Evidence of mutually inclined planetary orbits has been reported for giant planets these last years. Here we aim to study the impact of eccentric and inclined massive giant planets on the terrestrial planet formation process, and investigate whether it can possibly lead to the existence of inclined terrestrial planets. We have performed 126 simulations of the late-stage planetary accretion in eccentric and inclined giant planet systems. The physical and orbital parameters of the giant planet systems result from n-body simulations of three giant planets in the late stage of the gas disc, under the combined action of Type II migration and planet-planet scattering. Fourteen two- and three-planet configurations have been selected, with diversified masses, semi-major axes (resonant configurations or not), eccentricities and inclinations (including coplanar systems) at the dispersal of the gas disc. We have then followed the gravitational interactions of these systems with an inner disc of planetesimals and embryos (9 runs per system), studying in detail the final configurations of the formed terrestrial planets. While coplanar giant systems harbour several terrestrial planets, generally as massive as the Earth and mainly on low eccentric and low inclined orbits, terrestrial planets formed in systems with mutually inclined giant planets are usually fewer, less massive (<0.5 M_{\Earth}) and with larger eccentricities and inclinations. This work shows that terrestrial planets can form on stable inclined orbits through the classical accretion theory, even in coplanar giant planet systems emerging from the disc phase.
The vast majority of well studied giant-planet systems, including the Solar System, are nearly coplanar which implies dissipation within a primordial gas disk. however, intrinsic instability may lead to planet-planet scattering, which often produces non-coplanar, eccentric orbits. Planet scattering theories have been developed to explain observed high eccentricity systems and also hot Jupiters; thus far their predictions for mutual inclination (I) have barely been tested. Here we characterize a highly mutually-inclined (I ~ 15-60 degrees), moderately eccentric (e >~ 0.1) giant planet system: K…
Exoplanet discoveries over recent years have shown that terrestrial planets are exceptionally common. Many of these planets are in compact systems that result in complex orbital dynamics. A key step toward determining the surface conditions of these planets is understanding the latitudinally dependent flux incident at the top of the atmosphere as a function of orbital phase. The two main properties of a planet that influence the time-dependent nature of the flux are the obliquity and orbital eccentricity of the planet. We derive the criterion for which the flux variation due to obliquity is eq…
We aim to investigate the influence of the eccentricity and inclination damping due to planet-disc interactions on the final configurations of the systems, generalizing previous studies on the combined action of the gas disc and planet-planet scattering during the disc phase. Instead of the simplistic $K$-prescription, our n-body simulations adopt the damping formulae for eccentricity and inclination provided by the hydrodynamical simulations of our companion paper. We follow the evolution of $11000$ numerical experiments of three giant planets in the late stage of the gas disc, exploring diff…
All circumbinary planets currently detected are in orbits that are almost coplanar to the binary orbit. While misaligned circumbinary planets are more difficult to detect, observations of polar aligned circumbinary gas and debris disks around eccentric binaries suggest that polar planet formation may be possible. A polar aligned planet has a stable orbit that is inclined by 90 degrees to the orbital plane of the binary with an angular momentum vector that is aligned to the binary eccentricity vector. With n- body simulations we model polar terrestrial planet formation using hydrodynamic gas di…
Öpik-type collision frequency for Kozai-driven projectiles: Target bodies on eccentric and inclined orbits
School of Aeronautics and Astronautics, Shenzhen Campus of Sun Yat-sen University（中山大学深圳校区航空航天学院）；Shenzhen Key Laboratory of Intelligent Microsatellite Constellation（深圳市智能微小卫星星座重点实验室）
HD106906 is a planetary system that hosts a wide-orbit companion, as well as an eccentric and flat debris disk, which hold important constraints on its formation and subsequent evolution. The recent observations of the companion constrain its orbit to be eccentric and inclined relative to the plane of the debris disk. Here, we show that, in the presence of the inclined companion, the debris disk quickly ($\lesssim5$ Myr) becomes warped and puffy. This suggests that the current configuration of the system is relatively recent. We explore the possibility that a recent close encounter with a free…
Hundreds of giant planets have been discovered so far and the quest of exo-Earths in giant planet systems has become intriguing. In this work, we aim to address the question of the possible long-term coexistence of a terrestrial companion on an orbit interior to a giant planet, and explore the extent of the stability regions for both non-resonant and resonant configurations. Our study focuses on the restricted three-body problem, where an inner terrestrial planet (massless body) moves under the gravitational attraction of a star and an outer massive planet on a circular or elliptic orbit. Usin…
Recent observational campaigns have shown that multi-planet systems seem to be abundant in our Galaxy. Moreover, it seems that these systems might have distant companions, either planets, brown-dwarfs or other stellar objects. These companions might be inclined with respect to the inner planets, and could potentially excite the eccentricities of the inner planets through the Eccentric Kozai-Lidov mechanism. These eccentricity excitations could perhaps cause the inner orbits to cross, disrupting the inner system. We study the stability of two-planet systems in the presence of a distant, incline…
To date, studies of $\textit{Laplace Surface}$ dynamics have concerned themselves with test particle orbits of fixed shape and orientation in the combined field of an oblate central body (to which the particle is bound) and a distant, inclined, companion which is captured to quadrupolar order. While amply sufficient for satellites around planets on near-circular orbits, the quadrupolar approximation fails to capture essential dynamical features induced by a wide binary companion (be it a star, a planet or a black hole) on a fairly eccentric orbit. With similar such astronomical settings in min…
Eccentricity is an important orbital parameter. Understanding its effect on planetary climate and habitability is critical for us to search for a habitable world beyond our solar system. The orbital configurations of M-dwarf planets are always tidally-locked at resonance states, which are quite different from those around Sun-like stars. M-dwarf planets need to be investigated separately. Here we use a comprehensive three-dimensional atmospheric general circulation model to systematically investigate how eccentricity influences climate and habitability of M-dwarf exoplanets. The simulation res…
With n-body simulations, we model terrestrial circumbinary planet (CBP) formation with an initial surface density profile motivated by hydrodynamic circumbinary gas disc simulations. The binary plays an important role in shaping the initial distribution of bodies. After the gas disc has dissipated, the torque from the binary speeds up the planet formation process by promoting body-body interactions but also drives the ejection of planet building material from the system at an early time. Fewer but more massive planets form around a close binary compared to a single star system. A sufficiently …
In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) induced by the perturbation of a distant gas-giant for the Kepler-68 system, by conducting thousands of numerical simulations. The results show that the formation of terrestrial planets is relevant to the speed of Type I migration, the mass of planets, and the existence of giant planet. The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the system. The inner planet pair can be trapped in 5:3 or 7:4 MMRs if the giant pla…
An Inclined, Eccentric Planet and an Inner Debris Disk Could Reproduce AU Mic Structure
University of Exeter（埃克塞特大学）；University of California Santa Cruz（加州大学圣克鲁兹分校）；John Hopkins University（约翰斯·霍普金斯大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）
The stability of planets in the alpha-Centauri AB stellar system has been studied extensively. However, most studies either focus on the orbital plane of the binary or consider inclined circular orbits. Here, we numerically investigate the stability of a possible planet in the alpha-Centauri AB binary system for S-type orbits in an arbitrary spatial configuration. In particular, we focus on inclined orbits and explore the stability for different eccentricities and orientation angles. We show that large stable and regular regions are present for very eccentric and inclined orbits, corresponding…
$γ$ Cep Ab is a typical S-type planet, which occupies a nearly perpendicular planetary orbit relative to the binary. Here we use the Markov Chain Monte Carlo (MCMC) sampler to conduct full N-body fitting and derive self-consistent orbital solutions for this hierarchical system. Then we employ the Eccentric Kozai-Lidov (EKL) mechanism to explain the extremely inclined orbit of S-type planet $γ$ Cep Ab. The EKL mechanism plays an essential role in exploring significant oscillations of the mutual inclination $i_{\mathrm{mut}}$ between the planet and the secondary star. We perform qualitative anal…
The insolation a planet receives from its parent star is the main driver of the climate and depends on the planet's orbital configuration. Planets with non-zero obliquity and eccentricity experience seasonal insolation variations. As a result, the climate exhibits a seasonal cycle, with its strength depending on the orbital configuration and atmospheric characteristics. In this study, using an idealized general circulation model, we examine the climate response to changes in eccentricity for both zero and non-zero obliquity planets. In the zero obliquity case, a comparison between the seasonal…
The discovery of a population of close-orbiting giant planets ($\le$ 1 au) has raised a number of questions about their origins and dynamical histories. These issues have still not yet been fully resolved, despite over 20 years of exoplanet detections and a large number of discovered exoplanets. In particular, it is unclear whether warm Jupiters (WJs) form in situ, or whether they migrate from further outside and are even currently migrating to form hot Jupiters (HJs). Here, we report the possible discovery and characterization of the planets in a highly mutually-inclined ($I_{\rm mut}\simeq 4…
Circumbinary gas disks are often observed to be misaligned to the binary orbit suggesting that planet formation may proceed in a misaligned disk. With N-body simulations we consider the formation of circumbinary terrestrial planets from a particle disk that is initially misaligned. We find that if terrestrial planets form in this way, in the absence of gas, they can only form close to coplanar or close to polar to the binary orbit. Planets around a circular binary form coplanar while planets around an eccentric binary can form coplanar or polar depending on the initial disk misalignment and th…
We analyse the evolution of a mildly inclined circumbinary disc that orbits an eccentric orbit binary by means of smoother particle hydrodynamic (SPH) simulations and linear theory. We show that the alignment process of an initially misaligned circumbinary disc around an eccentric orbit binary is significantly different than around a circular orbit binary and involves tilt oscillations. The more eccentric the binary, the larger the tilt oscillations and the longer it takes to damp these oscillations. A circumbinary disc that is only mildly inclined may increase its inclination by a factor of a…
In this work, we extensively investigate the formation of near 4:2:1 mean motion resonances (MMRs) configuration by performing two sets of N-body simulations. We model the eccentricity damping, gas drag, type I and type II planetary migration of planetesimals, planetary embryos and giant planets in the first sets. For the simulations of giant planets with type II migration, the massive terrestrial planets, with a mass up to several Earth masses, are likely produced in the systems. We further show that by shepherding and/or scattering mechanisms through Jovian planet's type II migration, the te…
Stars are commonly formed in binary systems, which provide a natural laboratory for studying planet formation in extreme conditions. In our first paper (Paper I) of a series Xie et al. (2011), we have shown that the intermediate stage - from planetesimals to planetary embryos/cores - of planet formation can proceed even in highly inclined binaries. Following Paper I, here we numerically study the late stage of terrestrial planet formation, i.e., from embryos to full planets, in binary systems of various orbital configurations. We identify an orbital alignment or anti-alignment effect; namely, …
The trans-Neptunian region of the solar system exhibits an intricate dynamical structure, much of which can be explained by an instability-driven orbital history of the giant planets. However, the origins of a highly inclined, and in certain cases retrograde, population of trans-Neptunian objects remain elusive within the framework of this evolutionary picture. In this work, we show that the existence of a distant, Neptune-like planet that resides on an eccentric and mildly inclined orbit fully accounts for the anomalous component the trans-Neptunian orbital distribution. Adopting the same par…
We study the orbital stability of a non-zero mass, close-in circular orbit planet around an eccentric orbit binary for various initial values of the binary eccentricity, binary mass fraction, planet mass, planet semi--major axis, and planet inclination by means of numerical simulations that cover $5 \times 10^4$ binary orbits. For small binary eccentricity, the stable orbits that extend closest to the binary (most stable orbits) are nearly retrograde and circulating. For high binary eccentricity, the most stable orbits are highly inclined and librate near the so-called generalised polar orbit …
Aims. There are a growing number of giant planets discovered moving around one stellar component of a binary star, most of which have very diverse eccentricity. These discoveries raise the question of their formation and long-term evolution because the stellar companion can strongly affect the planet formation process. We aim to study the dynamical influence of a wide binary companion on the evolution of a single giant planet migrating in a protoplanetary disk. Methods. Using a symplectic n-body integrator adapted for binary star systems and modeling the dissipation due to the disk by appropri…
Discoveries of exoplanets using the radial velocity method are progressively reaching out to increasingly longer orbital periods as the duration of surveys continues to climb. The improving sensitivity to potential Jupiter analogs is revealing a diversity of orbital architectures that are substantially different from that found in our solar system. An excellent example of this is the recent discovery of HR 5183b; a giant planet on a highly eccentric ($e = 0.84$) $\sim$75~year orbit. The presence of such giant planet orbits are intrinsically interesting from the perspective of the dynamical his…
We use a secular model to describe the non-resonant dynamics of trans-Neptunian objects in the presence of an external ten-earth-mass perturber. The secular dynamics is analogous to an "eccentric Kozai mechanism" but with both an inner component (the four giant planets) and an outer one (the eccentric distant perturber). By the means of Poincaré sections, the cases of a non-inclined or inclined outer planet are successively studied, making the connection with previous works. In the inclined case, the problem is reduced to two degrees of freedom by assuming a non-precessing argument of periheli…
