Instabilities in planetary systems can result in the ejection of planets from their host system, resulting in free-floating planets (FFPs). If this occurs in a star cluster, the FFP may remain bound to the star cluster for some time and interact with the other cluster members until it is ejected. Here, we use $N$-body simulations to characterise close star-planet and planet-planet encounters and the dynamical fate of the FFP population in star clusters containing $500-2000$ single or binary star members. We find that FFPs ejected from their planetary system at low velocities typically leave the star cluster 40% earlier than their host stars, and experience tens of close ($<1000$ AU) encounters with other stars and planets before they escape. The fraction of FFPs that experiences a close encounter depends on both the stellar density and the initial velocity distribution of the FFPs. Approximately half of the close encounters occur within the first 30 Myr, and only 10% occur after 100 Myr. The periastron velocity distribution for all encounters is well-described by a modified Maxwell-Bolzmann distribution, and the periastron distance distribution is linear over almost the entire range of distances considered, and flattens off for very close encounters due to strong gravitational focusing. Close encounters with FFPs can perturb existing planetary systems and their debris structures, and they can result in re-capture of FFPs. In addition, these FFP populations may be observed in young star clusters in imaging surveys; a comparison between observations and dynamical predictions may provide clues to the early phases of stellar and planetary dynamics in star clusters.
In the paper, we have discussed the problem of the existence of the metallic hydrogen in the superconducting state inside the cold giant planet. We have shown that the {\it cold} planet represents the final state of the thermal evolution of free-floating giant planet.
Recent gravitational microlensing observations predict a vast population of free-floating giant planets that outnumbers main sequence stars almost twofold. A frequently-invoked mechanism for generating this population is a dynamical instability that incites planet-planet scattering and the ejection of one or more planets in isolated main sequence planetary systems. Here, we demonstrate that this process alone probably cannot represent the sole source of these galactic wanderers. By using straightforward quantitative arguments and N-body simulations, we argue that the observed number of exoplan…
Free-floating planets are recently drawing a special interest of the scientific community. Gravitational microlensing is up to now the exclusive method for the investigation of free-floating planets, including their spatial distribution function and mass function. In this work, we examine the possibility that the future Euclid space-based observatory may allow to discover a substantial number of microlensing events caused by free-floating planets. Based on latest results about the free-floating planet mass function in the mass range $[10^{-5}, 10^{-2}]M_{\odot}$, we calculate the optical depth…
Evidence of exoplanets with orbits that are misaligned with the spin of the host star may suggest that not all bound planets were born in the protoplanetary disk of their current planetary system. Observations have shown that free-floating Jupiter-mass objects can exceed the number of stars in our galaxy, implying that capture scenarios may not be so rare. To address this issue, we construct a three-dimensional simulation of a three-body scattering between a free-floating planet and a star accompanied by a Jupiter-mass bound planet. We distinguish between three different possible scattering ou…
Free-floating planets are the remnants of violent dynamical rearrangements of planetary systems. It is possible that even our own solar system ejected a large planet early in its evolution. WFIRST will have the ability to detect free-floating planets over a wide range of masses, but it will not be able to directly measure their masses. Microlensing parallax observations can be used to measure the masses of isolated objects, including free-floating planets, by observing their microlensing events from two locations. The intra-L2 separation between WFIRST and Euclid is large enough to enable micr…
The recent discovery of free-floating planets and their theoretical interpretation as celestial bodies, either condensed independently or ejected from parent stars in tight clusters, introduced an intriguing possibility. Namely, that some exoplanets are not condensed from the protoplanetary disk of their parent star. In this novel scenario a free-floating planet interacts with an already existing planetary system, created in a tight cluster, and is captured as a new planet. In the present work we study this interaction process by integrating trajectories of planet-sized bodies, which encounter…
Genomic complexity can be used as a clock with which the moment in which life originated can be measured. Some authors who have studied this problem have come to the conclusion that it is not possible that terrestrial life originated here and that, in reality, life originated giga-years ago, before the solar system existed. If we accept this conclusion there is no other option than to admit that panspermia is something viable.The goal of this study is to propose a viable hypothesis for the transport of SLF from one planetary system to another. During the formation period of a planetary system …
Microlensing is generally thought to probe planetary systems only out to a few Einstein radii. Microlensing events generated by bound planets beyond about 10 Einstein radii generally do not yield any trace of their hosts, and so would be classified as free floating planets (FFPs). I show that it is already possible, using adaptive optics (AO), to constrain the presence of potential hosts to FFP candidates at separations comparable to the Oort Cloud. With next-generation telescopes, planets at Kuiper-Belt separations can be probed. Next generation telescopes will also permit routine vetting for…
Planets are thought to form via accretion from a remnant disk of gas and solids around a newly formed star. During this process material in the disk either remains bound to the star as part of either a planet, a smaller celestial body, or makes up part of the interplanetary medium; falls into the star; or is ejected from the system. Herein we use dynamical models to probe the abundance and properties of ejected material during late-stage planet formation and estimate their contribution to the free-floating planet population. We present 300 N-body simulations of terrestrial planet formation aro…
Recent observations have shown the presence of extra-solar planets in Galactic open stellar clusters, as in the Praesepe (M44). These systems provide a favorable environment for planetary formation due to the high heavy-element content exhibited by the majority of their population. The large stellar density, and corresponding high close-encounter event rate, may induce strong perturbations of planetary orbits with large semimajor axes. Here we present a set of N-body simulations implementing a novel scheme to treat the tidal effects of external stellar perturbers on planetary orbit eccentricit…
A microlensing survey by Sumi et al. (2011) exhibits an overabundance of short-timescale events (STEs; t_E<2 days) relative to what is expected from known stellar populations and a smooth power-law extrapolation down to the brown dwarf regime. This excess has been interpreted as a population of ~Jupiter-mass objects that outnumber main-sequence stars by nearly twofold; however the microlensing data alone cannot distinguish between events due to wide-separation (a>~10 AU) and free-floating planets. Assuming these STEs are indeed due to planetary-mass objects, we aim to constrain the fraction of…
A free-floating planet is a planetary-mass object that orbits around a non-stellar massive object (e.g. a brown dwarf) or around the Galactic Center. The presence of exomoons orbiting free-floating planets has been theoretically predicted by several models. Under specific conditions, these moons are able to retain an atmosphere capable of ensuring the long-term thermal stability of liquid water on their surface. We model this environment with a one-dimensional radiative-convective code coupled to a gas-phase chemical network including cosmic rays and ion-neutral reactions. We find that, under …
The next decade will see two large-scale space-based near-infrared surveys, Euclid and WFIRST. This paper shows that the subtle differences between the filters proposed for these surveys and those from ground-based photometric systems will produce a ground-space colour term that is dependent on water absorption in the spectra of astronomical objects. This colour term can be used to identify free-floating planets in star forming regions, mimicking a successful ground-based technique that uses a filter sensitive to water absorption. This paper shows that this colour term is an effective discrimi…
Open clusters(OCs) are usually young and suitable for studying the formation and evolution of planetary systems. Hitherto, only four planets have been found with radial velocity measurements in OCs. Meanwhile, a lot of free-floating planets(FFPs) have been detected. We utilize N-body simulations to investigate the evolution and final configurations of multi-planetary systems in very young open clusters with an age <10 Myr. After an evolution of 10 Myr, 61%-72% of the planets remain bounded and more than 55% of the planetary systems will maintain their initial orbital configurations. For system…
We calculate the microlensing event rate and typical time-scales for the free-floating planet (FFP) population that is predicted by the core accretion theory of planet formation. The event rate is found to be ~$1.8\times 10^{-3}$ of that for the stellar population. While the stellar microlensing event time-scale peaks at around 20 days, the median time-scale for FFP events (~0.1 day) is much shorter. Our values for the event rate and the median time-scale are significantly smaller than those required to explain the \cite{Sum+11} result, by factors of ~13 and ~16, respectively. The inclusion of…
Astrometric observations of microlensing events can be used to obtain important information about lenses. During these events, the shift of the position of the multiple image centroid with respect to the source star location can be measured. This effect, which is expected to occur on scales from micro-arcseconds to milli-arcseconds, depends on the lens-source-observer system physical parameters. Here, we consider the astrometric and photometric observations by space and ground-based telescopes of microlensing events towards the Galactic bulge caused by free floating planets (FFPs). We show tha…
Current microlensing surveys are sensitive to free-floating planets down to Earth-mass objects. All published microlensing events attributed to unbound planets were identified based on their short timescale (below two days), but lacked an angular Einstein radius measurement (and hence lacked a significant constraint on the lens mass). Here, we present the discovery of a Neptune-mass free-floating planet candidate in the ultrashort ($t_{\rm E}=0.320\pm0.003$ days) microlensing event OGLE-2016-BLG-1540. The event exhibited strong finite-source effects, which allowed us to measure its angular Ein…
The detection of anomalies in gravitational microlensing events is nowadays one of the main goals among the microlensing community. In the case of single-lens events, these anomalies can be caused by the finite source effects, that is when the source disk size is not negligible, and by the Earth rotation around the Sun (the so-called parallax effect). The finite source and parallax effects may help to define the mass of the lens, uniquely. Free-floating planets (FFPs) are extremely dim objects, and gravitational microlensing provides at present the exclusive method to investigate these bodies.…
We numerically studied close encounters between a young stellar system hosting a massive, gravitationally fragmenting disk and an intruder diskless star with the purpose to determine the evolution of fragments that have formed in the disk prior to the encounter. Numerical hydrodynamics simulations in the non-inertial frame of reference of the host star were employed to simulate the prograde and retrograde co-planar encounters. The initial configuration of the target system (star plus disk) was obtained via a separate numerical simulation featuring the gravitational collapse of a solar-mass pre…
K2 Campaign 9 (K2C9) offers the first chance to measure parallaxes and masses of members of the large population of free-floating planets (FFPs) that has previously been inferred from measurements of the rate of short-timescale microlensing events. Using detailed simulations of the nominal campaign (ignoring the loss of events due to Kepler's emergency mode) and ground-based microlensing surveys, we predict the number of events that can be detected if there is a population of 1-Jupiter-mass FFPs matching current observational constraints. Using a Fisher matrix analysis we also estimate the num…
Habitability of Tidally Heated H$_2$-Dominated Exomoons around Free-Floating Planets
Ludwig-Maximilians-Universität München（慕尼黑大学）；Max-Planck-Institut für extraterrestrische Physik（马克斯·普朗克地外物理研究所）；Exzellenzcluster ‘Origins’（起源卓越集群）；European Space Agency (ESA)（欧洲空间局）；European Space Astronomy Centre (ESAC)（欧洲空间天文中心）；European Southern Observatory（欧洲南方天文台）
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…
Planet formation theories predict the existence of free-floating planets that have been ejected from their parent systems. Although they emit little or no light, they can be detected during gravitational microlensing events. Microlensing events caused by rogue planets are characterized by very short timescales $t_{\rm E}$ (typically below two days) and small angular Einstein radii $θ_{\rm E}$ (up to several uas). Here we present the discovery and characterization of two ultra-short microlensing events identified in data from the Optical Gravitational Lensing Experiment (OGLE) survey, which may…
Gravitational microlensing is a powerful method for detecting and characterizing free-floating planetary-mass objects (FFPs). FFPs could have exomoons rotating them. In this work, we study the probability of realizing these systems (i.e., free-floating moon-planet ones) through microlensing observations. These systems make mostly close caustic configurations with a considerable finite-source effect. We investigate finite-source microlensing light curves owing to free-floating moon-planet systems. We conclude that crossing planetary caustics causes an extensive extra peak at light curves' wing …
KMT-2024-BLG-0816/OGLE-2024-BLG-0519 -- A Microlensing Event with Candidate Free-Floating Planet Lens and Blended Light
University of Warsaw（华沙大学）；Korea Astronomy and Space Science Institute（韩国天文学与空间科学研究所）；Westlake University（西湖大学）；University of Canterbury（坎特伯雷大学）；Max-Planck-Institute for Astronomy（马克斯·普朗克天体物理学研究所）；Ohio State University（俄亥俄州立大学）；Chungbuk National University（忠北国立大学）；National University of Science and Technology (UST)（国立科学技术大学）；Weizmann Institute of Science（魏茨曼科学研究所）
In recent years free-loating planets (FFPs) have drawn a great interest among astrophysicists. Gravitational microlensing is a unique and exclusive method for their investigation which may allow obtaining precious information about their mass and spatial distribution. The planned Euclid space-based observatory will be able to detect a substantial number of microlensing events caused by FFPs towards the Galactic bulge. Making use of a synthetic population algorithm, we investigate the possibility of detecting finite source effects in simulated microlensing events due to FFPs. We find a signific…
The Wide Field Infrared Survey Telescope (WFIRST) is expected to detect hundreds of free-floating planets, but it will not be able to measure their masses. However, simultaneous microlensing observations by both Euclid and WFIRST spacecraft, separated by ~ 100, 000 km in orbits around the Sun-Earth L2 Lagrange point, will enable measurements of microlensing parallax for low-mass lenses such as free-floating planets. Using simple Fisher matrix estimates of the parallax measurement uncertainties, we show that high-cadence observations by Euclid could be used to measure ~ 1 free-floating planet m…
This White Paper describes the opportunities for discovery of Jupiter-mass objects with 300K atmospheres. The discovery and characterization of such cold objects is vital for understanding the low-mass terminus of the initial mass function and for optimizing the study of exoplanets by the next generation of large telescopes, space probes and space missions.
Free-floating Planets Produced by Planet-Planet Scatterings: Ejection Velocity and Survival Rate of Their Moons
Tsung-Dao Lee Institute, Shanghai Jiao-Tong University（上海交大李政道研究所）；Center for Astrophysics and Planetary Science, Department of Astronomy, Cornell University（康奈尔大学天文学系天文与行星科学中心）
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 majority of stars form in star clusters and many are thought to have planetary companions. We demonstrate that multi-planet systems are prone to instabilities as a result of frequent stellar encounters in these star clusters much more than single-planet systems. The cumulative effect of close and distant encounters on these planetary systems are investigated using Monte Carlo scattering experiments. We consider two types of planetary configurations orbiting Sun-like stars: (i) five Jupiter-mass planets in the semi-major axis range 1-42 AU orbiting a Solar mass star, with orbits that are in…
Circumbinary planets whose orbits become unstable may be ejected, accreted, or even captured by one of the stars. We quantify the relative rates of these channels, for a binary of secondary star's mass fraction 0.1 with an orbit of 1AU. The most common outcome is ejection, which happens ~80% of the time. If binary systems form circumbinary planets readily and sloppily, this process may fill the Milky Way with free-floating planets. A significant fraction of the time, ~20%, the unstable planet strikes the primary or secondary. We tracked whether a Jupiter-like planet would undergo tidal strippi…
Free-floating planets (FFPs) are the lightest products of star formation and they carry important information on the initial conditions of the environment in which they were formed. They were first discovered in the 2000s but still few of them have been identified and confirmed due to observational challenges. This is a review of the last advances in the detection of these objects and the understanding of their origin. Several studies indicate that the observed fraction of FFPs outnumbers the prediction of turbulent fragmentation and suggest that many were formed in planetary systems that were…
Many asteroids that make close encounters with terrestrial planets are in a binary configuration. Here we calculate the relevant encounter timescales and investigate the effects of encounters on a binary's mutual orbit. We use a combination of analytical and numerical approaches with a wide range of initial conditions. Our test cases include generic binaries with close, moderate, and wide separations, as well as seven well-characterized near-Earth binaries. We find that close approaches (<10 Earth radii) occur for almost all binaries on 1-10 million year timescales. At such distances, our resu…
The Persistent Missing Mass Problem in Planet Formation
University of California, San Diego（加州大学圣地亚哥分校）；McGill University（麦吉尔大学）；University of Maryland（马里兰大学）；Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；The Ohio State University（俄亥俄州立大学）
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…
Free-floating (or rogue) planets are planets that are liberated (or ejected) from their host systems. Although simulations predict their existence in substantial numbers, direct observational evidence for free-floating planets with masses below ~5 MJup is still lacking. Several cycle-1 observing programs with JWST aim to hunt for them in four different star-forming clusters. These surveys are designed to be sensitive to masses of 1-15 MJup (assuming a hot-start formation), which corresponds to spectral types of early L to late T for the ages of these clusters. If the existing simulations are n…
The Centaur population is composed by minor bodies wandering between the giant planets and that frequently perform close gravitational encounters with these planets, which leads to a chaotic orbital evolution. Recently, the discovery of two well-defined narrow rings was announced around the Centaur 10199 Chariklo. The rings are assumed to be in the equatorial plane of Chariklo and to have circular orbits. The existence a well-defined system of rings around a body in such perturbed orbital region poses an interesting new problem. Are the rings of Chariklo stable when perturbed by close gravitat…
Simultaneous space- and ground-based microlensing surveys, such as K2's Campaign 9 (K2C9) and $WFIRST$, facilitate measuring the masses and distances of free-floating planet (FFP) candidates. FFPs are identified as single-lens events with a short timescale, of-order 1 day. Measuring the mass of the lensing object requires determining the finite size of the source star $ρ$, as well as the microlens parallax $π_{\rm E}$. A planet that is bound to but widely separated from a host star can produce a light curve similar to that of an FFP. This tension can be resolved with high-resolution imaging of…
Modern models of terrestrial planet formation require solids depletion interior to 0.5-0.7 au in the planetesimal disk to explain the small mass of Mercury. Earth and Venus analogues emerge after ~100 Myr collisional growth while Mercury form in the diffusive tails of the planetesimal disk. We carried out 250 N-body simulations of planetesimal disks with mass confined to 0.7-1.0 au to study the statistics of close encounters which were recently proposed as an explanation for the high iron mass fraction in Mercury by Deng (2020). We formed 39 Mercury analogues in total and all proto-Mercury ana…
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
The mass and distance functions of free-floating planets (FFPs) would give major insights into the formation and evolution of planetary systems, including any systematic differences between those in the disk and bulge. We show that the only way to measure the mass and distance of individual FFPs over a broad range of distances is to observe them simultaneously from two observatories separated by $D\sim {\cal O}(0.01\,AU)$ (to measure their microlens parallax $π_{\rm E}$) and to focus on the finite-source point-lens (FSPL) events (which yield the Einstein radius $θ_{\rm E}$). By combining the e…
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 …
Gravitational microlensing is the only method capable of exploring the entire population of free-floating planets down to Mars-mass objects, because the microlensing signal does not depend on the brightness of the lensing object. A characteristic timescale of microlensing events depends on the mass of the lens: the less massive the lens, the shorter the microlensing event. A previous analysis of 474 microlensing events found an excess of very short events (1-2 days) - more than known stellar populations would suggest - indicating the existence of a large population of unbound or wide-orbit Jup…
We use numerical integrations to investigate the dynamical evolution of resonant Trojan and quasi-satellite companions during the late stages of migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. Our migration simulations begin with Jupiter and Saturn on orbits already well separated from their mutual 2:1 mean-motion resonance. Neptune and Uranus are decoupled from each other and have orbital eccentricities damped to near their current values. From this point we adopt a planet migration model in which the migration speed decreases exponentially with a characteristic timescale…
In recent years several planets have been discovered at wide orbits (>100 AU) around their host stars. Theoretical studies encounter difficulties in explaining their formation and origin. Here we propose a novel scenario for the production of planetary systems at such orbits, through the dynamical recapture of free floating planets (FFPs) in dispersing stellar clusters. This process is a natural extension of the recently suggested scenario for the formation of wide stellar binaries. We use N-body simulations of dispersing clusters with 10-1000 stars and comparable numbers of FFPs to study this…
