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 contrary, when the luminosity-to-mass ratio of the planet exceeds a threshold that depends on the disc's properties, its eccentricity and inclination undergo an exponential growth. In the limit of a large luminosity, the growth rate of the eccentricity is 2.5~times larger than that of the inclination, in agreement with previous numerical work. Depending on their luminosity, planetary embryos therefore exhibit much more diverse behaviours than the mild damping of eccentricity and inclination considered hitherto.
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）
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。
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…
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…
Orbital eccentricity is one of the basic planetary properties, whose distribution may shed light on the history of planet formation and evolution. Here, in a series of works on Planetary Orbit Eccentricity Trends (dubbed POET), we study the distribution of planetary eccentricities and their dependence on stellar/planetary properties. In this paper, the first work of the POET series, we investigate whether and how the eccentricities of small planets depend on stellar metallicities (e.g., [Fe/H]). Previous studies on giant planets have found a significant correlation between planetary eccentrici…
We present a new mechanism of generating large planetary eccentricities. This mechanism applies to planets within the inner cavities of their companion protoplanetary disks. A massive disk with an inner truncation may become eccentric due to non-adiabatic effects associated with gas cooling, and can retain its eccentricity in long-lived coherently-precessing eccentric modes; as the disk disperses, the inner planet will encounter a secular resonance with the eccentric disk when the planet and the disk have the same apsidal precession rates; the eccentricity of the planet is then excited to a la…
Planetary Desert around Compact Binaries: Dynamical Instability Triggered by Resonance-Induced Eccentricity Excitation
Institute for Astronomy, School of Physics, Zhejiang University（浙江大学物理学院天体物理研究所）；Center for Cosmology and Computational Astrophysics, Institute for Advanced Study in Physics, Zhejiang University（浙江大学物理高等研究院宇宙学与计算天体物理中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Department of Astronomy, Center for Astrophysics and Planetary Science, Cornell University（康奈尔大学天文学系天文与行星科学中心）
Most giant exoplanets discovered by radial velocity surveys have much higher eccentricities than those in the solar system. The planet--planet scattering mechanism has been shown to match the broad eccentricity distribution, but the highest-eccentricity planets are often attributed to Kozai-Lidov oscillations induced by a stellar companion. Here we investigate whether the highly eccentric exoplanet population can be produced entirely by scattering. We ran 500 N-body simulations of closely packed giant-planet systems that became unstable under their own mutual perturbations. We find that the su…
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 presence of an early-formed giant planet in the protoplanetary disk has mixed influence on the growth of other planetary embryos. Gravitational perturbation from the planet can increase the relative velocities of planetesimals at the mean motion resonances to very high values and impede accretion at those locations. However, gas drag can also align the orbital pericenters of equal-size planetesimals in certain disk locations and make them dynamically quiet and "accretion-friendly" locations for planetesimals of similar sizes. Following the previous paper, where we investigated the effect o…
A number of multiplanet systems are observed to contain planets very close to mean motion resonances, although there is no significant pileup of precise resonance pairs. We present theoretical and numerical studies on the outcome of capture into first-order mean motion resonances (MMRs) using a parametrized planet migration model that takes into account nonlinear eccentricity damping due to planet-disk interaction. This parametrization is based on numerical hydrodynamical simulations and is more realistic than the simple linear parametrization widely used in previous analytic studies. We find …
Planets migrating in their natal discs can be captured into mean-motion resonance (MMR), in which the planets' periods are related by integer ratios. Recent observations indicate that planets in MMR can be either apsidally aligned or anti-aligned. How these different configurations arise is unclear. In this paper, we study the MMR capture process of migrating planets, focusing on the property of the apsidal angles of the captured planets. We show that the standard picture of MMR capture, in which the planets undergo convergent migration and experience eccentricity damping due to planet-disc in…
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…
Planet-Planet Scattering Explains the Mass-Eccentricity Relation of Warm Jupiters
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；National Center for Supercomputing Applications（国家超级计算应用中心）；University of California, San Diego（加州大学圣地亚哥分校）；National Astronomical Observatory of Japan（日本国立天文台）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；U.S. National Science Foundation National Optical-Infrared Astronomy Research Laboratory（美国国家科学基金会国家光学-红外天文研究实验室）
By means of high resolution hydrodynamical, three-dimensional calculations with nested-meshes, we evaluate the eccentricity reached by a low-mass, luminous planet embedded in an inviscid disc with constant thermal diffusivity and subjected to thermal forces. We find that a cell size of at most one tenth of the size of the region heated by the planet is required to get converged results. When the planet's luminosity is supercritical, we find that it reaches an eccentricity of order $10^{-2}$--$10^{-1}$, which increases with the luminosity and broadly scales with the disc's aspect ratio. Restric…
Planetary obliquity and eccentricity influence climate by shaping the spatial and temporal patterns of stellar energy incident at a planet's surface, affecting both the annual mean climate and magnitude of seasonal variability. Previous work has demonstrated the importance of both planetary obliquity and eccentricity for climate and habitability, but most studies have not explicitly modeled the response of life to these parameters. While exaggerated seasons may be stressful to some types of life, a recent study found an increase in marine biological activity for moderately high obliquities <45…
Long-term statistical simulations of the past evolution of high-inclination Centaurs showed that their orbits tend to be polar with respect to the solar system's invariable plane over a large semi-major axis range in trans-neptunian space. Here, we lay the analytical foundation of the study of the inclination pathways of planet-crossing asteroids that explains these findings. We show that the Tisserand relation partitions the inclination-semi-major axis parameter space of the three-body problem into distinct regions depending on the asteroid's Tisserand parameter T or equivalently its orbital …
Early analyses of exoplanet statistics from the Kepler Mission revealed that a model population of multiple-planet systems with low mutual inclinations (${\sim1^{\circ}-2^{\circ}}$) adequately describes the multiple-transiting systems but underpredicts the number of single-transiting systems. This so-called "Kepler dichotomy" signals the existence of a sub-population of multi-planet systems possessing larger mutual inclinations. However, the details of these inclinations remain uncertain. In this work, we derive constraints on the intrinsic mutual inclination distribution by statistically expl…
Kepler-1656b is a 5 $R_E$ planet with an orbital period of 32 days initially detected by the prime Kepler mission. We obtained precision radial velocities of Kepler-1656 with Keck/HIRES in order to confirm the planet and to characterize its mass and orbital eccentricity. With a mass of $48 \pm 4 M_E$, Kepler-1656b is more massive than most planets of comparable size. Its high mass implies that a significant fraction, roughly 80%, of the planet's total mass is in high density material such as rock/iron, with the remaining mass in a low density H/He envelope. The planet also has a high eccentric…
