Two populations of minor bodies in the outer Solar System remain particularly elusive: Scattered Disk objects and Sedna-like objects. These populations are important dynamical tracers, and understanding the details of their spatial- and size-distributions will enhance our understanding of the formation and on-going evolution of the Solar System. By using newly-derived limits on the maximum heliocentric distances that recent pencil-beam surveys for Trans-Neptunian Objects were sensitive to, we determine new upper limits on the total numbers of distant SDOs and Sedna-like objects. While generally consistent with populations estimated from wide-area surveys, we show that for magnitude-distribution slopes of α > 0.7-1.0, these pencil-beam surveys provide stronger upper limits than current estimates in literature.
This article reviews the different mechanisms affecting the orbits of trans-Neptunian objects, ranging from internal perturbations (planetary scattering, mean-motion resonances, secular effects) to external perturbations (galactic tides, passing stars). We outline the theoretical tools that can be used to model and study them, focussing on analytical approaches. We eventually compare these mechanisms to the observed distinct populations of trans-Neptunian objects and conclude on how they participate to the sculpting of the whole distribution.
Context: The discovery of distant trans-Neptunian objects has led to heated discussions about the structure of the outer Solar System. Aims: We study the dynamical evolution of small bodies from the Hill regions of migrating giant gaseous clumps that form in the outer solar nebula via gravitational fragmentation. We attempt to determine whether the observed features of the orbital distribution of distant trans-Neptunian objects could be caused by this process. Methods: We consider a simple model that includes the Sun, two point-like giant clumps with masses of ~ 10 Jupiter masses, and a set of…
The Trans-Neptunian Objects (TNOs) may preserve evidence of planet building in their orbital and size-distributions. While all populations show steep size-distributions for large objects, recently relative deficit of Neptunian Trojans and scattering objects with diameters $D<100\,\mathrm{km}$ were detected. We have investigated this deficit with a 32 square degree survey, detecting 77 TNOs to a limiting $r$-band magnitude of 24.6. Our Plutinos sample (18 objects in 3:2 mean motion resonance with Neptune) also shows a deficit of $D<100\,\mathrm{km}$ objects. We reject a single power-law size-di…
The Pluto system is an archetype for the multitude of icy dwarf planets and accompanying satellite systems that populate the vast volume of the solar system beyond Neptune. New Horizons' exploration of Pluto and its five moons gave us a glimpse into the range of properties that their kin may host. Furthermore, the surfaces of Pluto and Charon record eons of bombardment by small trans-Neptunian objects, and by treating them as witness plates we can infer a few key properties of the trans-Neptunian population at sizes far below current direct-detection limits. This chapter summarizes what we hav…
The trans-Neptunian region of the solar system exhibits an intricate dynamical structure, much of which can be explained by an instability-driven orbital history of the giant planets. However, the origins of a highly inclined, and in certain cases retrograde, population of trans-Neptunian objects remain elusive within the framework of this evolutionary picture. In this work, we show that the existence of a distant, Neptune-like planet that resides on an eccentric and mildly inclined orbit fully accounts for the anomalous component the trans-Neptunian orbital distribution. Adopting the same par…
Trans-Neptunian objects and Centaurs are small solar system bodies that reside in the outer parts of the solar system. These objects present photometric behaviours that are influenced due to a change in their aspect angle. Using absolute photometric measurements and rotational light-curves at different location on their orbits allow to model their photometric behaviour and obtain physical properties such as pole orientation, shape, density, and even detecting different peculiarities as departure from hydrostatic equilibrium or rings. In this work, I present how these models are performed in or…
The dependences of inclinations of orbits of secondaries in the discovered trans-Neptunian binaries on the distance between the primary and the secondary, on the eccentricity of orbits of the secondary around the primary, on the ratio of diameters of the secondary and the primary, and on the elements of heliocentric orbits of these binaries are studied. These dependences are interpreted using the model of formation of a satellite system in a collision of two rarefied condensations composed of dust and/or objects less than 1 m in diameter. It is assumed in this model that a satellite system for…
The formation of trans-Neptunian satellite systems at the stage of rarefied preplanetesimals (i.e., condensations of dust and/or objects less than 1 m in diameter) is discussed. It is assumed that trans-Neptunian objects (including those with satellites) could form as a result of compression of parental rarefied preplanetesimals. The formulas for calculating the angular momentum of two colliding condensations with respect to their center of mass, which were applied earlier in (Ipatov, 2010) in the comparison of such momenta with the angular momenta of observed satellite systems, are used to es…
Neptunian Trojans (NTs), trans-Neptunian objects in 1:1 mean-motion resonance with Neptune, are generally thought to have been captured from the original trans-Neptunian protoplanetary disk into co-orbital resonance with the ice giant during its outward migration. It is possible, therefore, that the colour distribution of NTs is a constraint on the location of any colour transition zones that may have been present in the disk. In support of this possible test, we obtained $g$, $r$, and $i$-band observations of 18 NTs, more than doubling the sample of NTs with known visible colours to 31 object…
Aims. We study the dynamical evolution of a system consisting of the giant planets and a massive planetesimal disk over the age of the Solar System. The main question addressed in this study is whether distant trans-Neptunian objects could have come about as a result of the combined action of planetary perturbations and the self-gravity of the disk. Methods. We carried out a series of full N-body numerical simulations of gravitational interactions between the giant planets and a massive outer disk of planetesimals. Results. Our simulations show that the collective gravity of the giant planets …
A relatively massive and moderately eccentric disk of trans-Neptunian objects (TNOs) can effectively counteract apse precession induced by the outer planets, and in the process shepherd highly eccentric members of its population into nearly-stationary configurations which are anti-aligned with the disk itself. We were sufficiently intrigued by this remarkable feature to embark on an extensive exploration of the full spatial dynamics sustained by the combined action of giant planets and a massive trans-Neptunian debris disk. In the process, we identified ranges of disk mass, eccentricity and pr…
We report photometric observations of the trans-Neptunian object 2004~TT$_{357}$ obtained in 2015 and 2017 using the 4.3~m Lowell's Discovery Channel Telescope. We derive a rotational period of 7.79$\pm$0.01~h and a peak-to-peak lightcurve amplitude of 0.76$\pm$0.03~mag. 2004 TT$_{357}$ displays a large variability that can be explained by a very elongated single object or can be due to a contact/close binary. The most likely scenario is that 2004 TT$_{357}$ is a contact binary. If it is in hydrostatic equilibrium, we find that the lightcurve can be explained by a system with a mass ratio q$_{…
In this work, we focused on observations of six trans-Neptunian objects (TNOs) whose apparent magnitudes are brighter than 20 mag. We present the results of astrometric and photometric observations of (134340) Pluto, (136108) Haumea, (136472) Makemake, (136199) Eris, (90482) Orcus and (20000) Varuna obtained at the Kyiv comet station (Code MPC 585) in 2017-2019. For observations, we used the 0.7-m reflector AZT-8 with the FLI PL4710 CCD camera and filters of the Johnson-Cousins photometric system. From our images, we measured the objects astrometric positions, calculated apparent magnitudes in…
A number of intriguing patterns have been identified in the distributions of the orbital elements of the known extreme trans-Neptunian objects or ETNOs --those with semimajor axis greater than 150 au and perihelion distance greater than 30 au. The announcement of the discovery of 2015 BP519, also known as Caju, has been hailed by some as a consistent piece of robust evidence for the existence of a yet-to-be-discovered massive planet far beyond the trans-Neptunian belt. In this Note, we use the latest data available to provide evidence against 2015 BP519 having followed the same dynamical pathw…
The discovery and characteristics of transneptunian binaries are reviewed. In the 20 years since their first discovery, a wealth of detail has emerged including the frequency of binaries in different populations, their relative sizes and separations, and colors. Taken globally, these properties give strong clues to the origin and evolution of the populations where these binaries are found. In the last ten years and increasing number of binary orbits have been determined which yields a new trove of information on their masses and densities as well as details of their orbits including inclinatio…
Dynamical features of a massive disk of distant trans-Neptunian objects are considered in the model of the formation of small bodies in the Hill region of a giant gas-dust clump that arose as a result of gravitational instability and fragmentation of the protoplanetary disk. The dynamical evolution of orbits of small bodies under the action of gravitational perturbations from the outer planets and self-gravity of the disk has been studied for a time interval of the order of a billion years. It is shown that the secular effects of the gravitational action of a massive disk of small bodies lead …
Secular dynamics inside MMRs plays an essential role in governing the dynamical structure of the trans-Neptunian region and sculpting the orbital distribution of trans-Neptunian objects (TNOs). In this study, semi-analytical developments are made to explore the von Zeipel-Lidov-Kozai (ZLK) resonance inside mean motion resonances (MMRs). To this end, a semi-secular model is formulated by averaging theory and then a single-degree-of-freedom integrable model is achieved based on the adiabatic invariance approximation. In particular, we introduce a modified adiabatic invariant, which is continuous…
Recently, Sheppard et al. (2016) presented the discovery of seven new trans-Neptunian objects with moderate eccentricities, perihelia beyond 40 AU, and semimajor axes beyond 50 AU. Like the few previously known objects on similar orbits, these objects' semimajor axes are just beyond the Kuiper belt edge and clustered around Neptunian mean motion resonances (MMRs). These objects likely obtained their observed orbits while trapped within MMRs, when the Kozai-Lidov mechanism raised their perihelia and weakened Neptune's dynamical influence. Using numerical simulations that model the production of…
Space-based observatories at the second Sun-Earth Lagrange Point (L2) offer a unique opportunity to efficiently determine the orbits of distant solar system objects by taking advantage of the parallax effect that arises from nearly simultaneous ground- and space-based observations. Given the typical orbit of an observatory about L2, the observational baseline of $\sim1.5\times10^6$ km between L2 and Earth results in an instantaneous parallax of $\sim$10''-100'', even for the most distant of detectable trans-Neptunian objects (TNOs) in our solar system. Current ground-based strategies for measu…
Asymmetric debris discs have been found around stars other than the Sun; asymmetries are sometimes attributed to perturbations induced by unseen planets. The presence or absence of asymmetries in our own trans-Neptunian belt remains controversial. The study of sensitive tracers in a sample of objects relatively free from the perturbations exerted by the four known giant planets and most stellar flybys may put an end to this debate. The analysis of the distribution of the mutual nodal distances of the known extreme trans-Neptunian objects (ETNOs) that measure how close two orbits may get to eac…
Numerical analysis of Lyapunov Times for Trans-Neptunian Objects and Main-Belt Asteroids: stability, accuracy, and methodological comparisons
Centrum Badań Kosmicznych Polskiej Akademii Nauk (CBK PAN)（波兰科学院太空研究中心）；Astronomical Observatory, University of Warsaw（华沙大学天文台）；Cilium Engineering Sp. z o.o.（Cilium工程公司）
In the current model of early Solar System evolution, the stable members of the Jovian and Neptunian Trojan populations were captured into resonance from the leftover reservoir of planetesimals during the outward migration of the giant planets. As a result, both Jovian and Neptunian Trojans share a common origin with the primordial disk population, whose other surviving members constitute today's trans-Neptunian object (TNO) populations. The cold classical TNOs are ultra-red, while the dynamically excited "hot" population of TNOs contains a mixture of ultra-red and blue objects. In contrast, J…
We present the first comprehensive thermal and rotational analysis of the second most distant trans-Neptunian object (225088) 2007 OR10. We combined optical light curves provided by the Kepler space telescope -- K2 extended mission and thermal infrared data provided by the Herschel Space Observatory. We found that (225088) 2007 OR10 is likely to be larger and darker than derived by earlier studies: we obtained a diameter of d=1535^{+75}_{-225} km which places (225088) 2007 OR10 in the biggest top three trans-Neptunian objects. The corresponding visual geometric albedo is p_V=0.089^{+0.031}_{-0…
We explore the distant giant planet hypothesis by integrating the large semi-major axis, large pericenter Trans-Neptunian Objects (TNOs) in the presence of the giant planets and an external perturber whose orbit is consistent with the proposed distant, eccentric, and inclined giant planet, so called planet 9. We find that TNOs with semi-major axes greater than 250 au experience some longitude of perihelion shepherding, but that a generic outcome of such evolutions is that the TNOs evolve to larger pericenter orbits, and commonly get raised to retrograde inclinations. This pericenter and inclin…
We present a measurement of H2O ice crystallinity on the surface of trans-neptunian objects (TNOs) with near-infrared narrow-band imaging. The newly developed photometric technique allows us to efficiently determine the strength of an 1.65-um absorption feature in crystalline H2O ice. Our data for three large objects, Haumea, Quaoar, and Orcus, which are known to contain crystalline H2O ice on the surfaces, show a reasonable result with high fractions of the crystalline phase. It can also be pointed out that if the H2O-ice grain size is larger than ~20 um, the crystallinities of these objects …
We report the rotational lightcurves of 21 trans-Neptunian objects (TNOs) in Neptune's 2:1 mean motion resonance obtained with the 6.5 m Magellan-Baade telescope and the 4.3 m Lowell Discovery Telescope. The main survey's goal is to find objects displaying a large lightcurve amplitude which is indicative of contact binaries or highly elongated objects. In our sample, two 2:1 resonant TNOs showed a significant short-term lightcurve amplitude: 2002 VD$_{130}$ and (531074) 2012 DX$_{98}$. The full lightcurve of 2012 DX$_{98}$ infers a periodicity of 20.80$\pm$0.06h and amplitude of 0.56$\pm$0.03m…
We carried out an extensive analysis of the stability of the outer solar system, making use of the frequency analysis technique over short-term integrations of nearly a hundred thousand test particles, as well as a statistical analysis of 200, 1 Gyr long numerical simulations, which consider the mutual perturbations of the giant planets and the 34 largest trans-Neptunian objects (we have called all 34 objects ``dwarf planets'', DPs, even if probably only the largest of them are true DPs). From the frequency analysis we produced statistical diffusion maps for a wide region of the $a$-$e$ phase-…
2007OR10 is currently the third largest known dwarf planet in the transneptunian region, with an effective radiometric diameter of ~1535 km. It has a slow rotation period of ~45 h that was suspected to be caused by tidal interactions with a satellite undetected at that time. Here we report on the discovery of a likely moon of 2007OR10, identified on archival Hubble Space Telescope WFC3/UVIS system images. Although the satellite is detected at two epochs, this does not allow an unambiguous determination of the orbit and the orbital period. A feasible 1.5-5.8x10^21 kg estimate for the system mas…
It is a well-known fact that the presence of a massive perturber interacting with a population of minor bodies following very eccentric orbits can strongly affect the distribution of their nodal distances. The details of this process have been explored numerically and its outcome confirmed observationally in the case of Jupiter, where a bimodal distribution of nodal distances of comets has been found. Here, we show evidence for a possible bimodal distribution of the nodal distances of the extreme trans-Neptunian objects (ETNOs) in the form of a previously unnoticed correlation between nodal di…
A critical step toward the emergence of planets in a protoplanetary disk consists in accretion of planetesimals, bodies 1-1000 km in size, from smaller disk constituents. This process is poorly understood partly because we lack good observational constraints on the complex physical processes that contribute to planetesimal formation. In the outer solar system, the best place to look for clues is the Kuiper belt, where icy planetesimals survived to this day. Here we report evidence that Kuiper belt planetesimals formed by the streaming instability, a process in which aerodynamically concentrate…
We use a secular model to describe the non-resonant dynamics of trans-Neptunian objects in the presence of an external ten-earth-mass perturber. The secular dynamics is analogous to an "eccentric Kozai mechanism" but with both an inner component (the four giant planets) and an outer one (the eccentric distant perturber). By the means of Poincaré sections, the cases of a non-inclined or inclined outer planet are successively studied, making the connection with previous works. In the inclined case, the problem is reduced to two degrees of freedom by assuming a non-precessing argument of periheli…
We use astrometry of Pluto and other TNOs to constrain the sky location, distance, and mass of the possible additional planet (Planet Nine) hypothesized by Batygin and Brown (2016). We find that over broad regions of the sky, the inclusion of a massive, distant planet degrades the fits to the observations. However, in other regions, the fits are significantly improved by the addition of such a planet. Our best fits suggest a planet that is either more massive or closer than argued for by Batygin and Brown (2016) based on the orbital distribution of distant trans-neptunian objects (or by Fienga…
Using data from the Infrared Array Camera on the Spitzer Space Telescope, we present photometric observations of a sample of 100 trans-Neptunian objects (TNOs) beyond 2.2 μm. These observations, collected with two broad-band filters centered at 3.6 and 4.5 μm, were done in order to study the surface composition of TNOs, which are too faint to obtain spectroscopic measurements. With this aim, we have developed a method for the identification of different materials that are found on the surfaces of TNOs. In our sample, we detected objects with colors that are consistent with the presence of smal…
From two observing runs during the 2014 summer at Calar Alto Observatory in Almería (Spain) and at Sierra Nevada Observatory in Granada (Spain), we were able to derive CCD photometry of the Trans-Neptunian Object 2008 OG$_{19}$. We analyzed the time series and obtained a double-peaked light curve with a peak to valley amplitude of (0.437 $\pm$ 0.011) mag and a rotational period of (8.727$\pm$ 0.003) h. This implies that this object is very elongated, closely resembling Varuna's case. The photometry also allowed us to obtain an absolute magnitude in R-band of (4.39 $\pm$ 0.07) mag. From this re…
Probing close-in satellites of Trans-Neptunian Objects through thermal and direct size measurements
Instituto de Astrofísica de Andalucía, IAA-CSIC（安达卢西亚天体物理研究所）；Deutsches Zentrum für Astrophysik (DZA)（德国天体物理学中心）；Max-Planck-Institut für extraterrestrische Physik（马克斯·普朗克地外物理学研究所）
Looking at the orbits of small bodies with large semimajor axes, we are compelled to see patterns. Some of these patterns are noted as strong indicators of new or hidden processes in the outer Solar System, others are substantially generated by observational biases, and still others may be completely overlooked. We can gain insight into the current and past structure of the outer Solar System through a careful examination of these orbit patterns. In this chapter, we discuss the implications of the observed orbital distribution of distant trans-Neptunian objects (TNOs). We start with some cauti…
Asteroids that follow similar orbits may have a dynamical connection as their current paths could be the result of a past interaction with a massive perturber. The pair of extreme trans-Neptunian objects or ETNOs (474640) 2004 VN112-2013 RF98 exhibits peculiar relative orbital properties, including a difference in longitude of the ascending node of just 1.61 degrees and 3.99 degrees in inclination. In addition, their reflectance spectra are similar in the visible portion of the spectrum. The origin of these similarities remains unclear. Neglecting observational bias, viable scenarios that coul…
Aims. Numerous trans-Neptunian objects are known to be in mean-motion resonance with Neptune. We aim to describe their long-term orbital evolution (both past and future) by means of a one-degree-of-freedom secular model. In this paper, we focus only on objects with a semi-major axis larger than 50 astronomical units (au). Methods. For each resonant object considered, a 500 000-year numerical integration is performed. The output is digitally filtered to get the parameters of the resonant secular model. Their long-term (Giga-year) orbital evolution is then represented by the level curves of the …
Although the majority of Centaurs are thought to have originated in the scattered disk, with the high-inclination members coming from the Oort cloud, the origin of the high inclination component of trans-Neptunian objects (TNOs) remains uncertain. We report the discovery of a retrograde TNO, which we nickname "Niku", detected by the Pan-STARRS 1 Outer Solar System Survey. Our numerical integrations show that the orbital dynamics of Niku are very similar to that of 2008 KV$_{42}$ (Drac), with a half-life of $\sim 500$ Myr. Comparing similar high inclination TNOs and Centaurs ($q > 10$ AU, $a < …
We analyze the uncertainty in grain size estimation of pure methane (CH4) and nitrogen saturated with methane (N2:CH4) ices, the most abundant volatile materials on trans-Neptunian objects (TNOs) and Kuiper belt objects (KBOs). We compare the single scattering albedo, which determines the grain size estimation of outer solar system regolith (Hansen, 2009), of these ices using the Mie scattering model and two other Hapke approximations (Hapke, 1993) in radiative transfer scattering models (RTM) at near-infrared (NIR) wavelengths (1-5 $μ$m). The equivalent slab (Hapke Slab) approximation model p…
Trans-Neptunian Binary Mutual Events in the 2020s and 2030s
Florida Space Institute, University of Central Florida（佛罗里达太空研究所，中佛罗里达大学）；Lowell Observatory（洛厄尔天文台）；Northern Arizona University（北亚利桑那大学）；Brigham Young University Department of Physics & Astronomy（杨百翰大学物理与天文学系）
Reflection spectroscopy in the Near Infrared (NIR) is used to investigate the surface composition of Trans-Neptunian objects (TNOs). In general, these spectra are difficult to interpret due to the low apparent brightness of the TNOs, causing low signal-to-noise ratio even in spectra obtained with the largest telescopes available on the Earth, making necessary to use filtering techniques to analyze and interpret them. The purpose of this paper is to present a methodology to analyze the spectra of TNOs. Specifically, we aim at filtering these spectra in the best possible way: maximizing the remo…
We present the first photometric observations of trans-Neptunian objects (TNOs) taken with the Kepler space telescope, obtained in the course of the K2 ecliptic survey. Two faint objects have been monitored in specifically designed pixel masks that were centered on the stationary points of the objects, when their daily motion was the slowest. In the design of the experiment, only the apparent path of these objects were retrieved from the detectors, i.e. the costs in terms of Kepler pixels were minimized. Because of the faintness of the targets we employ specific reduction techniques and co-add…
