Planetary-scale collisions are common during the last stages of formation of solid planets, including the Solar system terrestrial planets. The problem of growing planets has been divided into studying the gravitational interaction of embryos relevant in million year timescales and treated with N-body codes and the collision between objects with a timescale of hours to days and treated with smoothed-particle hydrodynamics. These are now being coupled with simple parameterized models. We set out to investigate if machine learning techniques can offer a better solution by predicting the outcome of collisions which can then be used in N-body simulations. We considered three different supervised machine learning approaches: gradient boosting regression trees, nested models, and gaussian processes. We found that the former produced the best results, and that it was slightly surpassed by ensembling different algorithms. With gaussian processes, we found the regions of parameter space that may yield the most information to machine learning algorithms. Thus, we suggest SPH calculations to focus first on mass ratios above 0.5.
Massive planetary cores ($\sim 10$ Earth masses) trigger rapid gas accretion to form gas giant planets \rev{such as} Jupiter and Saturn. We investigate the core growth and the possibilities for cores to reach such a critical core mass. At the late stage, planetary cores grow through collisions with small planetesimals. Collisional fragmentation of planetesimals, which is induced by gravitational interaction with planetary cores, reduces the amount of planetesimals surrounding them, and thus the final core masses. Starting from small planetesimals that the fragmentation rapidly removes, less ma…
Planet formation simulations are capable of directly integrating the evolution of hundreds to thousands of planetary embryos and planetesimals, as they accrete pairwise to become planets. In principle such investigations allow us to better understand the final configuration and geochemistry of the terrestrial planets, as well as to place our solar system in the context of other exosolar systems. These simulations, however, classically prescribe collisions to result in perfect mergers, but computational advances have begun to allow for more complex outcomes to be implemented. Here we apply mach…
We investigate the distribution of encounter velocities and impact angles describing collisions in the habitable zone of the early planetary system. Here we present a catalogue of collision characteristics for a particular mass ratio of the colliding bodies and seven different planetesimal masses ranging from a tenth of Ceres' mass to 10 times the mass of the Moon. We show that there are virtually no collisions with impact speeds lower than the surface escape velocity and a similar velocity-impact angle distribution for different planetesimal masses if velocities are normalized using the escap…
It is observed that hypervelocity space dust, which is continuously bombarding the Earth, creates immense momentum flows in the atmosphere. Some of this fast space dust inevitably will interact with the atmospheric system, transferring energy and moving particles around, with various possible consequences. This paper examines, with supporting estimates, the possibility that through collisions, the Earth-grazing component of space dust can facilitate planetary escape of atmospheric particles, whether they be the atoms and molecules forming the atmosphere or bigger sized particles. As one intere…
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 present a mathematical model for the propagation of the shock waves that occur during planetary collisions. Such collisions are thought to occur during the formation of terrestrial planets, and they have the potential to erode the planet's atmosphere. We show that under certain assumptions, this evolution of the shock wave can be determined using the method of self similar solutions. This self similar solution is of type II, which means that it only applies to a finite region behind the shock front. This region is bounded by the shock front and the sonic point. Energy and matter continuousl…
Planet-planet collisions are a common outcome of instability in systems of transiting planets close to the star, as well as occurring during in-situ formation of such planets from embryos. Previous N-body studies of instability amongst transiting planets have assumed that collisions result in perfect merging. Here, we explore the effects of implementing a more realistic collision prescription on the outcomes of instability and in-situ formation at orbital radii of a few tenths of an au. There is a strong effect on the outcome of the growth of planetary embryos, so long as the debris thrown off…
This paper considers the dynamics of scattering of planetesimals or planetary embryos by a planet on a circumstellar orbit. We classify six regions in the planet's mass versus semimajor axis parameter space according to the dominant outcome for scattered objects: ejected, accreted, remaining, escaping, Oort Cloud, depleted Oort Cloud. We use these outcomes to consider which planetary system architectures maximise the observability of specific signatures, given that signatures should be detected first around systems with optimal architectures (if such systems exist in nature). Giant impact debr…
Gas-giant planets, such as Jupiter, Saturn and massive exoplanets, were formed via the gas accretion onto the solid cores each with a mass of roughly ten Earth masses. However, rapid radial migration due to disk-planet interaction prevents the formation of such massive cores via planetesimal accretion. Comparably rapid core growth via pebble accretion requires very massive protoplanetary disks because most pebbles fall into the central star. Although planetesimal formation, planetary migration, and gas-giant core formation have been studied with much effort, the full evolution path from dust t…
The main asteroid belt (MB) is low in mass but dynamically excited. Here we propose a new mechanism to excite the MB during the giant planet ('Nice model') instability, which is expected to have featured repeated close encounters between Jupiter and one or more ice giants ('Jumping Jupiter' -- JJ). We show that, when Jupiter temporarily reaches a high enough level of excitation, both in eccentricity and inclination it induces strong forced vectors of eccentricity and inclination across the MB region. Because during the JJ instability Jupiter's orbit `jumps' around, the forced vectors keep chan…
The large number of exoplanets found to orbit their host stars in very close orbits have significantly advanced our understanding of the planetary formation process. It is now widely accepted that such short-period planets cannot have formed {\em in situ}, but rather must have migrated to their current orbits from a formation location much farther from their host star. In the late stages of planetary formation, once the gas in the proto-planetary disk has dissipated and migration has halted, gas-giants orbiting in the inner disk regions will excite planetesimals and planetary embryos, resultin…
Collisions are the core agent of planet formation. In this work, we derive an analytic description of the dynamical outcome for any collision between gravity-dominated bodies. We conduct high-resolution simulations of collisions between planetesimals; the results are used to isolate the effects of different impact parameters on collision outcome. During growth from planetesimals to planets, collision outcomes span multiple regimes: cratering, merging, disruption, super-catastrophic disruption, and hit-and-run events. We derive equations (scaling laws) to demarcate the transition between collis…
Reproducing Uranus and Neptune remains a challenge for simulations of solar system formation. The ice giants' peculiar obliquities suggest that they both suffered giant collisions during their formation. Thus, there must have been an epoch of accretion dominated by collisions among large planetary embryos in the primordial outer solar system. We test this idea using N-body numerical simulations including the effects of a gaseous protoplanetary disk. One strong constraint is that the masses of the ice giants are very similar -- the Neptune/Uranus mass ratio is $\sim1.18$. We show that similar-s…
Models and observations suggest that ice-particle aggregation at and beyond the snowline dominates the earliest stages of planet-formation, which therefore is subject to many laboratory studies. However, the pressure-temperature gradients in proto-planetary disks mean that the ices are constantly processed, undergoing phase changes between different solid phases and the gas phase. Open questions remain as to whether the properties of the icy particles themselves dictate collision outcomes and therefore how effectively collision experiments reproduce conditions in pro- toplanetary environments.…
In planetary systems with sufficiently small inter-planet spacing, close encounters can lead to planetary collisions/mergers or ejections. We study the spin property of the merger products of two giant planets in a statistical manner using numerical simulations and analytical modeling. Planetary collisions lead to rapidly rotating objects and a broad range of obliquities. We find that, under typical conditions for two-planet scatterings, the distributions of spin magnitude $S$ and obliquity $Θ_{\rm SL}$ of the merger products have simple analytical forms: $f_{S} \propto S$ and $f_{\cosΘ_{\rm S…
In order to study the origin of the architectures of low mass planetary systems, we perform numerical surveys of the evolution of pairs of coplanar planets in the mass range $(1-4)\ \rmn{M}_{\oplus}.$ These evolve for up to $2\times10^7 \rmn{yr}$ under a range of orbital migration torques and circularization rates assumed to arise through interaction with a protoplanetary disc. Near the inner disc boundary, significant variations of viscosity, interaction with density waves or with the stellar magnetic field could occur and halt migration, but allow ircularization to continue. This was modelle…
Giant impacts refer to collisions between two objects each of which is massive enough to be considered at least a planetary embryo. The putative collision suffered by the proto-Earth that created the Moon is a prime example, though most Solar System bodies bear signatures of such collisions. Current planet formation models predict that an epoch of giant impacts may be inevitable, and observations of debris around other stars are providing mounting evidence that giant impacts feature in the evolution of many planetary systems. This chapter reviews giant impacts, focussing on what we can learn a…
We investigate how the choice of equation of state (EOS) and resolution conspire to affect the outcomes of giant impact (GI) simulations. We focus on the simple case of equal mass collisions of two Earth-like $0.5\,M_\oplus$ proto-planets showing that the choice of EOS has a profound impact on the outcome of such collisions as well as on the numerical convergence with resolution. In simulations where the Tillotson EOS is used, impacts generate an excess amount of vapour due to the lack of a thermodynamically consistent treatment of phase transitions and mixtures. In oblique collisions this enh…
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…
We consider the observational signatures of giant impacts between planetary embryos. While the debris released in the impact remains in a clump for only a single orbit, there is a much longer lasting asymmetry caused by the fact that all debris must pass through the collision-point. The resulting asymmetry is stationary, it does not orbit the star. The debris is concentrated in a clump at the collision-point, with a more diffuse structure on the opposite side. The asymmetry lasts for typically around 1000 orbital periods of the progenitor, which can be several Myr at distances of ~50 AU. We de…
Planetary systems with more than two bodies will experience orbital crossings at a time related to the initial orbital separations of the planets. After a crossing, the system enters a period of chaotic evolution ending in the reshaping of the system's architecture via planetary collisions or ejections. We carry out N-body integrations on a large number of systems with equally-spaced planets (in units of the Hill radius) to determine the distribution of instability times for a given planet separation. We investigate both the time to the initiation of instability through a close encounter and t…
Modeling the formation of the ice giants Uranus and Neptune is a long-lasting problem in planetary science. Due to gas-drag, collisional damping, and resonant shepherding, the planetary embryos repel the planetesimals away from their reach and thus they stop growing (Levison et al. 2010). This problem persists independently of whether the accretion took place at the current locations of the ice giants or closer to the Sun. Instead of trying to push the runaway/oligarchic growth of planetary embryos up to 10-15 Earth masses, we envision the possibility that the planetesimal disk could generate …
Rapid Formation of Gas-giant Planets via Collisional Coagulation from Dust Grains to Planetary Cores. II. Dependence on Pebble Bulk Density and Disk Temperature
Luminous debris disks of warm dust in the terrestrial planet zones around solar-like stars are recently found to vary, indicative of ongoing large-scale collisions of rocky objects. We use Spitzer 3.6 and 4.5 μm time-series observations in 2012 and 2013 (extended to 2014 in one case) to monitor 5 more debris disks with unusually high fractional luminosities ("extreme debris disk"), including P1121 in the open cluster M47 (80 Myr), HD 15407A in the AB Dor moving group (80 Myr), HD 23514 in the Pleiades (120 Myr), HD 145263 in the Upper Sco Association (10 Myr), and the field star BD+20 307 (>1 …
High-multiplicity Kepler systems (referred to as Kepler multis) are often tightly packed and may be on the verge of instability. Many systems of this type could have experienced past instabilities, where the compact orbits and often low densities make physical collisions likely outcomes. We use numerical simulations to study the dynamical instabilities and planet-planet interactions in a synthetically generated sample of closely-packed, high-multiplicity systems. We focus specifically on systems resembling Kepler-11, a Kepler multi with six planets, and run a suite of dynamical integrations, s…
We show that the existence of prograde equatorial satellites is consistent with a collisional tilting scenario for Uranus. In fact, if the planet was surrounded by a proto-satellite disk at the time of the tilting and a massive ring of material was temporarily placed inside the Roche radius of the planet by the collision, the proto-satellite disk would have started to precess incoherently around the equator of the planet, up to a distance greater than that of Oberon. Collisional damping would then have collapsed it into a thin equatorial disk, from which the satellites eventually formed. The f…
The origin of Uranus and Neptune remains a challenge for planet formation models. A potential explanation is that the planets formed from a population of a few planetary embryos with masses of a few Earth masses which formed beyond Saturn's orbit and migrated inwards. These embryos can collide and merge to form Uranus and Neptune. In this work we revisit this formation scenario and study the outcomes of such collisions using 3D hydrodynamical simulations. We investigate under what conditions the perfect-merging assumption is appropriate, and infer the planets' final masses, obliquities and rot…
Pairwise collisions between terrestrial embryos are the dominant means of accretion during the last stage of planet formation. Hence, their realistic treatment in N-body studies is critical to accurately model the formation of terrestrial planets and to develop interpretations of telescopic and spacecraft observations. In this work, we compare the effects of two collision prescriptions on the core-mantle differentiation of terrestrial planets: a model in which collisions are always completely accretionary (``perfect merging'') and a more realistic model based on neural networks that has been t…
Collisions between large, similar-sized bodies are believed to shape the final characteristics and composition of terrestrial planets. Their inventories of volatiles such as water, are either delivered or at least significantly modified by such events. Besides the transition from accretion to erosion with increasing impact velocity, similar-sized collisions can also result in hit-and-run outcomes for sufficiently oblique impact angles and large enough projectile-to-target mass ratios. We study volatile transfer and loss focusing on hit-and-run encounters by means of Smooth Particle Hydrodynami…
I examine the standard model of planet formation, including pebble accretion, using numerical simulations. Planetary embryos large enough to become giant planets do not form beyond the ice line within a typical disk lifetime unless icy pebbles stick at higher speeds than in experiments using rocky pebbles. Systems like the Solar System (small inner planets, giant outer planets) can form if (i) icy pebbles are stickier than rocky pebbles, and (ii) the planetesimal formation efficiency increases with pebble size, which prevents the formation of massive terrestrial planets. Growth beyond the ice …
The Earth's comparatively massive moon, formed via a giant impact on the proto-Earth, has played an important role in the development of life on our planet, both in the history and strength of the ocean tides and in stabilizing the chaotic spin of our planet. Here we show that massive moons orbiting terrestrial planets are not rare. A large set of simulations by Morishima et al., 2010, where Earth-like planets in the habitable zone form, provides the raw simulation data for our study. We use limits on the collision parameters that may guarantee the formation of a circumplanetary disk after a p…
Eberhard Karls Universität Tübingen（埃伯哈德·卡尔斯·图宾根大学（图宾根大学））；Johannes Kepler University Linz（林茨约翰内斯·开普勒大学）；SDB Science-driven Business Ltd（SDB科学驱动商业有限公司）；University of Vienna（维也纳大学）
Fast and accurate treatment of collisions in the context of modern N-body planet formation simulations remains a challenging task due to inherently complex collision processes. We aim to tackle this problem with machine learning (ML), in particular via residual neural networks. Our model is motivated by the underlying physical processes of the data-generating process and allows for flexible prediction of post-collision states. We demonstrate that our model outperforms commonly used collision handling methods such as perfect inelastic merging and feed-forward neural networks in both prediction …
In (pre)-planetary environments, dust and sand grains regularly collide. They electrically charge and discharge during these events. In this work, we study if cosmic radiation has any influence on the equilibrium charge state on timescales of minutes. We developed an experiment that was carried out during the ascent of a stratospheric balloon. With increasing altitude, the radiation activity increases by a factor of 54. However, we found only a very minor decrease in grain charges of up to 30%. This implies that charge-moderated processes from thunderstorms on Earth, over early phases of plane…
Comets and small planetesimals are believed to contain primordial building blocks in the form of millimeter to centimeter sized pebbles. One of the viable growing mechanisms to form these small bodies is through the streaming instability (SI) in which pebbles cluster and gravitationally collapse towards a planetesimal or comet in the presence of gas drag. However, most SI simulations are global and lack the resolution to follow the final collapse stage of a pebble cloud within its Hill radius. We aim to track the collapse of a gravitationally bound pebble cloud subject to mutual collisions and…
Long-Term Evolution of Close-in Sub-Neptunes and Outer Planetary Embryos: Atmospheric Mass Loss and Origin of Planets Inside and Outside the Radius Gap
Shanghai Jiao Tong University（上海交通大学）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大李政道研究所）
Numerical simulations of the stochastic end stage of planet formation typically begin with a population of embryos and planetesimals that grow into planets by merging. We analyzed the impact parameters of collisions leading to the growth of terrestrial planets from recent $N$-body simulations that assumed perfect merging and calculated more realistic outcomes using a new analytic collision physics model. We find that collision outcomes are diverse and span all possible regimes: hit-and-run, merging, partial accretion, partial erosion, and catastrophic disruption. The primary outcomes of giant …
Planetary systems with sufficiently small orbital spacings can experience planetary mergers and ejections. The branching ratio of mergers vs ejections depends sensitively on the treatment of planetary close encounters. Previous works have adopted a simple "sticky-sphere" prescription, whose validity is questionable. We apply both smoothed particle hydrodynamics and $N$-body integrations to investigate the fluid effects in close encounters between gas giants and the long-term evolution of closely-packed planetary systems. Focusing on parabolic encounters between Jupiter-like planets with $M_J$ …
A diversity of resonance configurations may be formed under different migration of two giant planets. And the researchers show that the HD 128311 and HD 73526 planetary systems are involved in a 2:1 mean motion resonance but not in apsidal corotation, because one of the resonance argument circulates over the dynamical evolution. In this paper, we investigate potential mechanisms to form the 2:1 librating-circulating resonance configuration. In the late stage of planetary formation, scattering or colliding among planetesimals and planetary embryos can frequently occur. Hence, in our model, we c…
Chondrules are one of the most primitive elements that can serve as a fundamental clue as to the origin of our Solar system. We investigate a formation scenario of chondrules that involves planetesimal collisions and the resultant impact jetting. Planetesimal collisions are the main agent to regulate planetary accretion that corresponds to the formation of terrestrial planets and cores of gas giants. The key component of this scenario is that ejected materials can melt when the impact velocity between colliding planetesimals exceeds about 2.5 km s$^{-1}$. The previous simulations show that the…
Planets grow via the collisional accretion of small bodies in a protoplanetary disk. Such small bodies feel strong gas drag and their orbits are significantly affected by the gas flow and atmospheric structure around the planet. We investigate the gas flow in the protoplanetary disk perturbed by the gravity of the planet by three-dimensional hydrodynamic simulation. We then calculate the orbital evolutions of particles in the gas structure obtained from the hydrodynamic simulation. Based on the orbital calculations, we obtain the collision rate between the planet and centimeter to kilometer si…
During the planetary formation process, mutual collisions among planetesimals take place, making an impact on their porosity evolution. The outcome of these collisions depends, among other parameters, on the tensile strength of the colliding objects. In the first stage of this work, we performed impact experiments into dust samples, assembled with material analogous to that of the primitive Solar System, to obtain highly compressed samples that represent the porosities measured in chondritic meteorites. In the second stage, we obtained the tensile strengths of the compressed dust samples by th…
We investigate the outcome of collisions of Ceres-sized planetesimals composed of a rocky core and a shell of water ice. These collisions are not only relevant for explaining the formation of planetary embryos in early planetary systems, but also provide insight into the formation of asteroid families and possible water transport via colliding small bodies. Earlier studies show characteristic collision velocities exceeding the bodies' mutual escape velocity which - along with the distribution of the impact angles - cover the collision outcome regimes 'partial accretion', 'erosion', and 'hit-an…
Characterizing the bulk atmosphere of a terrestrial planet is important for determining surface pressure and potential habitability. Molecular nitrogen (N$_2$) constitutes the largest fraction of Earth$'$s atmosphere and is likely to be a major constituent of many terrestrial exoplanet atmospheres. Due to its lack of significant absorption features, N$_2$ is extremely difficult to remotely detect. However, N$_2$ produces an N$_2$-N$_2$ collisional pair, (N$_2$)$_2$, which is spectrally active. Here we report the detection of (N$_2$)$_2$ in Earth$'$s disk-integrated spectrum. By comparing spect…
In this paper, we present results from a multi-stage numerical campaign to begin to explain and determine why extreme debris disk detections are rare, what types of impacts will result in extreme debris disks and what we can learn about the parameters of the collision from the extreme debris disks. We begin by simulating many giant impacts using a smoothed particle hydrodynamical code with tabulated equations of state and track the escaping vapour from the collision. Using an $N$-body code, we simulate the spatial evolution of the vapour generated dust post-impact. We show that impacts release…
Studies of high-multiplicity, tightly-packed planetary systems suggest that dynamical instabilities are common and affect both the orbits and planet structures, where the compact orbits and typically low densities make physical collisions likely outcomes. Since the structure of many of these planets is such that the mass is dominated by a rocky core, but the volume is dominated by a tenuous gas envelope, the sticky-sphere approximation, used in dynamical integrators, may be a poor model for these collisions. We perform five sets of collision calculations, including detailed hydrodynamics, samp…
We explore scenarios for the origin of two different density planets in the Kepler 36 system in adjacent orbits near the 7:6 mean motion resonance. We find that fine tuning is required in the stochastic forcing amplitude, the migration rate and planet eccentricities to allow two convergently migrating planets to bypass mean motion resonances such as the 4:3, 5:4 and 6:5, and yet allow capture into the 7:6 resonance. Stochastic forcing can eject the system from resonance causing a collision between the planets, unless the disk inducing migration and stochastic forcing is depleted soon after res…
The formation of satellites is thought to be a natural by-product of planet formation in our Solar System, and thus, moons of extrasolar planets (exomoons) may be abundant in extrasolar planetary systems, as well. Exomoons have yet to be discovered. However, moons larger than 0.1 Earth masses can be detected and characterized using current transit techniques. Here, we show that collisions between rocky planets with masses between a quarter to ten Earth masses can create impact-generated debris disks that could accrete into moons. Collisions between like-sized objects, at oblique impact angles,…
Wind erosion is a destructive mechanism that completely dissolves a weakly bound object like a planetesimal into its constituent particles, if the velocity relative to the ambient gas and the local gas pressure are sufficiently high. In numerical simulations we study the influence of such wind erosion on pebble and planetesimal accretion by a planetary body up to $10 R_\mathrm{Earth}$. Due to the rapid size reduction of an in-falling small body, the accretion outcome changes significantly. Erosion leads to a strong decrease in the accretion efficiency below a threshold size of the small body o…
The hundreds of exoplanets that have been discovered in the past two decades offer a new perspective on planetary structure. Instead of being the archetypal examples of planets, those of our Solar System are merely possible outcomes of planetary system formation and evolution, and conceivably not even terribly common outcomes (although this remains an open question). Here, we review the diverse range of interior structures that are known to, and speculated to, exist in exoplanetary systems -- from mostly degenerate objects that are more than 10 times as massive as Jupiter, to intermediate-mass…
We analyze the formation and evolution of terrestrial-like planets around solar-type stars in the absence of gaseous giants. In particular, we focus on the physical and dynamical properties of those that survive in the system's Habitable Zone (HZ). This study is based on a comparative study between N-body simulations that include fragmentation and others that consider all collisions as perfect mergers. We use an N-body code, presented in a previous paper, that allows planetary fragmentation. We carry out three sets of 24 simulations for 400 Myr. Two sets are developed adopting a model that inc…
