HR8799 is a nearby A-type star with a debris disk and three planetary candidates recently imaged directly. We undertake a coherent analysis of various portions of observational data on all known components of the system. The goal is to elucidate the architecture and evolutionary status of the system. We try to further constrain the age and orientation of the system, orbits and masses of the companions, as well as the location of dust. From the high luminosity of debris dust and dynamical constraints, we argue for a rather young system's age of <50Myr. The system must be seen nearly, but not exactly, pole-on. Our analysis of the stellar rotational velocity yields an inclination of 13-30deg, whereas i>20deg is needed for the system to be dynamically stable, which suggests a probable inclination range of 20-30deg. The spectral energy distribution is naturally reproduced with two dust rings associated with two planetesimal belts. The inner "asteroid belt" is located at ~10AU inside the orbit of the innermost companion and a "Kuiper belt" at >100AU is just exterior to the orbit of the outermost companion. The dust masses in the inner and outer ring are estimated to be ~1E-05 and 4E-02 M_earth, respectively. We show that all three planetary candidates may be stable in the mass range suggested in the discovery paper by Marois et al. 2008 (between 5 and 13 Jupiter masses), but only for some of all possible orientations. Stable orbits imply a double (4:2:1) mean-motion resonance between all three companions. We finally show that in the cases where the companions themselves are orbitally stable, the dust-producing planetesimal belts are also stable against planetary perturbations.
We present a novel, model-independent framework for studying the architecture of an exoplanetary system at the system level. This framework allows us to characterise, quantify, and classify the architecture of an individual planetary system. Our aim in this endeavour is to generate a systematic method to study the arrangement and distribution of various planetary quantities within a single planetary system. We propose that the space of planetary system architectures be partitioned into four classes: similar, mixed, anti-ordered, and ordered. We applied our framework to observed and synthetic m…
Architectures of Planetary Systems II: Trends with Host Star Mass and Metallicity
The Catholic University of America（天主教大学）；NASA Goddard Space Flight Center（NASA戈达德太空飞行中心）；Center for Research and Exploration in Space Science and Technology, NASA/GSFC（NASA/戈达德太空飞行中心空间科学与技术研究与探索中心）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Michigan（密歇根大学）
The aim of this talk is to present the most recent advances in establishing plausible planetary system architectures determined by the gravitational tidal interactions between the planets and the disc in which they are embedded during the early epoch of planetary system formation. We concentrate on a very well defined and intensively studied process of the disc-planet interaction leading to the planet migration. We focus on the dynamics of the systems in which low-mass planets are present. Particular attention is devoted to investigation of the role of resonant configurations. Our studies, apa…
Current protoplanetary dust coagulation theory does not predict dry silicate planetesimals, in tension with the Earth. While remedies to this predicament have been proposed, they have generally failed numerical studies, or are in tension with the Earth's (low, volatility dependent) volatile and moderately volatile elemental abundances. Expanding on the work of Boley et al. (2014), we examine the implications of molten grain collisions and find that they may provide a solution to the dry silicate planetesimal problem. Further, the source of the heating, be it the hot inner disk or an FU Orionis…
Planetary Architectures of Kepler Compact Multis with Binary Star Companions
University of California Santa Cruz（加州大学圣克鲁兹分校）；Mullard Space Science Laboratory, University College London（伦敦大学学院穆拉德空间科学实验室）；California Institute of Technology（加州理工学院）
In models of planetary accretion, pebbles form by dust coagulation and rapidly migrate toward the central star. Planetesimals may continuously form from pebbles over the age of the protoplanetary disk by yet uncertain mechanisms. Meanwhile, large planetary embryos grow efficiently by accumulation of leftover pebbles that are not incorporated in planetesimals. Although this process, called pebble accretion, is offering a new promising pathway for formation of giant planets' cores, architectures of planetary systems formed through the process remain elusive. In the present paper, we perform simu…
In the first paper of this series, we proposed a model-independent framework for characterising the architecture of planetary systems at the system level. There are four classes of planetary system architecture: similar, mixed, anti-ordered, and ordered. In this paper, we investigate the formation pathways leading to these four architecture classes. To understand the role of nature versus nurture in sculpting the final (mass) architecture of a system, we apply our architecture framework to synthetic planetary systems -- formed via core-accretion -- using the Bern model. General patterns emerge…
Current observations indicate that the planet formation process often produces multiple planet systems with nearly circular orbits, regular spacing, a narrow range of inclination angles, and similar planetary masses of order $m_{\rm p}\sim10M_\oplus$. Motivated by the observational sample, this paper determines the tidal equilibrium states for this class of extrasolar planetary systems. We start by considering two planet systems with fixed orbital spacing and variable mass ratios. The basic conjecture explored in this paper is that the planet formation process will act to distribute planetary …
Planetary population synthesis is a tool to understand the physics of planetary system formation. It builds on a model that includes a multitude of physical processes. The outcome can be statistically compared with exoplanet observations. Here, we review the population synthesis method and then use one population to explore how different planetary system architectures emerge and which conditions lead to their formation. The systems can be classified into four main architectures: Class I of near-in situ compositionally ordered terrestrial and ice planets, Class II of migrated sub-Neptunes, Clas…
Doppler planet searches revealed that many giant planets orbit close to their host star or in highly eccentric orbits. These and subsequent observations inspired new theories of planet formation that invoke gravitation interactions in multiple planet systems to explain the excitation of orbital eccentricities and even short-period giant planets. Recently, NASA's Kepler mission has identified over 300 systems with multiple transiting planet candidates, including many potentially rocky planets. Most of these systems include multiple planets with closely-spaced orbits and sizes between that of Ea…
Recent high-resolution observations show that protoplanetary disks have various kinds of structural properties or inhomogeneities. These are the consequence of a mixture of a number of physical and chemical processes taking place in the disks. Here, we discuss the results of our comprehensive investigations on how disk inhomogeneities affect planetary migration. We demonstrate that disk inhomogeneities give rise to planet traps - specific sites in protoplanetary disks at which rapid type I migration is halted. We show that up to three types of traps (heat transitions, ice lines and dead zones)…
Architectures of Planetary Systems III: Excitation of Eccentricities and Inclinations
The Catholic University of America（天主教大学）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）；Center for Research and Exploration in Space Science and Technology, NASA/GSFC（NASA/GSFC空间科学与技术研究探索中心）；Department of Astronomy, University of Wisconsin-Madison（威斯康星大学麦迪逊分校天文学系）；Department of Physics, University of Michigan（密歇根大学物理系）；Department of Astronomy, University of Michigan（密歇根大学天文学系）
Population studies of the orbital characteristics of exoplanets in multi-planet systems have highlighted the existence of an anticorrelation between the average orbital eccentricity of planets and the number of planets of their host system, that is, its multiplicity. This effect was proposed to reflect the varying levels of violence in the dynamical evolution of planetary systems. Previous work suggested that the relative violence of the dynamical evolution of planetary systems with similar orbital architectures can be compared through the computation of their angular momentum deficit (AMD). W…
The pair-correlations between the positions of the six known planets in the exoplanetary system HD 10180 are studied. There are six non-trivial and almost equally spaced peaks. This demonstrates longer-ranged positional order between the orbits and suggests a seventh orbit at 0.92 AU that is consistent with these correlations.
Recent ALMA observations on disk substructures suggest the presence of embedded protoplanets in a large number disks. The primordial configurations of these planetary systems can be deduced from the morphology of the disk substructure and serve as initial conditions for numerical investigation of their future evolution. Starting from the initial configurations of 12 multi-planetary systems deduced from ALMA disks, we carried out two-stage N-body simulation to investigate the evolution of the planetary systems at the disk stage as well as the long term orbital stability after the disk dispersal…
We investigated the underlying architecture of planetary systems by deriving the distribution of planet multiplicity (number of planets) and the distribution of orbital inclinations based on the sample of planet candidates discovered by the Kepler mission. The scope of our study included solar-like stars and planets with orbital periods less than 200 days and with radii between 1.5 and 30 Earth radii, and was based on Kepler planet candidates detected during Quarters 1 through 6. We created models of planetary systems with different distributions of planet multiplicity and inclinations, simula…
We measure the rotation periods of 19 stars in the {\it Kepler} transiting planetary systems, $P_{\rm rot, astero}$ from asteroseismology and $P_{\rm rot, phot}$ from photometric variation of their lightcurve. Two stars exhibit two clear peaks in the Lomb-Scargle periodogram, neither of which agrees with the seismic rotation period. Other four systems do not show any clear peak, whose stellar rotation period is impossible to estimate reliably from the photometric variation; their stellar equators may be significantly inclined with respect to the planetary orbital plane. For the remaining 13 sy…
In the framework of the Europlanet-RI program, a prototype of Virtual Observatory dedicated to Planetary Science was defined. Most of the activity was dedicated to the elaboration of standards to retrieve and visualize data in this field, and to provide light procedures to teams who wish to contribute with on-line data services. The architecture of this VO system and selected solutions are presented here, together with existing demonstrators.
We study the orbital architecture, physical characteristics of planets, formation and long-term evolution of the Kepler-30 planetary system, detected and announced in 2012 by the KEPLER team. We show that the Kepler-30 system belongs to a particular class of very compact and quasi-resonant, yet long-term stable planetary systems. We re-analyse the light curves of the host star spanning Q1-Q17 quarters of the KEPLER mission. A huge variability of the Transit Timing Variations (TTV) exceeding 2 days is induced by a massive Jovian planet located between two Neptune-like companions. The innermost …
We constrain the intrinsic architecture of Kepler planetary systems by modeling the observed multiplicities of the transiting planets (tranets) and their transit timing variations (TTVs). We robustly determine that the fraction of Sun-like stars with Kepler-like planets, $η_{\rm Kepler}$, is $30\pm3\%$. Here Kepler-like planets are planets that have radii $R_{\rm p} \gtrsim R_\oplus$ and orbital periods $P<400$~days. Our result thus significantly revises previous claims that more than 50\% of Sun-like stars have such planets. Combining with the average number of Kepler planets per star ($\sim0…
We analyze data from the Quarter 1-17 Data Release 24 (Q1--Q17 DR24) planet candidate catalog from NASA's Kepler mission, specifically comparing systems with single transiting planets to systems with multiple transiting planets, and identify a distinct population of exoplanets with a necessarily distinct system architecture. Such an architecture likely indicates a different branch in their evolutionary past relative to the typical Kepler system. The key feature of these planetary systems is an isolated, Earth-sized planet with a roughly one-day orbital period. We estimate that at least 24 of t…
We suggest the existence of a correlation between the planetary radius and orbital period for planets with radii smaller than 4 R_Earth. Using the Kepler data, we find a correlation coefficient of 0.5120, and suggest that the correlation is not caused solely by survey incompleteness. While the correlation coefficient could change depending on the statistical analysis, the statistical significance of the correlation is robust. Further analysis shows that the correlation originates from two contributing factors. One seems to be a power-law dependence between the two quantities for intermediate p…
We develop a semi-analytical model for computing planetary system formation with the aim of explaining the observed diversity of planetary systems architectures and relate this primordial diversity with the initial properties of the disc where they were born. We adopt different initial conditions based on recent results in protoplanetary discs observations, to generate a variety of planetary systems and analyze them statistically. We explore the relevance of the mass and size of the disc, its metallicity, the mass of the central star and the time-scale of gaseous disc dissipation, in defining …
Although the sample of exoplanets in binaries has been greatly expanded, the sample heterogeneity and observational bias are obstacles toward a clear figure of exoplanet demographics in the binary environment. To overcome the obstacles, we conduct a statistical study that focuses on S-type planetary systems detected by the Radial Velocity method. We try to account for observational biases by estimating, from available RV data, planet detection efficiencies for each individual system. Our main results are as follows: (1) Single (multiple) planetary systems are mostly found in close (wide) binar…
We examine the effects that dynamical instability has on shaping the orbital properties of exoplanetary systems. Using N-body simulations of non-EMS (Equal Mutual Separation), multi-planet systems we find that the lower limit of the instability timescale $t$ is determined by the minimal mutual separation $K_{\rm min}$ in units of the mutual Hill radius. Planetary systems showing instability generally include planet pairs with period ratio $<1.33$. Our final period ratio distribution of all adjacent planet pairs shows dip-peak structures near first-order mean motion resonances similar to those …
In the search for life beyond our Solar system, attention should be focused on those planets that have the potential to maintain habitable conditions over the prolonged periods of time needed for the emergence and expansion of life as we know it. The observable planetary architecture is one of the determinants for long-term habitability as it controls the orbital evolution and ultimately the stellar fluxes received by the planet. With an ensemble of n-body simulations and obliquity models of hypothetical planetary systems, we demonstrate that the amplitude and period of eccentricity, obliquity…
Recent ALMA observations have identified a variety of dust gaps in protoplanetary disks, which are commonly interpreted to be generated by unobserved planets. Predicting mass of such embedded planets is of fundamental importance in comparing those disk architectures with the observed diversity of exoplanets. The prediction, however, depends on the assumption that whether the same gap structure exists in the dust component alone or in the gas component as well. We assume a planet can only open a gap in the gas component when its mass exceeds the pebble isolation mass by considering the core acc…
Five newly observed transit light curves of the TrES-3 planetary system are presented. Together with other light curve data from literature, 23 transit light curves in total, which cover an overall timescale of 911 epochs, have been analyzed through a standard procedure. From these observational data, the system's orbital parameters are determined and possible transit timing variations are investigated. Given that a null transit-timing-variation produces a fit with reduced chi^2=1.52, our results agree with previous work, that transit timing variations might not exist in these data. However, a…
The planetary systems detected so far already exhibit a wide diversity of architectures, and various methods are proposed to study quantitatively this diversity. Straightforward ways to quantify the difference between two systems and more generally, two sets of multiplanetary systems, are useful tools in the study of this diversity. In this work we present a novel approach, using a Weighted extension of the Energy Distance (WED) metric, to quantify the difference between planetary systems on the logarithmic period-radius plane. We demonstrate the use of this metric and its relation to previous…
Planetary ephemerides are a good tool for studying general relativity at the scale of our solar system. We present here new evaluations of advances of perihelia for Mercury and Saturn.
Context. Low-mass extrasolar planets are presently being discovered at an increased pace by radial velocity and transit surveys, opening a new window on planetary systems. Aims. We are conducting a high-precision radial velocity survey with the HARPS spectrograph which aims at characterizing the population of ice giants and super-Earths around nearby solar-type stars. This will lead to a better understanding of their formation and evolution, and yield a global picture of planetary systems from gas giants down to telluric planets. Methods. Progress has been possible in this field thanks in part…
tau Ceti is the closest single Sun-like star to the solar system and hosts a multi-planet system with four confirmed planets. The possible presence of additional planets, especially potentially habitable worlds, remains of great interest. We analyze the structure of the tau Ceti planetary system via the DYNAMITE algorithm, combining information from exoplanet population statistics and orbital dynamics with measurements of this specific system. We also expand DYNAMITE to incorporate radial velocity information. Our analysis suggests the presence of four additional planets, three of which match …
The Kepler mission observed thousands of transiting exoplanet candidates around hundreds of thousands of FGK dwarf stars. He, Ford, & Ragozzine (2019) (arXiv:1907.07773) applied forward modeling to infer the distribution of intrinsic architectures of planetary systems, developed a clustered Poisson point process model for exoplanetary systems (SysSim) to reproduce the marginal distributions of the observed Kepler population, and they showed that orbital periods and planet radii are clustered within a given planetary system. Here, we extend the clustered model to explore correlations between pl…
(abridged) Observations of exoplanets indicate the existence of several correlations in the architecture of planetary systems. Exoplanets within a system tend to be of similar size and mass, evenly spaced, and are often ordered in size and mass. Small planets are frequently packed in tight configurations, while large planets often have wider orbital spacing. Together, these correlations are called the peas in a pod trends in the architecture of planetary systems. In this paper these trends are investigated in theoretically simulated planetary systems and compared with observations. Whether the…
The structure of planetary systems around their host stars depends on their initial formation conditions. Massive planets will likely be formed as a consequence of rapid migration of planetesimals and low mass cores into specific trapping sites in protoplanetary discs. We present analytical modeling of inhomogeneities in protoplanetary discs around a variety of young stars, - from Herbig Ae/Be to classical T Tauri and down to M stars, - and show how they give rise to planet traps. The positions of these traps define the initial orbital distribution of multiple protoplanets. We investigate both…
Because of the diversity of stellar masses and orbital sizes of binary systems, and the complex interaction between star-star, star-planet and planet-planet, it has been difficult to fully characterize the planetary systems associated with binary systems. Here, we report high-precision astrometric observations of the low-mass binary system GJ 896AB, revealing the presence of a Jupiter-like planetary companion (GJ 896Ab). The planetary companion is associated to the main star GJ 896A, with an estimated mass of 2.3 Jupiter masses and an orbit period of 284.4 days. A simultaneous analysis of the …
We re-analyze the global orbital architecture and dynamical stability of the $μ$ Arae planetary system. We have updated the best-fit elements and minimal masses of the planets based on literature radial velocity (RV) measurements, now spanning 15 years. This is twice the RVs interval used for the first characterization of the system in 2006. It consists of a Saturn- and two Jupiter-mass planets in low-eccentric orbits resembling the Earth-Mars-Jupiter configuration in the Solar system, as well as the close-in warm Neptune with a mass of ~14 Earth masses. Here, we constrain this early solution …
We revisit the problem of the existence of KAM tori in extrasolar planetary systems. Specifically, we consider the $\upsilon$ Andromedæ system, by modelling it with a three-body problem. This preliminary study allows us to introduce a natural way to evaluate the robustness of the planetary orbits, which can be very easily implemented in numerical explorations. We apply our criterion to the problem of the choice of a suitable orbital configuration which exhibits strong stability properties and is compatible with the observational data that are available for the $\upsilon$ Andromedæ system itsel…
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…
Nearby stars are prime targets for exoplanet searches and characterization using a variety of detection techniques. Combining constraints from the complementary detection methods of high contrast imaging (HCI) and radial velocity (RV) can further constrain the planetary architectures of these systems because these methods place limits at different regions of the companion mass and semi-major axis parameter space. We aim to constrain the planetary architectures from the combination of HCI and RV data for 6 nearby stars within 6 pc: $τ$ Ceti, Kapteyn's star, AX Mic, 40 Eri, HD 36395, and HD 4258…
Planet formation is generally described in terms of a system containing the host star and a protoplanetary disc, of which the internal properties (e.g. mass and metallicity) determine the properties of the resulting planetary system. However, (proto)planetary systems are predicted and observed to be affected by the spatially-clustered stellar formation environment, either through dynamical star-star interactions or external photoevaporation by nearby massive stars. It is challenging to quantify how the architecture of planetary systems is affected by these environmental processes, because stel…
The HR8799 planetary system with four ~10 mJup planets in wide orbits up to 70 au, and periods up to 500 yr has been detected with the direct imaging. Its intriguing orbital architecture is not fully resolved due to time-limited astrometry covering ~20 years. Earlier, we constructed a heuristic model of the system based on rapid, convergent migration of the planets. We developed a better structured and CPU-efficient variant of this model. We re-analyzed the self-consistent, homogeneous astrometric dataset in Konopacky (2016). The best-fitting configuration agrees with our earlier findings. The…
The scattering of small bodies by planets is an important dynamical process in planetary systems. We present an analytical model to describe this process using the simplifying assumption that each particle's dynamics is dominated by a single planet at a time. As such the scattering process can be considered as a series of three body problems during each of which the Tisserand parameter with respect to the relevant planet is conserved. This constrains the orbital parameter space into which a particle can be scattered. Such arguments have previously been applied to the process by which comets ar…
Observations of exoplanetary systems provide clues about the intrinsic distribution of planetary systems, their architectures, and how they formed. We develop a forward modelling framework for generating populations of planetary systems and "observed" catalogues by simulating the Kepler detection pipeline (SysSim). We compare our simulated catalogues to the Kepler DR25 catalogue of planet candidates, updated to include revised stellar radii from Gaia DR2. We constrain our model based on the observed 1D marginal distributions of orbital periods, period ratios, transit depths, transit depth rati…
Mixed-variable symplectic integrators are widely used in orbital dynamics. However, they have been developed for Solar system-type architectures, and can not handle evolving hierarchy, in particular in systems with two or more stellar components. Such configuration may have occurred in the history of HD 106906, a tight pair of F-type stars surrounded by a debris disk and a planetary-mass companion on a wide orbit. We present the new algorithm ODEA, based on the symplectic algorithm SWIFT HJS, that can model any system (binary,...) with unstable architecture. We study the peculiar system HD 106…
We present evidence of tidally-driven inspiral in the Kepler-1658 (KOI-4) system, which consists of a giant planet (1.1$R_\mathrm{J}$, 5.9$M_\mathrm{J}$) orbiting an evolved host star (2.9$R_\odot$, 1.5$M_\odot$). Using transit timing measurements from Kepler, Palomar/WIRC, and TESS, we show that the orbital period of Kepler-1658b appears to be decreasing at a rate $\dot{P} = 131_{-22}^{+20}$~ms~yr$^{-1}$, corresponding to an infall timescale $P/\dot{P}\approx2.5$~Myr. We consider other explanations for the data including line-of-sight acceleration and orbital precession, but find them to be i…
We study the influence of outer Solar System architecture on the structural evolution of the Oort Cloud (OC) and the flux of Earth-crossing comets. In particular, we seek to quantify the role of the giant planets as "planetary protectors". To do so, we have run simulations in each of four different planetary mass configurations to understand the significance of each of the giant planets. Because the outer planets modify the structure of the OC throughout its formation, we integrate each simulation over the full age of the Solar System. Over this time, we follow the evolution of cometary orbits…
Early dynamical evolution of close-in planetary systems is shaped by an intricate combination of planetary gravitational interactions, orbital migration, and dissipative effects. While the process of convergent orbital migration is expected to routinely yield resonant planetary systems, previous analyses have shown that the semi-major axes of initially resonant pairs of planets will gradually diverge under the influence of long-term energy damping, producing an overabundance of planetary period ratios in slight excess of exact commensurability. While this feature is clearly evident in the orbi…
