Resonant and Secular Families of the Kuiper Belt

We review ongoing efforts to identify occupants of mean-motion resonances(MMRs) and collisional families in the Edgeworth–Kuiper belt. Directintegrations of trajectories of Kuiper belt objects (KBOs) reveal the 1:1(Trojan), 5:4, 4:3, 3:2 (Plutino), 5:3, 7:4, 9:5, 2:1 (Twotino), and 5:2 MMRsto be inhabited. Apart from the Trojan, resonant KBOs typically have largeorbital eccentricities and inclinations. The observed pattern of resonanceoccupation is consistent with resonant capture and adiabatic excitation bya migratory Neptune; however, the dynamically cold initial conditions priorto resonance sweeping that are typically assumed by migration simulationsare probably inadequate. Given the dynamically hot residents of the 5:2 MMRand the substantial inclinations observed in all exterior MMRs, a fraction ofthe primordial belt was likely dynamically pre-heated prior to resonancesweeping. A pre-heated population may have arisen as Neptune gravitationallyscattered objects into trans-Neptunian space. The spatial distribution of Twotinosoffers a unique diagnostic of Neptune's migration history. The Neptunian Trojanpopulation may rival the Jovian Trojan population, and the former's existence isargued to rule out violent orbital histories for Neptune. Finally, lowest-order seculartheory is applied to several hundred non-resonant KBOs with well-measured orbitsto update proposals of collisional families. No convincing family is detected.     

Coupling dynamical and collisional evolution of small bodies: II. Forming the Kuiper belt, the Scattered Disk and the Oort Cloud

The Oort Cloud, the Kuiper belt and the Scattered Disk are dynamically distinct populations of small bodies evolving in the outer regions of the Solar System. Whereas their collisional activity is now quiet, gravitational interactions with giant planets may have shaped these populations both dynamically and collisionally during their formation. Using a hybrid approach [Charnoz, S., Morbidelli, A., 2003. Icarus 166, 141-166], the present paper tries to couple the primordial collisional and dynamical evolution of these three populations in a self-consistent way. A critical parameter is the primordial size-distribution. We show that the initial planetesimal size distribution that allows an effective mass depletion of the Kuiper belt by collisional grinding, would decimate also the population of comet-size bodies that end in the Oort Cloud and, in particular, in the Scattered Disk. As a consequence, the Oort Cloud and the Scattered Disk would be too anemic, by a factor 20 to 100, relative to the estimates achieved from the observation of the fluxes of long period and Jupiter family comets, respectively. For these two reservoirs to have a sufficient number of comets, the initial size distribution in the planetesimal disk had to be such that the mass depletion by collisional erosion of the Kuiper belt was negligible. Consequently the current mass deficit of the Kuiper belt needs to be explained by dynamical mechanisms.     

From KBOs to Centaurs: The thermal connection

Abstract— We present results of thermal evolution calculations for objects originating in the Kuiper belt and transferring inwards, to the region of the outer planets. Kuiper belt objects (KBOs) are considered to be part of a reservoir that supplies the flux of small icy bodies, mainly Centaurs and Jupiter‐family comets, to regions interior to the orbit of Neptune. We study the internal thermal evolution, for ?10⁸ yr, of three typical KBOs and use the end state of the simulation as initial conditions for evolutionary calculations of two typical Centaurs. Some evolutionary trends can be identified for the KBOs, depending on key physical parameters, such as size and composition. The subsequent evolution in the Centaur region results in both specific features for each modeled object (mainly surface and sub‐surface composition) and common characteristics of thermally evolved Centaurs.     

A derivation of the luminosity function of the Kuiper belt from a broken power-law size distribution

We have derived a model of the Kuiper belt luminosity function exhibited by a broken power-law size distribution. This model allows direct comparison of the observed luminosity function to the underlying size distribution. We discuss the importance of the radial distribution model in determining the break diameter. We determine a best-fit break-diameter of the Kuiper belt size-distribution of 30<Db<90 km via a maximum-likelihood fit of our model to the observed luminosity function. We also confirm that the observed luminosity function for m(R)∼21-28 is consistent with a broken power-law size distribution, and exhibits a break at .     

Cometary nuclear magnitudes from sky survey observations

The determination of the nuclear magnitudes of comets, and with it nuclear size frequency distributions, is strongly complicated by cometary activity. By now, only nuclear size frequency distributions for Jupiter Family comets are available, and they are still subject of uncertainties. For comets of other dynamical classes, nuclear magnitudes are known for only a few comets. The size frequency distributions are thus not well constrained.In this work we study whether nuclear magnitudes of comets can be constrained from sky survey observations as published by the Minor Planet Center. Observations from sky survey programs in which the comet was classified as a point-like source are analyzed in this respect.From the available published observations from 1998 to 2008, we derive nuclear magnitudes, as well as nuclear radii, for 84 comets. Among these are comets of the Jupiter Family, dynamically old and new isotropic comets, Halley-type comets and Centaurs. For Jupiter Family comets and for isotropic comets, the size frequency distributions are presented.Uncertainties of derived nuclear magnitudes arise from photometry and from potentially undetected activity. However, a comparison with objects with well known nuclear parameters shows that, despite substantial observational uncertainties, nuclear magnitudes are constrained to ±0.6 mag, thereby providing first indications for nuclear sizes. This is particularly relevant for isotropic comets with so far ill-constrained size distributions. Exponents of the differential size frequency distributions of for Jupiter Family comets and for isotropic comets are presented. The values derived here form a basis for future, dedicated observational studies which provide higher measurement accuracy.     

Mass of the Kuiper belt

The Kuiper belt includes tens of thousand of large bodies and millions of smaller objects. The main part of the belt objects is located in the annular zone between 39.4 and 47.8 au from the Sun; the boundaries correspond to the average distances for orbital resonances 3:2 and 2:1 with the motion of Neptune. One-dimensional, two-dimensional, and discrete rings to model the total gravitational attraction of numerous belt objects are considered. The discrete rotating model most correctly reflects the real interaction of bodies in the Solar system. The masses of the model rings were determined within EPM2017—the new version of ephemerides of planets and the Moon at IAA RAS—by fitting spacecraft ranging observations. The total mass of the Kuiper belt was calculated as the sum of the masses of the 31 largest trans-Neptunian objects directly included in the simultaneous integration and the estimated mass of the model of the discrete ring of TNO. The total mass is \((1.97 \pm 0.35)\times 10^{-2} \ m_{\oplus }\). The gravitational influence of the Kuiper belt on Jupiter, Saturn, Uranus, and Neptune exceeds at times the attraction of the hypothetical 9th planet with a mass of \(\sim 10 \ m_{\oplus }\) at the distances assumed for it. It is necessary to take into account the gravitational influence of the Kuiper belt when processing observations and only then to investigate residual discrepancies to discover a possible influence of a distant large planet.     

Colors and collision rates within the Kuiper belt: problems with the collisional resurfacing scenario

We present a numerical check of the collisional resurfacing (CR) hypothesis proposed to explain the observed color diversity within the Kuiper Belt (where surface reddening due to space weathering is counteracted by regular resurfacing of neutral material after mutual collisions). Deterministic simulations are performed in order to estimate the relative spatial distribution of kinetic energy received by collisions, , for a population of target Kuiper Belt objects (KBOs) embedded in a swarm of impactors distributed within the belt. Four different impactor disks have been considered, depending on the excitation and the external limit of the belt and the density of the scattered KBOs (SKBOs) population. The obtained results are compared to the relative color index distribution within the observed Kuiper Belt, in order to derive possible similarities between the high vs low objects spatial distribution in our simulations and the bluer vs redder KBOs distribution in the “real” Kuiper Belt. Such similarities are found for several important features, in particular the general correlations between highly impacted objects and high rms excitation and low perihelion q values that are in good agreement with equivalent correlations found for the bluest objects of the observed belt. Nevertheless, simulations disagree with observations on two crucial points. (1) The plutinos are significantly more collisionally affected than the rest of our test KBO population, whereas there is no observed tendency toward bluer plutinos. (2) There is always a much stronger correlation between and eccentricities than inclinations, whereas observations show just the opposite feature. The presence of numerous SKBO impactors could significantly damp these problematic features, but cannot erase them. Whether these contradictions invalidate the whole CR scenario or not remains yet uncertain, since the physical processes at play are still far from being fully understood and the sample of available observational data is still relatively limited. But it seems nevertheless that the scenario might not hold in its simple present form.     

Discovery and rediscovery of Trojan asteroids

During 1987–1994, observational campaigns with different telescopes at several observatories have been initiated by the author in order to discover new Trojans. The importance of Trojan asteroids comes from celestial mechanics, where they represent the physical solution of the famous Lagrange triangular problem. Their importance lies also in the fact, that they may have some relation with comets. Furthermore, the Trojan belt may be as large as the belt of asteroids. Moreover, recently families have been discovered between the already well known Trojans. Enough reasons to continue to search for these interesting objects.     

The Effect of Sweeping Secular Resonances on the Classical Kuiper Belt

Abstract The Kuiper Belt is a disk of small icy objects orbiting the Sun beyond Neptune. The region between 40-48AU in this disk is supposed to consist of dynamical “cold” objects on low-inclination orbits and is called the “Classical Kuiper Belt”. Recent observations reveal that there is a “hot” population with inclinations being as large as 30? residing in this region. Secular resonance sweeping, which took place in the late stage of formation of the planetary system when the residual nebula gas was dispersing, is a possible mechanism that can excite the orbits in this region. In this paper, we investigate in detail the excitation of orbital inclination by this mechanism. It is shown that the excitation depends sensitively on the angle δ between the midplane of the nebula gas and the invariable plane of the solar system. The excitation is very small when δ = 0?, but if the gas midplane coincides with the ecliptic, i.e. if δ ≈ 1.6?, then objects in the region of classical Kuiper belt can be excited to orbital inclinations as high as 30?, provided the nebula gas has the proper initial density and disperses at a proper rate. We also considered the orbital excitation by secular resonance sweeping with Jupiter on an inclined orbit and with migrating Jovian planets, and found the excitation is only slightly affected.     

Monte Carlo Simulations of Oort Cloud Comets: the Influence of Mantle Blow-off on the Inclination Distribution of Jupiter Family

We have developed an efficient Monte Carlo method by which we can evaluate the evolution of comets. There are many poorly known evolutional parameters, and we have investigated the influence of these parameters on the final populations and the inclination distributions of short-period comets. We compare the observed and calculated inclination distributions of different comet populations and obtain a good fit for the inclinations of the Jupiter family comets by assuming a mantle blow-off and a sudden brightening of the comet when its perihelion distance is lowered in a major jump. This revised version was published online in July 2006 with corrections to the Cover Date.     

Collision with meteoroids as one of the possible mechanisms for the splitting of cometary nuclei

Results are presented of a statistical analysis of dynamic parameters for 114 comets with split nuclei. A list of the objects includes actually split comets, fragments of cometary pairs, lost comets with designation D, and comets with large-scale atmospheric features. Some aspects of the hypothesis that splitting is caused by collisions of cometary nuclei with meteoroid swarms are investigated. To verify the hypothesis, an analysis is conducted of the positions of split comets’ orbits relative to 58 meteor streams from Cook’s catalogue. The calculations give the number (N) of orbital nodes of split comets relative to the plane of each swarm within a distance of 0.001, 0.005, 0.01, 0.05, and 0.1 AU from each swarm. A special algorithm is proposed for determining the degree of redundancy of N by finding the expected value and dispersion for the number of the nodes. The comparison of N with the expected value, together with the consideration of the dispersion, reveals a redundancy of N in 29 cases. Therefore, collisions of comets with meteoroid swarms can be considered as one of the possible causes of comet splitting. A similar testing is conducted for the asteroid belt and Kuiper belt as potential sources of a vast number of sporadic meteoroids. Based on the results of the calculations, the former may be considered as the most effective region of splitting of periodic comets.     

Constraints on the Formation Regions of Comets from their D:H Ratios

Studies of the D:H ratio in H₂O within the Solar nebula provide a relationship between the degree of enrichment of deuterium and the distance from the young Sun. In the context of cometary formation, such models suggest that comets which formed in different regions of the Solar nebula should have measurably different D:H ratios. We aim to illustrate how the observed comets can give information about the formation regions of the reservoirs in which they originated. After a discussion of the current understanding of the regions in which comets formed, simple models of plausible formation regions for two different cometary reservoirs (the Edgeworth–Kuiper belt and the Oort Cloud) are convolved with a deuterium-enrichment profile for the pre-solar nebula. This allows us to illustrate how different formation regions for these objects can lead to great variations in the deuterium enrichment distributions that we would observe in comets today. We also provide an illustrative example of how variations in the population within a source region can modify the resulting observational profile. The convolution of a deuterium-enrichment profile with examples of proto-cometary populations gives a feel for how observations could be used to draw conclusions on the formation region of comets which are currently fed into the inner Solar system from at least two reservoirs. Such observations have, to date, been carried out on only three comets, but future work with instruments such as ALMA and Herschel should vastly improve the dataset, leading to a clearer consensus on the formation of the Oort cloud and Edgeworth–Kuiper belt.     

Trans-neptunian objects

Summary. The trans-neptunian objects (TNOs) constitute a new class of solar system object that was discovered only recently to exist beyond the orbit of Neptune. About 400 trans-neptunian objects have been detected over the past nine years and more than ten new objects are being discovered every month. All of the TNOs known to date fit into three dynamical classes: the classical, the resonant and the scattered objects. The total mass of the TNOs currently orbiting the Sun is estimated from the observed luminosity distribution to be of the order of 10–20% of the Earth's mass. However, theoretical investigations of the formation and evolution of the trans-neptunian belt into its currently observed shape suggest that it was much more massive in the past. The physical characterisation of TNOs starts to reveal some of the basic properties of these objects, such as size, shape and rotation and provides a first glance into the diversity of their surfaces. TNOs cover a very diverse range of colours, possibly reflecting different surface compositions. First evidence for the presence of water ice was found in a spectrum of one TNO while others do not show the characteristic absorption bands. The TNOs are now regarded as the likely source of some short-period comets. Owing to giant-planet and collisional perturbations, some TNOs may evolve into Centaurs, i.e. objects orbiting the Sun in the region between Jupiter and Neptune, which are further perturbed to become Jupiter-family short-period comets. Together with smaller debris generated by collisional shattering, the TNOs might represent a belt that has evolved from a more massive circumstellar disc into its present structure. Received 15 May 2001 / Published online 5 October 2001     

The colors of cometary nuclei—Comparison with other primitive bodies of the Solar System and implications for their origin

We present new color results of cometary nuclei obtained with the Hubble Space Telescope (HST) whose superior resolution enables us to accurately isolate the nucleus signals from the surrounding comae. By combining with scrutinized available data obtained with ground-based telescopes, we accumulated a sample of 51 cometary nuclei, 44 ecliptic comets (ECs) and 7 nearly-isotropic comets (NICs) using the nomenclature of Levison [Levison, H.F., 1996. In: Rettig, T.W., Hahn, J.M. (Eds.), Completing the Inventory of the Solar System. In: ASP Conf. Ser., vol. 107, pp. 173-192]. We analyze color distributions and color-color correlations as well as correlations with other physical parameters. We present our compilation of colors of 232 outer Solar System objects—separately considering the different dynamical populations, classical KBOs in low and high-inclination orbits (respectively CKBO-LI and CKBO-HI), resonant KBOs (practically Plutinos), scattered-disk objects (SDOs) and Centaurs—of 12 candidate dead comets, and of 85 Trojans. We perform a systematic analysis of all color distributions, and conclude by synthesizing the implications of the dynamical evolution and of the colors for the origin of the minor bodies of the Solar System. We find that the color distributions are remarkably consistent with the scenarios of the formation of TNOs by Gomes [Gomes, R.S., 2003. Icarus 161, 404-418] generalized by the “Nice” model [Levison, H.F., Morbidelli, A., VanLaerhoven, Ch., Gomes, R., Tsiganis, L., 2008. Icarus 196, 258-273], and of the Trojans by Morbidelli et al. [Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465]. The color distributions of the Centaurs are globally similar to those of the CKBO-HI, the Plutinos and the SDOs. However the potential bimodality of their distributions allows to possibly distinguish two groups based on their (B−R) index: Centaur I with (B−R)>1.7 and Centaurs II with (B−R)<1.4. Centaurs I could be composed of TNOs (prominently CKBO-LI) and ultra red objects from a yet unstudied family. Centaurs II could consist in a population of evolved objects which have already visited the inner Solar System, and which has been scattered back beyond Jupiter. The diversity of colors of the ECs, in particular the existence of very red objects, is consistent with an origin in the Kuiper belt. Candidate dead comets represent an ultimate state of evolution as they appear more evolved than the Trojans and Centaurs II.     

Neptune migration model with one extra planet

We explore conventional Neptune migration model with one additional planet of mass at 0.1-2.0M_⊕. This planet inhabited in the 3:2 mean motion resonance with Neptune during planet migration epoch, and then escaped from the Kuiper belt when jovian planets parked near the present orbits. Adding this extra planet and assuming the primordial disk truncated at about 45 AU in the conventional Neptune migration model, it is able to explain the complex structure of the observed Kuiper belt better than the usual Neptune migration model did in several respects, which are the following. (1) High-inclination Plutinos with i?15-35° are produced. (2) Generating the excitation of the classical Kuiper belt objects, which have moderate eccentricities and inclinations. (3) Producing the larger ratio of Neptune’s 3:2 to 2:1 resonant particles, and the lower ratio of particles in the 3:2 resonance to those in the classical belt, which may be more consistent with observations. (4) Finally, several Neptune’s 5:2 resonant particles are obtained. However, numerical experiments imply that this model is a low-probability event. In addition to the low probability, two features produced by this model may be inconsistent with the observations. They are small number of low-inclination particles in the classical belt, and the production of a remnant population with near-circular and low-inclination orbit within . According to our present study, including one extra planet in the conventional Neptune migration model as the scenario we explored here may be unsuitable because of the low probability, and the two drawbacks mentioned above, although this model can explain better several features which is hard to produce by the conventional Neptune migration model. The issues of low-probability event and the lack of low-inclination KBOs in the classical belt are interesting and may be studied further under a more realistic consideration.     

Masses of the Main Asteroid Belt and the Kuiper Belt from the Motions of Planets and Spacecraft

Dynamicalmass estimates for the main asteroid belt and the trans-Neptunian Kuiper belt have been found from their gravitational influence on the motion of planets. Discrete rotating models consisting ofmovingmaterial points have been used tomodel the total attraction fromsmall or as yet undetected bodies of the belts. The masses of the model belts have been included in the set of parameters being refined and determined and have been obtained by processing more than 800 thousand modern positional observations of planets and spacecraft. We have processed the observations and determined the parameters based on the new EPM2017 version of the IAA RAS planetary ephemerides. The large observed radial extent of the belts (more than 1.2 AU for the main belt and more than 8 AU for the Kuiper belt) and the concentration of bodies in the Kuiper belt at a distance of about 44 AU found from observations have been taken into account in the discrete models. We have also used individual mass estimates for large bodies of the belts as well as for objects that spacecraft have approached and for bodies with satellites. Our mass estimate for the main asteroid belt is (4.008 ± 0.029) × 10^?4/m_⊕ (3σ). The bulk of the Kuiper belt objects are in the ring zone from 39.4 to 47.8 AU. The estimate of its total mass together with the mass of the 31 largest trans-Neptunian Kuiper belt objects is (1.97 ± 0.30) × 10^?2m_⊕ (3σ), which exceeds the mass of the main asteroid belt almost by a factor of 50. The mass of the 31 largest trans-Neptunian objects (TNOs) is only about 40% of the total one.     

Tidal Breakup of Comets

In the context of the survival of periodic comets of different origins, rotational breakup and tidal disruption could be important, especially of the short period comets injected from the Kuiper belt. This is because long-period comets from the distant Oort cloud tend to be subject to thermal stress and volatile 'explosion' far more severely. A simple calculation using the Öpik method of random planetary close encounters was performed to estimate the probability of tidal disruption of comets and scattered Kuiper belt objects (SKBOs) during their orbital migration. It was found that a large fraction of the short period comets and SKBOs might have been internally fragmented by single or multiple close encounters with the outer planets.     

Resonance and Capture of Jupiter Comets

A number of Jupiter family comets such as Otermaand Gehrels 3make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L ₁and L ₂, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L ₁and L ₂is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L ₁and the other around L ₂) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold tubes associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit.     

Considerations on the magnitude distributions of the Kuiper belt and of the Jupiter Trojans

By examining the absolute magnitude (H) distributions (hereafter HD) of the cold and hot populations in the Kuiper belt and of the Trojans of Jupiter, we find evidence that the Trojans have been captured from the outer part of the primordial trans-neptunian planetesimal disk. We develop a sketch model of the HDs in the inner and outer parts of the disk that is consistent with the observed distributions and with the dynamical evolution scenario known as the ‘Nice model’. This leads us to predict that the HD of the hot population should have the same slope of the HD of the cold population for 6.5<H<9, both as steep as the slope of the Trojans' HD. Current data partially support this prediction, but future observations are needed to clarify this issue. Because the HD of the Trojans rolls over at H∼9 to a collisional equilibrium slope that should have been acquired when the Trojans were still embedded in the primordial trans-neptunian disk, our model implies that the same roll-over should characterize the HDs of the Kuiper belt populations, in agreement with the results of Bernstein et al. [Bernstein, G.M., and 5 colleagues, 2004. Astron. J. 128, 1364-1390] and Fuentes and Holman [Fuentes, C.I., Holman, M.J., 2008. Astron. J. 136, 83-97]. Finally, we show that the constraint on the total mass of the primordial trans-neptunian disk imposed by the Nice model implies that it is unlikely that the cold population formed beyond 35 AU.     

The Common Origin of the High Inclination TNO's

Numerical integrations of the four major planets orbits inside a primordialplanetesimals disk show that a fraction of Neptune primordial scatteredobjects are deposited into the classical Kuiper Belt at Solar System age. Theseobjects exhibit inclinations as high as 40° and can account forpresent high inclinations population in the classical Kuiper Belt. The samemechanism can also originate high perihelion scattered objects like 2000 CR₁₀₅. The process that in the end produced such objects can be divided into two phases, a migration phase where nonconservative dynamics acted to producesome stable objects already at 10⁸ years and a nonmigrating phase that helped to establish some other objects as stable TNO's. Low inclination CKBO's have inprinciple an origin through the resonance sweeping process, although someresults from numerical integrations at least suggest a possible origin also fromthe primordial Neptune scattered population.