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 close-in small planets' orbits may be tilted together through Kozai--Lidov mechanism, forming a ``cold'' system that is significantly inclined against the equator of the central host. Moving to the intermediately-placed planets around solar-like stars, we find that the planets' mass gradient governs the systems' long-term evolution post-encounter: more massive planets have better chances to survive. Also, a system's angular momentum deficit, a quantity describing how eccentric/inclined the orbits are, measured immediately after the encounter, closely relates to the longevity of the systems -- whether or not and when the systems turn unstable in the ensuing evolution millions of years post-encounter. We compare the orbits of the surviving planets in the unstable systems through (1) the immediate consequence of the stellar fly or (2) internal interplanetary scattering long post-encounter and find that those for the former are systematically colder. Finally, we show that massive wide-orbit multi-planet systems like that of HR 8799 can be easily disrupted and encounters at a few hundreds of au suffice.
We review the role of stellar flybys and encounters in shaping planet-forming discs around young stars, based on the published literature on this topic in the last 30 years. Since most stars $\leq~2$ Myr old harbour protoplanetary discs, tidal perturbations affect planet formation. First, we examine the probability of experiencing flybys or encounters: More than 50\% of stars with planet-forming discs in a typical star forming environment should experience a close stellar encounter or flyby within 1000 au. Second, we detail the dynamical effects of flybys on planet-forming discs. Prograde, par…
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…
The architecture and evolution of planetary systems are shaped in part by stellar flybys. Within this context, we look at stellar encounters which are too weak to immediately destabilize a planetary system but are nevertheless strong enough to measurably perturb the system's dynamical state. We estimate the strength of such perturbations on secularly evolving systems using a simple analytic model and confirm those estimates with direct N-body simulations. We then run long-term integrations and show that even small perturbations from stellar flybys can influence the stability of planetary syste…
Our improving understanding of the life cycle of planetary systems prompts investigations of the role of the Galactic environment before, during and after Asymptotic Giant Branch (AGB) stellar evolution. Here, we investigate the interplay between stellar mass loss, Galactic tidal perturbations, and stellar flybys for evolving stars which host one planet, smaller body or stellar binary companion and reside in the Milky Way's bulge or disc. We find that the potential evolutionary pathways from a main sequence (MS) to a white dwarf (WD) planetary system are a strong function of Galactocentric dis…
Due to the high stellar densities in young clusters, planetary systems formed in these environments are likely to have experienced perturbations from encounters with other stars. We carry out direct $N$-body simulations of multi-planet systems in star clusters to study the combined effects of stellar encounters and internal planetary dynamics. These planetary systems eventually become part of the Galactic field population the parental cluster dissolves, which is where most presently-known exoplanets are observed. We show that perturbations induced by stellar encounters lead to distinct signatu…
During the evolution of proto-planetary disc, photo-evaporations of both central and external stars play important roles. Considering the complicated radiation surroundings in the clusters, where the star formed, the proto-planetary discs survive in different lifetimes due to flyby events. In this paper, we mainly focus on the disc around a T Tauri star, which encounters with another main-sequence star with different temperatures in hyperbolic orbits with different peri-center distances, eccentricities and inclinations. We find the criterion for gap-opening due to photo-evaporation of central …
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…
We aim to observationally and statistically constrain the influence of flybys in the formation and evolution of debris disks. We compiled a sample of 254 debris disks with ages between 2 Myr and 8 Gyr that are either part of an association or isolated, drawing the binary and planetary companions of the systems mainly from the literature. Using the Gaia eDR3 astrometric data and radial velocities of our sample, as well as all the sources in a specific region of the sky, we reconstructed the relative linear motions in the last 5 Myr and made predictions for the next 2 Myr. Relating the Hill radi…
Tidal encounters in star clusters perturb discs around young protostars. In Cuello et al. (2019a, Paper I) we detailed the dynamical signatures of a stellar flyby in both gas and dust. Flybys produce warped discs, spirals with evolving pitch angles, increasing accretion rates, and disc truncation. Here we present the corresponding observational signatures of these features in optical/near-infrared scattered light and (sub-) millimeter continuum and CO line emission. Using representative prograde and retrograde encounters for direct comparison, we post-process hydrodynamical simulations with ra…
Capture of interstellar objects during stellar encounters
Laboratoire d’Astrophysique de Bordeaux, CNRS and Université de Bordeaux（波尔多天体物理学实验室，法国国家科学研究中心和波尔多大学）；Planetary Science Institute（行星科学研究所）；Te Kura Matū, University of Canterbury（坎特伯雷大学数学学院）
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…
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…
Most stars form in clusters where relatively close encounters with other stars are common and can leave imprints on the orbital architecture of planetary systems. In this paper, we investigate the inclination excitation of debris disk particles due to such stellar encounters. We derive an analytical expression that describes inclination excitation in the hierarchical limit where the stellar flyby is distant. We then obtain numerical results for the corresponding particle inclination distribution in the non-hierarchical regime using a large ensemble of N-body simulations. For encounters with ex…
RW Aurigae (RW Aur) is a binary star system with a long molecular arm trailing the primary star. Cabrit et al. (2006) noted the resemblance between this extended structure and the tidal arm stripped from the primary star in the simulations of star-disc encounters by Clarke & Pringle (1993). In this paper we use new hydrodynamical models and synthetic observations to fit many of the parameters of RW Aur. Using hydrodynamic models we find that the morphological appearance of RW Aur can be indeed explained by a tidal encounter with the secondary star. We reproduce all the major morphological and …
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…
Aims: We aim to investigate the consequences of a fast massive stellar remnant - a black hole (BH) or a neutron star (NS) - encountering a planetary system. Methods: We modelled a close encounter between the actual Solar System (SS) and a $2\,M_\odot$ NS and a $10\,M_\odot$ BH, using a few-body symplectic integrator. We used a range of impact parameters, orbital phases at the start of the simulation derived from the current SS orbital parameters, encounter velocities, and incidence angles relative to the plane of the SS. Results: We give the distribution of possible outcomes, such as when the …
Warps survive beyond fly-by encounters in protoplanetary disks. RW Aur A as a case study
Università degli Studi di Milano（米兰大学）；Heidelberg University（海德堡大学）；Universidad de Santiago de Chile（智利圣地亚哥大学）；Millennium Nucleus on Young Exoplanets and their Moons (YEMS)（年轻系外行星及其卫星千年核）；Center for Interdisciplinary Research in Astrophysics Space Exploration (CIRAS)（天体物理学空间探索跨学科研究中心）
We extend the formalism of a previous paper to include the effects of flybys and instantaneous perturbations such as supernovae on the long-term secular evolution of hierarchical multiple systems with an arbitrary number of bodies and hierarchy, provided that the system is composed of nested binary orbits. To model secular encounters, we expand the Hamiltonian in terms of the ratio of the separation of the perturber with respect to the barycentre of the multiple system, to the separation of the widest orbit. Subsequently, we integrate over the perturber orbit numerically or analytically. We ve…
Most stars form in a clustered environment. Both single and binary stars will sometimes encounter planetary systems in such crowded environments. Encounter rates for binaries may be larger than for single stars, even for binary fractions as low as 10-20 per cent. In this work, we investigate scatterings between a Sun-Jupiter pair and both binary and single stars as in young clusters. We first perform a set of simulations of encounters involving wide ranges of binaries and single stars, finding that wider binaries have larger cross sections for the planet's ejection. Secondly, we consider such …
Planetary systems appear to form contemporaneously around young stars within young star-forming regions. Within these environments, the chances of survival, as well as the long-term evolution of these systems, are influenced by factors such as dynamical interactions with other stars and photoevaporation from massive stars. These interactions can also cause young stars to be ejected from their birth regions and become runaways. We present examples of such runaway stars in the vicinity of the Orion Nebula Cluster (ONC) found in Gaia DR2 data that have retained their discs during the ejection pro…
A recent study suggests that the observed multiplicity of super-Earth (SE) systems is correlated with stellar overdensities: field stars in high phase-space density environments have an excess of single-planet systems compared to stars in low density fields. This correlation is puzzling as stellar clustering is expected to influence mostly the outer part of planetary systems. Here we examine the possibility that stellar flybys indirectly excite the mutual inclinations of initially coplanar SEs, breaking their co-transiting geometry. We propose that flybys excite the inclinations of exterior su…
We present a methodology to interpret observations of protoplanetary discs where a flyby, also called a tidal encounter, is suspected. In case of a flyby, protoplanetary discs can be significantly disturbed. The resulting dynamical and kinematical signatures can last for several thousands of years after the flyby and hence deeply affect the evolution of the disc. These effects are stronger for closer encounters and more massive perturbers. For the very same flyby parameters, varying the inclination of the perturber's orbit produces a broad range of disc structures: spirals, bridges, warps and …
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…
We numerically investigate how an asteroid's elongation controls the sensitivity of its surface to tidal effects during a distant planetary encounter beyond the Roche limit. We analyze the surface slope and its variation by considering the shape elongation, as well as the spin period and orbital conditions. A more elongated asteroid tends to have a higher slope variation, while there may not be a monotonic increase of the total area having such a variation
We present TES, a new n-body integration code for the accurate and rapid propagation of planetary systems in the presence of close encounters. TES builds upon the classic Encke method and integrates only the perturbations to Keplerian trajectories to reduce both the error and runtime of simulations. Variable step size is used throughout to enable close encounters to be precisely handled. A suite of numerical improvements are presented that together makes TES optimal in terms of energy error. Lower runtimes are found in all test problems considered when compared to direct integration using ias1…
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…
A Kinematic History of Stellar Encounters with Beta Pictoris
Centro de Astrobiología (CAB), CSIC-INTA（天体生物学中心）；Universidad Complutense de Madrid（马德里康普顿斯大学）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Lund University（隆德大学）；Instituto de Astrofísica de Canarias（加那利天体物理研究所）；Universidad de La Laguna (ULL)（拉各拉纳大学）
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 …
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…
The flyby anomaly is the unexpected variation of the asymptotic post-encounter velocity of a spacecraft with respect to the pre-encounter velocity as it performs a slingshot manoeuvre. This effect has been detected in, at least, six flybys of the Earth but it has not appeared in other recent flybys. In order to find a pattern in these, apparently contradictory, data several phenomenological formulas have been proposed but all have failed to predict a new result in agreement with the observations. In this paper we use a multivariate dimensional analysis approach to propose a fitting of the data…
Planetary bodies such as asteroids, comets, and planetary moons are high-value science targets as they hold important information about the formation and evolution of our solar system. However, due to their low-gravity, variable sizes and shapes, dedicated orbiting spacecraft missions around these target bodies is difficult. Therefore, many planetary bodies are observed during flyby encounters, and consequently, the mapping coverage of the target body is limited. In this work, we propose the use of a spacecraft swarm to provide complete surface maps of a planetary body during a close encounter…
The Mars flyby of C/2013 A1 (Siding Spring) represented a unique opportunity for imaging a long-period comet and resolving its nucleus and rotation period. Because of the small encounter distance and the high relative velocity, the goal of successfully observing C/2013 A1 from the Mars orbiting spacecrafts posed strict accuracy requirements on the comet's ephemerides. These requirements were hard to meet, as comets are known for being highly unpredictable: astrometric observations can be significantly biased and nongravitational perturbations affect comet trajectories. Therefore, even prior to…
We specify the range to which perturbations penetrate a planetesimal system. Such perturbations can originate from massive planets or from encounters with other stars. The latter can have an origin in the star cluster in which the planetary system was born, or from random encounters once the planetary system has escaped its parental cluster. The probability of a random encounter, either in a star cluster or in the Galactic field depends on the local stellar density, the velocity dispersion and the time spend in that environment. By adopting order of magnitude estimates we argue that the majori…
The primary aim of this work is to examine the effect of parabolic stellar encounters on the evolution of a Jovian-mass giant planet forming within a protoplanetary disc. We consider the effect on both the mass accretion and the migration history as a function of encounter distance. We use a grid-based hydrodynamics code to perform 2D simulations of a system consisting of a giant planet embedded within a gaseous disc orbiting around a star, which is perturbed by a passing star on a prograde, parabolic orbit. The disc model extends out to 50 AU, and parabolic encounters are considered with impa…
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…
Continuous habitability of a planet is a critical condition for advanced forms of life to appear, but it can be endangered by astronomical events such as stellar encounters. The purpose of this study is to analyze close stellar encounters able to change planetary orbits initially in circumstellar habitable zones and to investigate the expected encounter rates in a variety of stellar environments. Using gravitational simulations for three-body systems, this study analyzed the dependencies of encounter impact-parameters with kinematic, geometric, and habitability parameters of the system. We als…
Both simulations and observations indicate that stars form in filamentary, hierarchically clustered associations, most of which disperse into their galactic field once feedback destroys their parent clouds. However, during their early evolution in these substructured environments, stars can undergo close encounters with one another that might have significant impacts on their protoplanetary disks or young planetary systems. We perform N-body simulations of the early evolution of dissolving, substructured clusters with a wide range of properties, with the aim of quantifying the expected number …
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…
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）
Most planetary systems -- including our own -- are born within stellar clusters, where interactions with neighboring stars can help shape the system architecture. This paper develops an orbit-averaged formalism to characterize the cluster's mean-field effects as well as the physics of long-period stellar encounters. Our secular approach allows for an analytic description of the dynamical consequences of the cluster environment on its constituent planetary systems. We analyze special cases of the resulting Hamiltonian, corresponding to eccentricity evolution driven by planar encounters, as well…
A dynamically relaxed dense cluster comprised of about 40 stars (the so-called S-stars) inhabits the central region of the Galaxy. Their stars revolve around the Sgr A$^*$ massive object. To understand the dynamical evolution of planetary systems in a particular environment like that around Sgr A$^*$, we carry out direct N--body simulations of planetary systems embedded in the S--star cluster. In this work, we investigate the short-term stability of the planets orbiting around S-stars after their close interactions with the central massive black hole of our galaxy. We find that planetary syste…
The MESSENGER spacecraft conducted its first flyby of Mercury on 14th January 2008, followed by two subsequent encounters on 6th October 2008 and 29th September 2009, prior to Mercury orbit insertion on 18th March 2011. We have reviewed MESSENGER flight telemetry and X-ray Spectrometer observations from the first two encounters, and correlate several prominent features in the data with the presence of astrophysical X-ray sources in the instrument field of view. We find that two X-ray peaks attributed in earlier work to the detection of suprathermal electrons from the Mercury magnetosphere, are…
Young stars are mostly found in dense stellar environments, and even our own Solar system may have formed in a star cluster. Here, we numerically explore the evolution of planetary systems similar to our own Solar system in star clusters. We investigate the evolution of planetary systems in star clusters. Most stellar encounters are tidal, hyperbolic, and adiabatic. A small fraction of the planetary systems escape from the star cluster within 50 Myr; those with low escape speeds often remain intact during and after the escape process. While most planetary systems inside the star cluster remain…
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…
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 …
The Nice model of the dynamical instability and migration of the giant planets can explain many properties of the present Solar System, and can be used to constrain its early architecture. In the jumping-Jupiter version of the Nice model, required from the terrestrial planet constraint and dynamical structure of the asteroid belt, Jupiter has encounters with an ice giant. Here we study the survival of the Galilean satellites in the jumping-Jupiter model. This is an important concern because the ice-giant encounters, if deep enough, could dynamically perturb the orbits of the Galilean satellite…
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…
Processes such as the solar wind sputtering and micrometeorite impacts can modify optical properties of surfaces of airless bodies. This explains why spectra of the main belt asteroids, exposed to these `space weathering' processes over eons, do not match the laboratory spectra of ordinary chondrite (OC) meteorites. In contrast, an important fraction of Near Earth Asteroids (NEAs), defined as Q-types in the asteroid taxonomy, display spectral attributes that are a good match to OCs. Here we study the possibility that the Q-type NEAs underwent recent encounters with the terrestrial planets and …
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…
We present radiation hydrodynamic simulations in which binary planets form by close encounters in a system of several super-Earth embryos. The embryos are embedded in a protoplanetary disk consisting of gas and pebbles and evolve in a region where the disk structure supports convergent migration due to Type I torques. As the embryos accrete pebbles, they become heated and thus affected by the thermal torque (Benítez-Llambay et al. 2015) and the hot-trail effect (Chrenko et al. 2017) which excites orbital eccentricities. Motivated by findings of Eklund & Masset (2017), we assume the hot-trail e…
