Realistic On-the-fly Outcomes of Planetary Collisions II: Bringing Machine Learning to N-body Simulations
Alexandre Emsenhuber, Saverio Cambioni, Erik Asphaug, Travis S. J. Gabriel, Stephen R. Schwartz, Roberto Furfaro
备注：
20 pages, 10 figures, 3 tables; accepted for publication in ApJ; Table 1 is available in full in an ancillary file; the code developed in this work is available at https://github.com/aemsenhuber/collresolve
Terrestrial planet formation theory is at a bottleneck, with the growing realization that pairwise collisions are treated far too simply. Here, and in our companion paper (Cambioni et al. 2019) that introduces the training methodology, we demonstrate the first application of machine learning to more realistically model the late stage of planet formation by giant impacts. We present surrogate models that give fast, reliable answers for the masses and velocities of the two largest remnants of a giant impact, as a function of the colliding masses and their impact velocity and angle, with the caveat that our training data do not yet include pre-impact rotation or variable thermal conditions. We compare canonical N-body scenarios of terrestrial planet formation assuming perfect merger (Chambers 2001) with our more realistic treatment that includes inefficient accretions and hit-and-run collisions. The result is a protracted tail of final events lasting ~200 Myr, and the conversion of about half the mass of the initial population to debris. We obtain profoundly different solar system architectures, featuring a much wider range of terrestrial planet masses and enhanced compositional diversity.
Most stars form as part of a stellar group. These young stars are mostly surrounded by a disk from which potentially a planetary system might form. Both, the disk and later on the planetary system, may be affected by the cluster environment due to close fly-bys. The here presented database can be used to determine the gravitational effect of such fly-bys on non-viscous disks and planetary systems. The database contains data for fly-by scenarios spanning mass ratios between the perturber and host star from 0.3 to 50.0, periastron distances from 30 au to 1000 au, orbital inclination from $0^{\ci…
Stellar flybys in star clusters are suspected to affect the orbital architecture of planetary systems causing eccentricity excitation and orbital misalignment between the planet orbit and the equatorial plane of the star. We explore whether the impulsive changes in the orbital elements of planets, caused by an hyperbolic stellar flyby, can be fully damped by the circumstellar disk surrounding the star. The time required to disperse stellar clusters is in fact comparable to circumstellar disk's lifetime. We have modelled in 3D a system made of a solar type star surrounded by a low density disk …
Most stars form in embedded clusters. Stellar flybys may affect the orbital architecture of the systems by exciting the eccentricity and causing dynamical instability. Since, incidentally, the timescale over which a cluster loses its gaseous component and begins to disperse is comparable to the circumstellar disk lifetime, we expect that closer, and more perturbing, stellar flybys occur when the planets are still embedded in their birth disk. We investigate the effects of the disk on the dynamics of planets after the stellar encounter to test whether it can damp the eccentricity and return the…
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…
Exoplanetary observations reveal that the occurrence rate of hot Jupiters is correlated with star clustering. In star clusters, interactions between planetary systems and close fly-by stars can significantly change the architecture of primordially coplanar, circular planetary systems. Flybys in dense clusters have a significant impact on hot Jupiter formation via activation of high eccentricity excitation mechanisms such as the Zeipel-Lidov-Kozai (ZLK) effect and planet-planet scattering. Previous studies have shown that if there are two giant planets in the planetary system, close flybys can …
Stellar flybys in star clusters may perturb the evolution of young planetary systems in terms of disk truncation, planetary migration and planetary mass accretion. We investigate the feedback of a young planetary system during a single close stellar encounter in a typical open young stellar cluster. We consider 5 masses for the stellar perturbers: 0.5, 0.8, 1, 3 and 8 M$_{Sun}$, in coplanar, prograde and retrograde orbits respect to the planetary disk, varying the pertruber-host star orbital periastron from 100 AU to 500 AU. We have made 3D modelizations with the smooth particle hydrodynamics …
Most of the observed extrasolar planets are found on tight and often eccentric orbits. The high eccentricities are not easily explained by planet-formation models, which predict that planets should be on rather circular orbits. Here we explore whether fly-bys involving planetary systems with properties similar to those of the gas giants in the solar system, can produce planets with properties similar to the observed planets. Using numerical simulations, we show that fly-bys can cause the immediate ejection of planets, and sometimes also lead to the capture of one or more planets by the intrude…
Stars formed in clusters can encounter other stars at close distances. In typical open clusters in the Solar neighbourhood containing hundreds or thousands of member stars, ten to twenty per cent of Solar-mass member stars are expected to encounter another star at distances closer than 100 au. These close encounters strongly perturb the planetary systems, directly causing ejection of planets or their capture by the intruding star, as well as exciting the orbits. Using extensive $N$-body simulations, we study such fly-by encounters between two Solar System analogues, each with four giant planet…
Out of the $\sim$ 3000 exoplanets detected so far, only fourteen planets are members of open clusters: among them an exoplanet system around Pr 0211 in the cluster M44 which consists of at least two planets with the outer planet moving on a highly eccentric orbit at 5.5 AU. One hypothesis is that a close fly-by of a neighbouring star was responsible for the eccentric orbit. We test this hypothesis. First we determine the type of fly-by that would lead to the observed parameters and then use this result to determine the history of such fly-bys in simulations of the early dynamics in an M44-like…
The chance that a planetary system will interact with another member of its host star's nascent cluster would be greatly increased if gas giant planets form in situ on wide orbits. In this paper, we explore the outcomes of planet-planet scattering for a distribution of multiplanet systems that all have one of the planets on an initial orbit of 100 AU. The scattering experiments are run with and without stellar flybys. We convolve the outcomes with distributions for protoplanetary disk and stellar cluster sizes to generalize the results where possible. We find that the frequencies of large mutu…
Several planets have been found that orbit their host star on retrograde orbits (spin-orbit angle ϕ > 90°). Currently, the largest measured projected angle between the orbital angular momentum axis of a planet and the rotation axis of its host star has been found for HAT-P-14b to be $\approx$ 171°. One possible mechanism for the formation of such misalignments is through long-term interactions between the planet and other planetary or stellar companions. However, with this process, it has been found to be difficult to achieve retrogradely orbiting planets, especially planets that almost exactl…
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…
The discovery of high incidence of hot Jupiters in dense clusters challenges the field-based hot Jupiter formation theory. In dense clusters, interactions between planetary systems and flyby stars are relatively common. This has a significant impact on planetary systems, dominating hot Jupiter formation. In this paper, we perform high precision, few-body simulations of stellar flybys and subsequent planet migration in clusters. A large parameter space exploration demonstrates that close flybys that change the architecture of the planetary system can activate high eccentricity migration mechani…
Among the numerous known extrasolar planets, only a handful have been imaged directly so far, at large orbital radii and in rather evolved systems. The Atacama Large Millimeter/submillimeter Array (ALMA) will have the capacity to observe these wide planetary systems at a younger age, thus bringing a better understanding of the planet formation process. Here we explore the ability of ALMA to detect the gaps carved by planets on wide orbits.
The noteworthy four-planet HR 8799 system teeters on the brink of gravitational instability and contains an A-type host star which is characteristic of the progenitors of the majority of known white dwarf planetary system hosts. Gozdziewski and Migaszewski (2020) have demonstrated that the system can retain all four planets for at least 1 Gyr along the main sequence if the planets evolve within an externally unperturbed 8:4:2:1 mean motion resonance configuration. Here we propagate forward their most stable fit beyond the main sequence, and incorporate external effects from Galactic tides and …
We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Ma, using populations from previous studies as initial conditions.We show that within the populations studied, mass and semi-major axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increas…
The discovery of Exoplanetary Systems has challenged some of the theories of planet formation, which assume unperturbed evolution of the host star and its planets. However, in star clusters the interactions with flyby stars and binaries may be relatively common during the lifetime of a planetary system. Here, via high-resolution $N$-body simulations of star-planet systems perturbed by interlopers (stars and binaries), we explore the reconfiguration to the planetary system due to the encounters. In particular, via an exploration focused on the strong scattering regime, we derive the fraction of…
Mixed-variable symplectic integrators are widely used in orbital dynamics. However, they have been developed for Solar system-type architectures, and can not handle evolving hierarchy, in particular in systems with two or more stellar components. Such configuration may have occurred in the history of HD 106906, a tight pair of F-type stars surrounded by a debris disk and a planetary-mass companion on a wide orbit. We present the new algorithm ODEA, based on the symplectic algorithm SWIFT HJS, that can model any system (binary,...) with unstable architecture. We study the peculiar system HD 106…
Flyby-induced high-eccentricity migration and the prevalence of hot Jupiters in M67
Institute of Astronomy, University of Cambridge（剑桥大学天文研究所）；Astronomy Unit, Department of Physics and Astronomy, Queen Mary University of London（伦敦大学玛丽女王学院物理与天文学系天体物理组）
Wide-orbit exoplanets are starting to be detected, and planetary formation models are under development to understand their properties. We propose a population of "Oort" planets around other stars, forming by a mechanism analogous to how the Solar System's Oort cloud of comets was populated. Gravitational scattering among planets is inferred from the eccentricity distribution of gas-giant exoplanets measured by the Doppler technique. This scattering is thought to commence while the protoplanetary disk is dissipating, $10^6-10^7$ yr after formation of the star, or perhaps soon thereafter, when …
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…
The Kepler mission discovered 2842 exoplanet candidates with 2 years of data. We provide updates to the Kepler planet candidate sample based upon 3 years (Q1-Q12) of data. Through a series of tests to exclude false-positives, primarily caused by eclipsing binary stars and instrumental systematics, 855 additional planetary candidates have been discovered, bringing the total number known to 3697. We provide revised transit parameters and accompanying posterior distributions based on a Markov Chain Monte Carlo algorithm for the cumulative catalogue of Kepler Objects of Interest. There are now 130…
(abridged) A complete census of planetary systems around a volume-limited sample of solar-type stars (FGK dwarfs) in the Solar neighborhood with uniform sensitivity down to Earth-mass planets within their Habitable Zones out to several AUs would be a major milestone in extrasolar planets astrophysics. This fundamental goal can be achieved with a mission concept such as NEAT - the Nearby Earth Astrometric Telescope. NEAT is designed to carry out space-borne extremely-high-precision astrometric measurements sufficient to detect dynamical effects due to orbiting planets of mass even lower than Ea…
The Saturnian Kilometric Radiation (SKR) is radiated from the auroral regions surrounding the kronian magnetic poles, above the ionosphere up to a few planetary radii. It directly compares to the auroral radio emissions emanating from other planetary magnetospheres such as the Earth and the giant planets. Our knowledge on SKR relied on remote observations of Voyager (flybys in 1980 and 1981) and Ulysses (distant observations in the 1990s) until Cassini started to orbit Saturn in 2004. Since then, it has been routinely observed from a large set of remote locations, but also in situ for the firs…
Time is arguably the key limiting factor for interstellar exploration. At high speeds, flyby missions to nearby stars by laser propelled wafersats taking 50-100 years would be feasible. Directed energy launch systems could accelerate on the other side also crafts weighing several tons to cruising speeds of the order of 1000\,km/s (c/300). At these speeds, superconducting magnetic sails would be able to decelerate the craft by transferring kinetic energy to the protons of the interstellar medium. A tantalizing perspective, which would allow interstellar probes to stop whenever time is not a lim…
Environmental interactions in Class II systems and their impact on the disk-planet architecture
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；IPAG（格勒诺布尔行星与天体物理实验室）；University of Warwick（华威大学）；Tsinghua University（清华大学）；Monash University（莫纳什大学）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯玻尔研究所）
The discovery of planetary systems outside of the solar system has challenged some of the tenets of planetary formation. Among the difficult-to-explain observations, are systems with a giant planet orbiting a very-low mass star, such as the recently discovered GJ~3512b planetary system, where a Jupiter-like planet orbits an $M$-star in a tight and eccentric orbit. Systems such as this one are not predicted by the core accretion theory of planet formation. Here we suggest a novel mechanism, in which the giant planet is born around a more typical Sun-like star ($M_{*,1}$), but is subsequently ex…
Convergent disk migration has long been suspected to be responsible for forming planetary systems with a chain of mean-motion resonances (MMR). Dynamical evolution over time could disrupt the delicate resonant configuration. We present TOI-1136, a 700-Myr-old G star hosting at least 6 transiting planets between $\sim$2 and 5 $R_\oplus$. The orbital period ratios deviate from exact commensurability by only $10^{-4}$, smaller than the $\sim$\,$10^{-2}$ deviations seen in typical Kepler near-resonant systems. A transit-timing analysis measured the masses of the planets (3-8$M_\oplus$) and demonst…
We report the results of the statistical analysis of planetary signals discovered in MOA-II microlensing survey alert system events from 2007 to 2012. We determine the survey sensitivity as a function of planet-star mass ratio, $q$, and projected planet-star separation, $s$, in Einstein radius units. We find that the mass ratio function is not a single power-law, but has a change in slope at $q \sim 10^{-4}$, corresponding to $\sim 20 M_{\oplus}$ for the median host star mass of $\sim 0.6 M_{\odot}$. We find significant planetary signals in 23 of the 1474 alert events that are well characteriz…
New transiting planet candidates are identified in sixteen months (May 2009 - September 2010) of data from the Kepler spacecraft. Nearly five thousand periodic transit-like signals are vetted against astrophysical and instrumental false positives yielding 1,091 viable new planet candidates, bringing the total count up to over 2,300. Improved vetting metrics are employed, contributing to higher catalog reliability. Most notable is the noise-weighted robust averaging of multi-quarter photo-center offsets derived from difference image analysis which identifies likely background eclipsing binaries…
Escalating observations of exo-minor planets and their destroyed remnants both passing through the solar system and within white dwarf planetary systems motivate an understanding of the orbital history and fate of exo-Kuiper belts and planetesimal discs. Here we explore how the structure of a 40-1000 au annulus of planetesimals orbiting inside of a solar system analogue that is itself initially embedded within a stellar cluster environment varies as the star evolves through all of its stellar phases. We attempt this computationally challenging link in four parts: (1) by performing stellar clus…
