The discovery of over 400 extrasolar planets allows us to statistically test our understanding of formation and dynamics of planetary systems via numerical simulations. Traditional N-body simulations of multiple-planet systems without gas disks have successfully reproduced the eccentricity (e) distribution of the observed systems, by assuming that the planetary systems are relatively closely packed when the gas disk dissipates, so that they become dynamically unstable within the stellar lifetime. However, such studies cannot explain the small semi-major axes (a) of extrasolar planetary systems, if planets are formed, as the standard planet formation theory suggests, beyond the ice line.
In this paper, we numerically study the evolution of three-planet systems in dissipating gas disks, and constrain the initial conditions that reproduce the observed semi-major axis and eccentricity distributions simultaneously. We adopt the initial conditions that are motivated by the standard planet formation theory, and self-consistently simulate the disk evolution, and planet migration by using a hybrid N-body and 1D gas disk code. We also take account of eccentricity damping, and investigate the effect of saturation of corotation resonances on the evolution of planetary systems. We find that the semi-major axis distribution is largely determined in a gas disk, while the eccentricity distribution is determined after the disk dissipation. We also find that there may be an optimum disk mass which leads to the observed a-e distribution. Our simulations generate a larger fraction of planetary systems trapped in mean-motion resonances (MMRs) than the observations, indicating that the disk's perturbation to the planetary orbits may be important to explain the observed rate of MMRs. We also find much lower occurrence of planets on retrograde orbits than the current observations of close-in planets suggest.
Aims. Comparing theoretical models with observations allows one to make key step forward towards an understanding of planetary systems. It however requires a model able to (i) predict all the necessary observable quantities (not only masses and orbits, but also radii, luminosities, magnitudes, or evaporation rates) and (ii) address the large range in relevant planetary masses (from Mars mass to super-Jupiters) and distances (from stellar-grazing to wide orbits). Methods. We have developed a combined global end-to-end planetary formation and evolution model, the Generation III Bern model, based…
Many observed giant planets lie on eccentric orbits. Such orbits could be the result of strong scatterings with other giant planets. The same dynamical instability that produces these scatterings may also cause habitable planets in interior orbits to become ejected, destroyed, or be transported out of the habitable zone. We say that a habitable planet has resilient habitability if it is able to avoid ejections and collisions and its orbit remains inside the habitable zone. Here we model the orbital evolution of rocky planets in planetary systems where giant planets become dynamically unstable.…
At least 25% of white dwarfs show atmospheric pollution by metals, sometimes accompanied by detectable circumstellar dust/gas discs or (in the case of WD 1145+017) transiting disintegrating asteroids. Delivery of planetesimals to the white dwarf by orbiting planets is a leading candidate to explain these phenomena. Here, we study systems of planets and planetesimals undergoing planet-planet scattering triggered by the star's post-main sequence mass loss, and test whether this can maintain high rates of delivery over the several Gyr that they are observed. We find that low-mass planets (Earth t…
Planetary debris is observed in the atmospheres of over 1,000 white dwarfs, and two white dwarfs are now observed to contain orbiting minor planets. Exoasteroids and planetary core fragments achieve orbits close to the white dwarf through scattering with major planets. However, the architectures that allow for this scattering to take place are time-consuming to explore with $N$-body simulations lasting $\sim 10^{10}$ yr; these long-running simulations restrict the amount of phase space that can be investigated. Here we use planar and three-dimensional (spatial) elliptic periodic orbits, as wel…
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…
Planetary systems formed in clusters may be subject to stellar encounter flybys. Here we create a diverse range of representative planetary systems with different orbital scales and planets' masses and examine encounters between them in a typical open cluster. We first explore the close-in multi-super earth systems $\lesssim0.1$ au. They are resistant to flybys in that only ones inside a few au can destabilise a planet or break the resonance between such planets. But these systems may capture giant planets onto wide orbits from the intruding star during distant flybys. If so, the original clos…
In this paper we address the stability of resonantly forced density waves in dense planetary rings. Already by Goldreich & Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the ring's viscosity and the surface mass density. In the recent paper Schmidt et al. (2016) we have pointed out that when - within a fluid description of the ring dynamics - the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping, but nonlinearity of the u…
WD 0145+234 is a white dwarf that is accreting metals from a circumstellar disc of planetary material. It has exhibited a substantial and sustained increase in 3-5 micron flux since 2018. Follow-up Spitzer photometry reveals that emission from the disc had begun to decrease by late 2019. Stochastic brightening events superimposed on the decline in brightness suggest the liberation of dust during collisional evolution of the circumstellar solids. A simple model is used to show that the observations are indeed consistent with ongoing collisions. Rare emission lines from circumstellar gas have be…
Being the first of its kind, the white dwarf WD 1145+017 exhibits a complex system of disintegrating debris which offers a unique opportunity to study its disruption process in real time. Even with plenty of transit observations there are no clear constraints on the masses or eccentricities of such debris. Using $N$-body simulations we show that masses greater than approximately $10^{20}$ kg (a tenth of the mass of Ceres) or orbits that are not nearly circular ($\mathrm{eccentricity}>10^{-3}$) dramatically increase the chances of the system becoming unstable within two years, which would contr…
Many potential mechanisms for delivering planetary debris to within a few Roche radii of white dwarfs rely on gravitational scattering events that feature perturbers which are giant planets or terrestrial planets. However, the population of these planets orbiting white dwarfs is still unknown, and for a substantial fraction of white dwarfs the largest planetary survivors of stellar evolution may be sub-terrestrial mass minor planets. Here, we attempt to identify the smallest mass perturbers that could pollute white dwarfs. Through computationally expensive numerical simulations of both unstabl…
The core accretion scenario of planet formation assumes that planetesimals and planetary embryos are formed during the primordial, gaseous phases of the protoplanetary disk. However, how the dust particles overcome the traditional growth barriers is not well understood. The recently proposed viscous ring-instability may explain the concentric rings observed in protoplanetary disks by assuming that the dust grains can reduce the gas conductivity, which can weaken the magneto-rotational instability. We present an analysis of this model with the help of GPU-based numerical hydrodynamic simulation…
Ocean planets are volatile rich planets, not present in our Solar System, which are thought to be dominated by deep, global oceans. This results in the formation of high-pressure water ice, separating the planetary crust from the liquid ocean and, thus, also from the atmosphere. Therefore, instead of a carbonate-silicate cycle like on the Earth, the atmospheric carbon dioxide concentration is governed by the capability of the ocean to dissolve carbon dioxide (CO2). In our study, we focus on the CO2 cycle between the atmosphere and the ocean which determines the atmospheric CO2 content. The atm…
Planets orbiting intermediate and low-mass stars are in jeopardy as their stellar hosts evolve to white dwarfs (WDs) because the dynamics of the planetary system changes due to the increase of the planet:star mass ratio after stellar mass-loss. In order to understand how the planet multiplicity affects the dynamical stability of post-main sequence (MS) systems, we perform thousands of N-body simulations involving planetary multiplicity as the variable and with a controlled physical and orbital parameter space: equal-mass planets; the same orbital spacing between adjacent planet's pairs; and or…
We present initial results of a new campaign of simulations focusing on the interaction of planetary winds with stellar environments using Adaptive Mesh Refinement methods. We have confirmed the results of Stone & Proga 2009 that an azimuthal flow structure is created in the planetary wind due to day/night temperatures differences. We show that a backflow towards the planet will occur with a strength that depends on the escape parameter. When a stellar outflow is included, we see unstable bow waves forming through the outflow's interaction with the planetary wind.
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…
Advanced System Engineering Approaches to Emerging Challenges in Planetary and Deep-Space Exploration
Escuela Técnica Superior de Ingeniería (ICAI), Universidad Pontificia Comillas, 28015 Madrid, Spain Department of Computer Applications in Science \& Engineering, BARCELONA Supercomputing Center, 08034 Barcelona, Spain Dept. of Mechanical Engineering, University of Maryland, College Park, USA School of Engineering, EPFL, 1015 Lausanne, Switzerland College of Engineering, University of Michigan, Ann Arbor, USA Grainger College of Engineering, University of Illinois at Urbana-Champaign, USA Dept. of Mechanical Engineering, Iowa State University, USA Dept. of Mechanical Engineering, University of Wisconsin-Madison, USA Departamento de Informática e Ingeniería de Sistemas, Universidad de Zaragoza, 50009 Zaragoza, Spain Estudis d'Informàtica, Multimèdia i Telecomunicació, Universitat Oberta de Catalunya, 08018 Barcelona, Spain
At least 30\% of main sequence stars host planets with sizes of between 1 and 4 Earth radii and orbital periods of less than 100 days. We use N-body simulations including a model for gas-assisted pebble accretion and disk--planet tidal interaction to study the formation of super-Earth systems. We show that the integrated pebble mass reservoir creates a bifurcation between hot super-Earths or hot-Neptunes ($\lesssim15M_{\oplus}$) and super-massive planetary cores potentially able to become gas giant planets ($\gtrsim15M_{\oplus}$). Simulations with moderate pebble fluxes grow multiple super-Ear…
We make use of a new hybrid method to simulate the long-term, multiple-orbit disc formation through tidal disruptions of rocky bodies by white dwarfs, at high-resolution and realistic semi-major axis. We perform the largest-yet suite of simulations for dwarf and terrestrial planets, spanning four orders of magnitude in mass, various pericentre distances and semi-major axes between 3 AU and 150 AU. This large phase space of tidal disruption conditions has not been accessible through the use of previous codes. We analyse the statistical and structural properties of the emerging debris discs, as …
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…
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…
Chaotic dynamics are expected during and after planet formation, and a leading mechanism to explain large eccentricities of gas giant exoplanets is planet-planet gravitational scattering. The same scattering has been invoked to explain misalignments of planetary orbital planes with respect to their host star's spin. However, an observational puzzle is presented by Kepler-56, which has two inner planets (b and c) that are nearly coplanar with each other, yet are more than 45 degrees inclined to their star's equator. Thus the spin-orbit misalignment might be primordial. Instead, we further devel…
The majority of binary star systems that host exoplanets will spend the first portion of their lives within a star-forming cluster that may drive dynamical evolution of the binary-planet system. We perform numerical simulations of S-type planets, with masses and orbital architecture analogous to the solar system's 4 gas giants, orbiting within the influence of a 0.5 solar-mass binary companion. The binary-planet system is integrated simultaneously with an embedded stellar cluster environment. ~10% of our planetary systems are destabilized when perturbations from our cluster environment drive t…
Free-floating Planets Produced by Planet-Planet Scatterings: Ejection Velocity and Survival Rate of Their Moons
Tsung-Dao Lee Institute, Shanghai Jiao-Tong University（上海交大李政道研究所）；Center for Astrophysics and Planetary Science, Department of Astronomy, Cornell University（康奈尔大学天文学系天文与行星科学中心）
The presence of forming planets embedded in their protoplanetary disks has been inferred from the detection of multiring structures in such disks. Most of these suspected planets are undetectable by direct imaging observations at current measurement sensitivities. Inward migration and accretion might make these putative planets accessible to the Doppler method, but the actual extent of growth and orbital evolution remains unconstrained. Under the premise that the gaps in the disk around HD 163296 originate from new-born planets, we investigate if and under which circumstances the gap-opening p…
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 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…
Radial velocity searches for exoplanets have detected many multi-planet systems around nearby bright stars. An advantage of this technique is that it generally samples the orbit outside of inferior/superior conjunction, potentially allowing the Keplerian elements of eccentricity and argument of periastron to be well characterized. The orbital architectures for some of these systems show signs of close planetary encounters that may render the systems unstable as described. We provide an in-depth analysis of two such systems: HD 5319 and HD 7924, for which the scenario of coplanar orbits results…
Dozens of habitable zone, approximately earth-sized exoplanets are known today. An emerging frontier of exoplanet studies is identifying which of these habitable zone, small planets are actually habitable (have all necessary conditions for life) and, of those, which are earth-like. Many parameters and processes influence habitability, ranging from the orbit through detailed composition including volatiles and organics, to the presence of geological activity and plate tectonics. While some properties will soon be directly observable, others cannot be probed by remote sensing for the foreseeable…
The Hungaria asteroid group is located interior to the main asteroid belt, with semimajor axes between 1.8 and 2 AU, low eccentricities and inclinations of 16-35 degrees. Recently, it has been proposed that Hungaria asteroids are a secularly declining population that may be related to the Late Heavy Bombardment (LHB) impactors (Ćuk et al. 2012, Bottke et al. 2012). While Ćuk et al. (2012) and Bottke et al. (2012) have reproduced a Hungaria-like population that declined exponentially, the real Hungarias were never confirmed to be unstable to the same degree. Here we find that the stability of H…
Planets form in the discs of gas and dust that surround young stars. It is not known whether gas giant planets on wide orbits form the same way as Jupiter or by fragmentation of gravitationally unstable discs. Here we show that a giant planet, which has formed in the outer regions of a protostellar disc, initially migrates fast towards the central star (migration timescale ~10,000 yr) while accreting gas from the disc. However, in contrast with previous studies, we find that the planet eventually opens up a gap in the disc and the migration is essentially halted. At the same time, accretion-po…
