Gl96 and Gl617A, based on radial velocity measurements obtained with the SOPHIE spectrograph at the Observatoire de Haute-Provence. Both stars were observed in the context of the SOPHIE exoplanet consortium's dedicated M-dwarf subprogramme, which aims to detect exoplanets around nearby M-dwarf stars through a systematic survey. For Gl96, we present the discovery of a new exoplanet at 73.9 d with a minimum mass of 19.66 earth masses. Gl96 b has an eccentricity of 0.44, placing it among the most …
The gravitational influence of a planet on a nearby disk provides a powerful tool for detecting and studying extrasolar planetary systems. Here we demonstrate that gaps can be opened in dynamically cold debris disks at the mean-motion resonances of an orbiting planet. The gaps are opened away from the orbit of the planet itself, revealing that not all disk gaps need contain a planetary body. These gaps are large and deep enough to be detectable in resolved disk images for a wide range of reasonable disk-planet parameters, though we are not aware of any such gaps detected to date. The gap shape…
A recent observational study suggests that the occurrence of hot Jupiters (HJs) around solar-type stars is correlated with stellar clustering. We study a new scenario for HJ formation, called "Flyby Induced High-e Migration", that may help explain this correlation. In this scenario, stellar flybys excite the eccentricity and inclination of an outer companion (giant planet, brown dwarf, or low-mass star) at large distance (10-300 au), which then triggers high-e migration of an inner cold Jupiter (at a few astronomical units) through the combined effects of von Zeipel-Lidov-Kozai (ZLK) eccentric…
Global N-body Simulation of Gap Edge Structures Created by Perturbations from a Small Satellite Embedded in Saturn's Rings II: The Effect of Satellite's Orbital Eccentricity and Inclination
We investigate the dynamics of a nonzero mass, circular orbit planet around an eccentric orbit binary for various values of the binary eccentricity, binary mass fraction, planet mass, and planet semi--major axis by means of numerical simulations. Previous studies investigated the secular dynamics mainly by approximate analytic methods. In the stationary inclination state, the planet and binary precess together with no change in relative tilt. For both prograde and retrograde planetary orbits, we explore the conditions for planetary orbital libration versus circulation and the conditions for st…
