The population of exoplanetary systems detected by Kepler provides opportunities to refine our understanding of planet formation. Unraveling the conditions needed to produce the observed exoplanets will sallow us to make informed predictions as to where habitable worlds exist within the galaxy. In this paper, we examine using N-body simulations how the properties of planetary systems are determined during the final stages of assembly. While accretion is a chaotic process, trends in the ensemble properties of planetary systems provide a memory of the initial distribution of solid mass around a star prior to accretion. We also use EPOS, the Exoplanet Population Observation Simulator, to account for detection biases and show that different accretion scenarios can be distinguished from observations of the Kepler systems. We show that the period of the innermost planet, the ratio of orbital periods of adjacent planets, and masses of the planets are determined by the total mass and radial distribution of embryos and planetesimals at the beginning of accretion. In general, some amount of orbital damping, either via planetesimals or gas, during accretion is needed to match the whole population of exoplanets. Surprisingly, all simulated planetary systems have planets that are similar in size, showing that the "peas in a pod" pattern can be consistent with both a giant impact scenario and a planet migration scenario. The inclusion of material at distances larger than what Kepler observes has a profound impact on the observed planetary architectures, and thus on the formation and delivery of volatiles to possible habitable worlds.
Architectures of Exoplanetary Systems. IV: A Multi-planet Model for Reproducing the Radius Valley and Intra-system Size Similarity of Planets around Kepler's FGK Dwarfs
A large number of observed exoplanets are part of multiple planet systems. Most of these systems are sufficiently close-in to be tidally evolving. In such systems, there is a competition between the excitation caused by planet-planet interactions and tidal damping. Using as an example two multiple planet systems, which host planets in the surface liquid water habitable zone (HZ): Kepler-62 and Kepler-186, we show the importance and effect of both planetary and stellar tides on the dynamical evolution of planets and on the climate of the HZ planets.
Many fundamental physical processes regarding planetary formation in protoplanetary disks are still imperfectly understood, with an elusive phenomenon being turbulence in such disks. Observations are available of planetary systems and of some protoplanetary disks, which can serve as a starting point for these investigations. Detected systems reveal different architectures of planets. One particularly interesting case to consider is the Kepler-223 system, which contains a rare configuration of four planets in a resonance chain, implying a certain migration history. We aim to use the orbital con…
We present an extended version of the Constant Time Lag analytical approach for the tidal evolution of circumbinary planets introduced in our previous work. The model is self-consistent, in the sense that all tidal interactions between pairs are computed, regardless of their size. We derive analytical expressions for the variational equations governing the spin and orbital evolution, which are expressed as high-order elliptical expansions in the semimajor axis ratio but retain closed form in terms of the binary and planetary eccentricities. These are found to reproduce the results of the numer…
[ABRIDGED]: Aims: two candidates in the KOI 1574 system are relatively long-period (about 114d and 191d) and in 5:3 resonance. We therefore search for TTVs in this particularly promising system. Methods: The full Kepler data was used, allowing to search for TTVs as well as for additional transit-like signals. Results: We detect strong anti-correlated TTVs of the 114d and 191d signals, dynamically confirming them as members of the same system. Dynamical simulations reproducing the observed TTVs allow us to also determine the masses of the planets. KOI 1574.01 (hereafter Kepler-87 b) was found t…
A question driving many studies is whether the thousands of exoplanets known today typically formed where we observe them or formed further out in the disk and migrated in. Early discoveries of giant exoplanets orbiting near their host stars and exoplanets in or near mean motion resonances were interpreted as evidence for migration and its crucial role in the beginnings of planetary systems. long-scale migration has been invoked to explain systems of planets in mean motion resonant chains consisting of three or more planets linked by integer period ratios. However, recent studies have reproduc…
The Kepler mission has recently discovered a number of exoplanetary systems, such as Kepler-11 and Kepler-32, in which ensembles of several planets are found in very closely packed orbits (often within a few percent of an AU of one another). These compact configurations present a challenge for traditional planet formation and migration scenarios. We present a dynamical study of the assembly of these systems, using an N-body method which incorporates a parametrized model of planet migration in a turbulent protoplanetary disc. We explore a wide parameter space, and find that under suitable condi…
We describe a fast, approximate method to characterize the orbits of satellites around a central binary in numerical simulations. A goal is to distinguish the free eccentricity -- random motion of a satellite relative to a dynamically cool orbit -- from oscillatory modes driven by the central binary's time-varying gravitational potential. We assess the performance of the method using the Kepler-16, Kepler-47, and Pluto-Charon systems. We then apply the method to a simulation of orbital damping in a circumbinary environment, resolving relative speeds between small bodies that are slow enough to…
Exoplanet systems with multiple planets in mean motion resonances have often been hailed as a signpost of disk driven migration. Resonant chains like Kepler-223 and Kepler-80 consist of a trio of planets with the three-body resonant angle librating and/or with a two-body resonant angle librating for each pair. Here we investigate whether close-in super-Earths and mini-Neptunes forming in situ can lock into resonant chains due to dissipation from a depleted gas disk. We simulate the giant impact phase of planet formation, including eccentricity damping from a gaseous disk, followed by subsequen…
Many multiple-planet systems have been found by the Kepler transit survey and various radial velocity (RV) surveys. Kepler planets show an asymmetric feature, namely, there are small but significant deficits/excesses of planet pairs with orbital period spacing slightly narrow/wide of the exact resonance, particularly near the first order mean motion resonance (MMR), such as 2:1 and 3:2 MMR. Similarly, if not exactly the same, an asymmetric feature (pileup wide of 2:1 MMR) is also seen in RV planets, but only for massive ones. We analytically and numerically study planets' orbital evolutions ne…
We assess the multi-planet systems discovered by the Kepler satellite in terms of current ideas about orbital migration and eccentricity damping due to planet-disk interactions. Our primary focus is on mean motion resonances. Only a few percent of planet pairs are in close proximity to a resonance. However, predicted migration rates (parameterized by $τ_n=n/{|\dot n|}$) imply that during convergent migration most planets would have been captured into first order resonances. Eccentricity damping (parameterized by $τ_e=e/{|\dot e|}$) offers a plausible resolution. Estimates suggest $τ_e/τ_n\sim …
We analyze the distribution of known multi-planet systems ($N \geq 3$) in the plane of mean-motion ratios, and compare it with the resonance web generated by two-planet mean-motion resonances (2P-MMR) and pure 3-planet commensurabilities (pure 3P-MMR). We find intriguing evidence of a statistically significant correlation between the observed distribution of compact low-mass systems and the resonance structure, indicating a possible causal relation. While resonance chains such as Kepler-60, Kepler-80 and TRAPPIST-1 are strong contributors, most of the correlation appears to be caused by system…
We study the effect of dynamical tides associated with the excitation of gravity waves in an interior radiative region of the central star on orbital evolution in observed systems containing Hot Jupiters. We consider WASP-43, Ogle-tr-113, WASP-12, and WASP-18 which contain stars on the main sequence (MS). For these systems there are observational estimates regarding the rate of change of the orbital period. We also investigate Kepler-91 which contains an evolved giant star. We adopt the formalism of Ivanov et al. for calculating the orbital evolution. For the MS stars we determine expected rat…
Most of super-Earths detected by the radial velocity (RV) method have significantly smaller eccentricities than the eccentricities corresponding to velocity dispersion equal to their surface escape velocity ("escape eccentricities"). If orbital instability followed by giant impacts among protoplanets that have migrated from outer region is considered, it is usually considered that eccentricities of the merged bodies become comparable to those of orbital crossing bodies, which are excited up to their escape eccentricities by close scattering. However, the eccentricity evolution in the {\it in s…
We consider the dynamical evolution of two planets orbiting in the vicinity of a first order mean motion reso- nance while simultaneously undergoing eccentricity damping and convergent migration. Following Goldreich & Schlichting (2014), we include a coupling between the dissipative semimajor axis evolution and the damping of the eccentricities. In agreement with past studies, we find that this coupling can lead to overstability of the resonance and that for a certain range of parameters capture into resonance is only temporary. Using a more general model, we show that whether overstable motio…
Abridged: The discovery of "hot Jupiters" very close to their parent stars confirmed that Jovian planets migrate inward via several potential mechanisms. We present empirical constraints on planet migration halting mechanisms. We compute model density functions of close-in exoplanets in the orbital semi-major axis - stellar mass plane to represent planet migration that is halted via several mechanisms, including the interior 1:2 resonance with the magnetospheric disk truncation radius, the interior 1:2 resonance with the dust sublimation radius, and several scenarios for tidal halting. The mod…
At least two multi-planetary systems in a 4:3 mean motion resonance have been found by radial velocity surveys. These planets are gas giants and the systems are only stable when protected by a resonance. Additionally the Kepler mission has detected at least 4 strong candidate planetary systems with a period ratio close to 4:3. This paper investigates traditional dynamical scenarios for the formation of these systems. We systematically study migration scenarios with both N-body and hydro-dynamic simulations. We investigate scenarios involving the in-situ formation of two planets in resonance. W…
Close-in planetary systems detected by the Kepler mission present an excess of periods ratio that are just slightly larger than some low order resonant values. This feature occurs naturally when resonant couples undergo dissipation that damps the eccentricities. However, the resonant angles appear to librate at the end of the migration process, which is often believed to be an evidence that the systems remain in resonance. Here we provide an analytical model for the dissipation in resonant planetary systems valid for low eccentricities. We confirm that dissipation accounts for an excess of pai…
We study the interaction of a proto-planetary disk and a planet on a highly inclined orbit in the linear regime. The evolution of the planet is dominated by dynamical friction for planet masses above several Earth-masses. Smaller planets are dominated by aerodynamic drag, especially for very high inclinations and retrograde orbits. The time-scales associated with migration and inclination damping are calculated. For certain values of the inclination, the inclination damping time-scale is longer than the migration time-scale and the disk lifetime. This result shows that highly inclined planets …
Some systems of close-in "super-Earths" contain five or more planets on non-resonant but compact and nearly coplanar orbits. The Kepler-11 system is an iconic representative of this class of system. It is challenging to explain their origins given that planet-disk interactions are thought to be essential to maintain such a high degree of coplanarity, yet these same interactions invariably cause planets to migrate into chains of mean motion resonances. Here we mine a large dataset of dynamical simulations of super-Earth formation by migration. These simulations match the observed period ratio d…
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…
We present two-dimensional hydrodynamical simulations of pairs of planets migrating simultaneously in the Type I regime in a protoplanetary disc. Convergent migration naturally leads to the trapping of these planets in mean-motion resonances. Once in resonance the planets' eccentricity grows rapidly, and disc-planet torques cause the planets to escape resonance on a time-scale of a few hundred orbits. The effect is more pronounced in highly viscous discs, but operates efficiently even in inviscid discs. We attribute this resonance-breaking to overstable librations driven by moderate eccentrici…
The giant impact phase of terrestrial planet formation establishes connections between super-Earths' orbital properties (semimajor axis spacings, eccentricities, mutual inclinations) and interior compositions (the presence or absence of gaseous envelopes). Using N-body simulations and analytic arguments, we show that spacings derive not only from eccentricities, but also from inclinations. Flatter systems attain tighter spacings, a consequence of an eccentricity equilibrium between gravitational scatterings, which increase eccentricities, and mergers, which damp them. Dynamical friction by res…
Evaporating rocky exoplanets, such as KIC 12557548b, eject large amounts of dust grains, which can trail the planet in a comet-like tail. When such objects occult their host star, the resulting transit signal contains information about the dust in the tail. We aim to use the detailed shape of the Kepler light curve of KIC 12557548b to constrain the size and composition of the dust grains that make up the tail, as well as the mass loss rate of the planet. Using a self-consistent numerical model of the dust dynamics and sublimation, we calculate the shape of the tail by following dust grains fro…
Observations have confirmed the existence of multiple-planet systems containing a hot Jupiter and smaller planetary companions. Examples include WASP-47, Kepler-730, and TOI-1130. We examine the plausibility of forming such systems in situ using $N$-body simulations that include a realistic treatment of collisions, an evolving protoplanetary disc and eccentricity/inclination damping of planetary embryos. Initial conditions are constructed using two different models for the core of the giant planet: a 'seed-model' and an 'equal-mass-model'. The former has a more massive protoplanet placed among…
We investigate the spin behavior of close-in rocky planets and the implications for their orbital evolution. Considering that the planet rotation evolves under simultaneous actions of the torque due to the equatorial deformation and the tidal torque, both raised by the central star, we analyze the possibility of temporary captures in spin-orbit resonances. The results of the numerical simulations of the exact equations of motions indicate that, whenever the planet rotation is trapped in a resonant motion, the orbital decay and the eccentricity damping are faster than the ones in which the rota…
The origins of the Galilean satellites - namely Io, Europa, Ganymede, and Callisto - is not fully understood yet. Here we use N-body numerical simulations to study the formation of Galilean satellites in a gaseous circumplanetary disk around Jupiter. Our model includes the effects of pebble accretion, gas-driven migration, and gas tidal damping and drag. Satellitesimals in our simulations first grow via pebble accretion and start to migrate inwards. When they reach the trap at the disk inner edge, scattering events and collisions take place promoting additional growth. Growing satellites event…
Beyond the $α$ model: scaling the wind-driven accretion rate in protoplanetary disks using systematic non-ideal magnetohydrodynamical simulations
Department of Earth and Planetary Sciences, Institute of Science Tokyo（东京科学地球与行星科学系）；Institute for Advanced Study and Department of Astronomy, Tsinghua University（清华大学高等研究院天文学系）
Context. Planet formation with pebbles has been proposed to solve a couple of long-standing issues in the classical formation model. Some sophisticated simulations have been done to confirm the efficiency of pebble accretion. However, there has not been any global N-body simulations that compare the outcomes of planet formation via pebble accretion with observed extrasolar planetary systems. Aims. In this paper, we study the effects of a range of initial parameters of planet formation via pebble accretion, and present the first results of our simulations. Methods. We incorporate the pebble acc…
