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 106906 as a testcase for the code. We define and compute a criterion based on acceleration ratios to indicate when the initial hierarchy is not relevant anymore. A new hierarchy is then computed. The code is applied to study the two fly-bys that occurred on system HD 106906, recently evidenced by De Rosa & Kalas (2019), to determine if they could account for the wide orbit of the planet. Thousands of simulations have been performed to account for the uncertainty on the perturbers coordinates and velocities. The algorithm is able to handle any change of hierarchy, temporary or not. We used it to fully model HD 106906 encounters. The simulations confirm that the fly-bys could have stabilized the planet orbit, and show that it can account for the planet probable misalignment with respect to the disk plane as well as the disk morphology. However, that requires a small distance at closest approach (< 0.05 pc), and this configuration is not guaranteed. ODEA is a very good choice for the study of non-Solar type architecture. It can now adapt to an evolving hierarchy, and is thus suitable to study capture of planets and dust. Further observations of the perturbers, in particular their radial velocity, are required to conclude on the effects of the fly-by on system HD 106906.
The search for habitable exoplanets inspires the question - how do habitable planets form? Planet habitability models traditionally focus on abiotic processes and neglect a biotic response to changing conditions on an inhabited planet. The Gaia hypothesis postulates that life influences the Earth's feedback mechanisms to form a self-regulating system, and hence that life can maintain habitable conditions on its host planet. If life has a strong influence, it will have a role in determining a planet's habitability over time. We present the ExoGaia model - a model of simple 'planets' host to evo…
We present N-body simulations of planetary system formation in thermally-evolving, viscous disc models. The simulations incorporate type I migration (including corotation torques and their saturation), gap formation, type II migration, gas accretion onto planetary cores, and gas disc dispersal through photoevaporation. The aim is to examine whether or not the oligarchic growth scenario, when combined with self-consistent disc models and up-to-date prescriptions for disc-driven migration, can produce planetary systems similar to those that have been observed. The results correlate with the init…
Partial condensation of dust from the Solar nebula is likely responsible for the diverse chemical compositions of chondrites and rocky planets/planetesimals in the inner Solar system. We present a forward physical-chemical model of a protoplanetary disc to predict the chemical compositions of planetary building blocks that may form from such a disc. Our model includes the physical evolution of the disc and the condensation, partial advection, and decoupling of the dust within it. The chemical composition of the condensate changes with time and radius. We compare the results of two dust condens…
The discovery of many giant planets in close-in orbits and the effect of planetary and stellar tides in their subsequent orbital decay have been extensively studied in the context of planetary formation and evolution theories. Planets orbiting close to their host stars undergo close encounters, atmospheric photoevaporation, orbital evolution, and tidal interactions. In many of these theoretical studies, it is assumed that the interior properties of gas giants remain static during orbital evolution. Here we present a model that allows for changes in the planetary radius as well as variations in…
The maximum temperature and radial temperature profile in a protoplanetary disc are important for the condensation of different elements in the disc. We simulate the evolution of a set of protoplanetary discs from the collapse of their progenitor molecular cloud cores as well as the dust decoupling within the discs as they evolve. We show how the initial properties of the cloud cores affect the thermal history of the protoplanetary discs using a simple viscous disc model. Our results show that the maximum midplane temperature in the disc occurs within 0.5 AU. It increases with the initial clou…
This paper considers whether the population of known transiting exoplanets provides evidence for additional outer planets on inclined orbits, due to the perturbing effect of such planets on the orbits of inner planets. As such, we develop a semi-analytical method for calculating the probability that two mutually inclined planets are observed to transit. We subsequently derive a simplified analytical form to describe how the mutual inclination between two planets evolves due to secular interactions with a wide orbit inclined planet and use this to determine the mean probability that the two inn…
We make publicly available an efficient, versatile, easy to use and extend tool for calculating the evolution of circular aligned planetary orbits due to the tidal dissipation in the host star. This is the first model to fully account for the evolution of the angular momentum of the stellar convective envelope by the tidal coupling, the transfer of angular momentum between the stellar convective and radiative zones, the effects of the stellar evolution on the tidal dissipation efficiency and stellar core and envelope spins, the loss of stellar convective zone angular momentum to a magnetically…
The core accretion hypothesis posits that planets with significant gaseous envelopes accreted them from their protoplanetary discs after the formation of rocky/icy cores. Observations indicate that such exoplanets exist at a broad range of orbital radii, but it is not known whether they accreted their envelopes in situ, or originated elsewhere and migrated to their current locations. We consider the evolution of solid cores embedded in evolving viscous discs that undergo gaseous envelope accretion in situ with orbital radii in the range $0.1-10\rm au$. Additionally, we determine the long-term …
Symplectic integrators have made it possible to study the long-term evolution of planetary systems with direct N-body simulations. In this paper we reassess the accuracy of such simulations by running a convergence test on 20Myr integrations of the Solar System using various symplectic integrators. We find that the specific choice of metric for determining a simulation's accuracy is important. Only looking at metrics related to integrals of motions such as the energy error can overestimate the accuracy of a method. As one specific example, we show that symplectic correctors do not improve the …
We study tidal dissipation in stars with masses in the range $0.1-1.6 M_\odot$ throughout their evolution, including turbulent effective viscosity acting on equilibrium tides and inertial waves in convection zones, and internal gravity waves in radiation zones. We consider a range of stellar evolutionary models and incorporate the frequency-dependent effective viscosity acting on equilibrium tides based on the latest simulations. We compare the tidal flow and dissipation obtained with the conventional equilibrium tide, which is strictly invalid in convection zones, finding that the latter typi…
We present a model of the early chemical composition and elemental abundances of planetary atmospheres based on the cumulative gaseous chemical species that are accreted onto planets forming by core accretion from evolving protoplanetary disks. The astrochemistry of the host disk is computed using an ionization driven, non-equilibrium chemistry network within viscously evolving disk models. We accrete gas giant planets whose orbital evolution is controlled by planet traps using the standard core accretion model and track the chemical composition of the material that is accreted onto the protop…
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…
The formation of planets depends on the underlying protoplanetary disc structure, which influences both the accretion and migration rates of embedded planets. The disc itself evolves on time-scales of several Myr during which both temperature and density profiles change as matter accretes onto the central star. Here we use a detailed model of an evolving disc to determine the growth of planets by pebble accretion and their migration through the disc. Cores that reach their pebble isolation mass accrete gas to finally form giant planets with extensive gas envelopes, while planets that do not re…
Planet formation in chemically diverse and evolving discs II. Chemical fingerprints in planetary atmospheres
INAF Istituto di Astrofisica e Planetologia Spaziali（意大利国家天体物理研究所）；INAF Osservatorio Astrofisico di Torino（意大利国家天体物理都灵天文台）；School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学学院）；Institut für Theoretische Astrophysik, Universität Heidelberg（海德堡大学理论天体物理研究所）；Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Universität Heidelberg（海德堡大学跨学科科学计算中心）；Université Paris-Saclay（巴黎萨克雷大学）；Université Paris Cité（巴黎西岱大学）
A large proportion of observed planetary systems contain several planets in a compact orbital configuration, and often harbor at least one close-in object. These systems are then most likely tidally evolving. We investigate how the effects of planet-planet interactions influence the tidal evolution of planets. We introduce for that purpose a new open-source addition to the Mercury N-body code, Mercury-T, which takes into account tides, general relativity and the effect of rotation-induced flattening in order to simulate the dynamical and tidal evolution of multi-planet systems. It uses a stand…
Exoplanets have been observed around stars at all stages of stellar evolution, in many cases orbiting in configurations that will eventually lead to the planets being engulfed or consumed by their host stars, such as Hot Jupiters or ultra-short period planets. Furthermore, objects such as polluted white dwarfs provide strong evidence that the consumption of planets by stars is a common phenomenon. This consumption causes several significant changes in the stellar properties, such as changes to the stellar spin, luminosity, chemical composition, or mass loss processes. Here, we explore this wid…
Planet traps are necessary to prevent forming planets from falling onto their host star by type I migration. Surface mass density and temperature gradient irregularities favor the apparition of traps and deserts. Such features are found at the dust sublimation lines and heat transition barriers. We study how planets may remain trapped or escape as they grow and as the disk evolves. We model the temporal viscous evolution of a protoplanetary disk by coupling its dynamics, thermodynamics, geometry and composition. The resulting mid-plane density and temperature profiles allow the modeling of the…
Recent three-dimensional magnetohydrodynamical simulations have identified a disk wind by which gas materials are lost from the surface of a protoplanetary disk, which can significantly alter the evolution of the inner disk and the formation of terrestrial planets. A simultaneous description of the realistic evolution of the gaseous and solid components in a disk may provide a clue for solving the problem of the mass concentration of the terrestrial planets in the solar system. We simulate the formation of terrestrial planets from planetary embryos in a disk that evolves via magnetorotational …
The accretion of pebbles on planetary cores has been widely studied in recent years and is found to be a highly effective mechanism for planetary growth. While most studies assume planetary cores as an initial condition in their simulation, the question how, where and when these cores form is often neglected. We study the impact of pebble accretion during the formation phase and subsequent evolution of planetary embryos in the early stages of circumstellar disk evolution. In doing so we aim to quantify the timescales and local dependency of planetary embryo formation, based on the solid evolut…
Super-Earths possess low-mass H$_2$/He atmospheres (typically less than 10% by mass). However, the origins of super-Earth atmospheres have not yet been ascertained. We investigate the role of rapid disk clearing by photoevaporation during the formation of super-Earths and their atmospheres. We perform unified simulations of super-Earth formation and atmospheric evolution in evolving disks that consider both photoevaporative winds and magnetically driven disk winds. For the growth mode of planetary cores, we consider two cases in which planetary embryos grow with and without pebble accretion. O…
We present the next step in a series of papers devoted to connecting the composition of the atmospheres of forming planets with the chemistry of their natal evolving protoplanetary disks. The model presented here computes the coupled chemical and dust evolution of the disk and the formation of three planets per disk model. Our three canonical planet traps produce a Jupiter near 1 AU, a Hot Jupiter and a Super-Earth. We study the dependency of the final orbital radius, mass, and atmospheric chemistry of planets forming in disk models with initial disk masses that vary by 0.02 $M_\odot$ above an…
Planets with masses larger than about 0.1 Earth-masses undergo rapid inward migration (type I migration) in a standard protoplanetary disk. Recent magnetohydrodynamical simulations revealed the presence of magnetically driven disk winds, which would alter the disk profile and the type I migration in the close-in region. We investigate orbital evolution of planetary embryos in disks that viscously evolve under the effects of disk winds. The aim is to discuss effects of altered disk profiles on type I migration. In addition, we aim to examine whether observed distributions of close-in super-Eart…
We present a numerical method to estimate the strengths of arbitrary three body mean motion resonances between two planets in circular coplanar orbits and a massless particle in an arbitrary orbit. This method allows us to obtain an atlas of the three body resonances in the Solar System showing where are located and how strong are thousands of resonances involving all the planets from 0 to 1000 au. This atlas confirms the dynamical relevance of the three body resonances involving Jupiter and Saturn in the asteroid belt but also shows the existence of a family of relatively strong three body re…
We analyze potential effects of an extraterrestrial civilization's use of orbiting mirrors to illuminate the dark side of a synchronously rotating planet on planetary transit light curves. Previous efforts to detect civilizations based on side effects of planetary-scale engineering have focused on structures affecting the host star output (e.g. Dyson spheres). However, younger civilizations are likely to be less advanced in their engineering efforts, yet still capable of sending small spacecraft into orbit. Since M dwarfs are the most common type of star in the solar neighborhood, it seems pla…
Observations and models of giant planets indicate that such objects are enriched in heavy elements compared to solar abundances. The prevailing view is that giant planets accreted multiple Earth masses of heavy elements after the end of core formation. Such late solid enrichment is commonly explained by the accretion of planetesimals. Planetesimals are expected to form at the edges of planetary gaps, and here we address the question of whether these planetesimals can be accreted in large enough amounts to explain the inferred high heavy element contents of giant planets. We perform a series of…
The signatures of planets hosted by M dwarfs are more readily detected with transit photometry and radial velocity methods than those of planets around larger stars. Recently, transit photometry was used to discover seven planets orbiting the late-M dwarf TRAPPIST-1. Three of TRAPPIST-1's planets fall in the Habitable Zone, a region where liquid water could exist on the planetary surface given appropriate planetary conditions. We aim to investigate the habitability of the TRAPPIST-1 planets by studying the star's activity and its effect on the planets. We analyze previously-published space- an…
Hypothetical exomoons around close-in giant planets may migrate inwards and/or outwards in virtue of the interplay of the star, planet and moon tidal interactions. These processes could be responsible for the disruption of lunar systems, the collision of moons with planets or could provide a mechanism for the formation of exorings. Several models have been developed to determine the fate of exomoons when subject to the tidal effects of their host planet. None of them have taken into account the key role that planetary evolution could play in this process. In this paper we put together numerica…
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…
The rapid advances in observations of the different populations of exoplanets, the characterization of their host stars and the links to the properties of their planetary systems, the detailed studies of protoplanetary disks, and the experimental study of the interiors and composition of the massive planets in our solar system provide a firm basis for the next big question in planet formation theory. How do the elemental and chemical compositions of planets connect with their formation? The answer to this requires that the various pieces of planet formation theory be linked together in an end-…
Wind accretion onto planets orbiting an evolving Solar-like star and their detectability
Universidad Autónoma de Sinaloa（锡那罗亚自治大学）；Instituto de Radioastronomía y Astrofísica, Universidad Nacional Autónoma de México（墨西哥国立自治大学射电天文学与天体物理研究所）；SECIHTI - Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo（米却肯圣尼古拉斯德伊达尔戈大学物理与数学研究所）；Instituto de Astrofísica de Andalucía, CSIC（安达卢西亚天体物理研究所）
Planetary systems with several planets in compact orbital configurations such as TRAPPIST-1 are surely affected by tidal effects. Its study provides us with important insight about its evolution. We developed a second generation of a N-body code based on the tidal model used in Mercury-T, re-implementing and improving its functionalities using Rust as programming language (including a Python interface for easy use) and the WHFAST integrator. The new open source code ensures memory safety, reproducibility of numerical N-body experiments, it improves the spin integration compared to Mercury-T an…
The final orbital configuration of a planetary system is shaped by both its early star-disk environment and late-stage gravitational interactions. Assessing the relative importance of each of these factors is not straightforward due to the observed diversity of planetary systems compounded by observational biases. Our goal is to understand how a planetary system may change when planetesimal accretion and planet migrations stop and secular gravitational effects take over. Our approach starts with a novel classification of planetary systems based on their orbital architecture, validated using Ap…
Many planets are observed in stellar binary systems, and their frequency may be comparable to that of planetary systems around single stars. Binary stellar evolution in such systems influences the dynamical evolution of the resident planets. Here we study the evolution of a single planet orbiting one star in an evolving binary system. We find that stellar evolution can trigger dynamical instabilities that drive planets into chaotic orbits. This instability leads to planet-star collisions, exchange of the planet between the binary stars ("star-hoppers"), and ejection of the planet from the syst…
Radial velocity and transit surveys indicate that solar-type stars bear super-Earths, with mass and period up to ~ 20 M_E and a few months, are more common than those with Jupiter-mass gas giants. In many cases, these super-Earths are members of multiple-planet systems in which their mutual dynamical interaction has influenced their formation and evolution. In this paper, we modify an existing numerical population synthesis scheme to take into account protoplanetary embryos' interaction with their evolving natal gaseous disk, as well as their close scatterings and resonant interaction with eac…
The Earth's ocean mass is only 2.3 x 10^{-4} of the whole planet mass. Even including water in the interior, it would be at most 10^{-3}-10^{-2}. Ancient Mars may have had a similar or slightly smaller water fraction. It is important to clarify the water delivery mechanism to rocky planets in habitable zones in exoplanetary systems, as well as that to the Earth and Mars. Here, we consider water delivery to planets by icy pebbles after the snowline inwardly passes the planetary orbits and derive the water mass fraction (f_{water}) of the final planet as a function of disk parameters and discuss…
We extend the models presented in Mordasini et al. (2009) to the formation of planets orbiting stars of different masses. We discuss the properties of the resulting synthetic planet population in terms of mass, orbit, and metallicity distributions. The population synthesis calculations we use are based on the planet formation model developed in Alibert et al. (2005a), which self-consistently takes into account planetary growth and migration in an evolving proto-planetary disk. Using this model, we generate synthetic populations of planets by following their growth in a large number of proto-pl…
Transitional disks are protoplanetary disks with large and deep central holes in the gas, possibly carved by young planets. Dong, R., & Dawson, R. 2016, ApJ, 825, 7 simulated systems with multiple giant planets that were capable of carving and maintaining such gaps during the disk stage. Here we continue their simulations by evolving the systems for 10 Gyr after disk dissipation and compare the resulting system architecture to observed giant planet properties, such as their orbital eccentricities and resonances. We find that the simulated systems contain a disproportionately large number of ci…
The formation of the solar system's terrestrial planets has been numerically modeled in various works, and many other studies have been devoted to characterizing our modern planets' chaotic dynamical state. However, it is still not known whether our planet's fragile chaotic state is an expected outcome of terrestrial planet accretion. We use a suite of numerical simulations to present a detailed analysis and characterization of the dynamical chaos in 145 different systems produced via terrestrial planet formation in Kaib and Cowan (2015). These systems were created in the presence of a fully f…
Nearly all known white dwarf planetary systems contain detectable rocky debris in the stellar photosphere. A glaring exception is the young and still evolving white dwarf WD J0914+1914, which instead harbours a giant planet and a disc of pure gas. The stability boundaries of this disc and the future prospects for this white dwarf to be polluted with rocks depend upon the mass and orbit of the planet, which are only weakly constrained. Here we combine an ensemble of plausible planet orbits and masses to determine where observers should currently expect to find the outer boundary of the gas disc…
Aims. We track the time evolution of planet traps and snowlines in a viscously evolving protoplanetary disk using an opacity table that accounts for the composition of the dust material. Methods. We coupled a dynamical and thermodynamical disk model with a temperature-dependent opacity table (that accounts for the sublimation of the main dust components) to investigate the formation and evolution of snowlines and planet traps during the first million years of disk evolution. Results. Starting from a minimum mass solar nebula (MMSN), we find that the disk mid-plane temperature profile shows sev…
Uncovering the Rapidly Evolving Orbits of the Dynamic TOI-201 System
Leiden University（莱顿大学）；Massachusetts Institute of Technology（麻省理工学院）；University of Michigan（密歇根大学）；University of New Mexico（新墨西哥大学）；University of Southern Queensland（昆士兰科技大学）；Max Planck Institute for Astronomy（马克斯·普朗克天文学研究所）；Center for Astrophysics | Harvard & Smithsonian（哈佛-史密森尼天体物理中心）；University of Birmingham（伯明翰大学）；Observatoire de la Côte d’Azur（蔚蓝海岸天文台）；University of Hawai’i（夏威夷大学）
The discovery of planets orbiting stars other than the Sun has accelerated over the past decade, and this trend will continue as new space- and ground-based observatories employ next-generation instrumentation to search the skies for habitable worlds. However, many factors and processes can affect planetary habitability and must be understood to accurately determine a planet's habitability potential. While climate models have long been used to understand and predict climate and weather patterns on the Earth, a growing community of researchers has begun to apply these models to extrasolar plane…
Dust grains migrating under Poynting-Robertson drag may be trapped in mean-motion resonances with planets. Such resonantly trapped grains are observed in the solar system. In extrasolar systems, the exozodiacal light produced by dust grains is expected to be a major obstacle to future missions attempting to directly image terrestrial planets. The patterns made by resonantly trapped dust, however, can be used to infer the presence of planets, and the properties of those planets, if the capture and evolution of the grains can be modelled. This has been done with N-body methods, but such methods …
We present a study on the formation of planetary systems around low mass stars similar to Trappist-1, through the accretion of either planetesimals or pebbles. The aim is to determine if the currently observed systems around low mass stars favour one scenario over the other. We ran numerous N-body simulations, coupled to a thermally evolving viscous disc model, including prescriptions for planet migration and photoevaporation. We examine the differences between the pebble and planetesimal accretion scenarios, but also look at the influences of disc mass, planetesimal size, and the percentage o…
Planetary migration is a key link between planet formation models and observed exoplanet statistics. So far the theory of migration has focused on the interaction of planets with an inviscid or viscously evolving disk. Turbulent viscosity is thought to be the main driver of disk evolution and is known to affect the migration process. Recently, the topic of wind-driven accretion is experiencing a renaissance, as evidence is mounting that PPDs may be less turbulent than previously thought, and 3-D non-ideal MHD modeling of the wind-launching process is maturing. Aim: We wish to investigate how w…
The physics of planet formation is investigated using a population synthesis approach. We develop a simple model for planetary growth including pebble and gas accretion, and orbital migration in an evolving protoplanetary disk. The model is run for a population of 2000 stars with a range of disk masses and radii, and initial protoplanet orbits. The resulting planetary distribution is compared with the observed population of extrasolar planets, and the model parameters are improved iteratively using a particle swarm optimization scheme. The characteristics of the final planetary systems are mai…
The composition of planets is largely determined by the chemical and dynamical evolution of the disk during planetesimal formation and growth. To predict the diversity of exoplanet compositions, previous works modeled planetesimal composition as the equilibrium chemical composition of a proto- planetary disk at a single time. However, planetesimals form over an extended period of time, during which, elements sequentially condense out of the gas as the disk cools and are accreted onto planetesi- mals. To account for the evolution of the disk during planetesimal formation, we couple models of di…
The formation of planets with gaseous envelopes takes place in protoplanetary accretion discs on time-scales of several millions of years. Small dust particles stick to each other to form pebbles, pebbles concentrate in the turbulent flow to form planetesimals and planetary embryos and grow to planets, which undergo substantial radial migration. All these processes are influenced by the underlying structure of the protoplanetary disc, specifically the profiles of temperature, gas scale height and density. The commonly used disc structure of the Minimum Mass Solar Nebular (MMSN) is a simple pow…
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）
