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.     

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.     

Simulations for the Original Distribution of KBOs

Using the N-body dynamical model that includes the sun, the 8 planets, Pluto, UB313 and massless particles, we simulate the orbital evolution of 551 Kuiper Belt Objects (KBOs) with known parameters. The initial conditions of the simulations are the currently observed orbital parameters. The integration backtracks from now to -10×10⁸ yr. The results show that about 10×10⁸ years ago, more than 1/3 of the presently observed KBOs resided in the region of the present Kuiper main belt, a few were located inside the Neptune orbit, and the rest were beyond 50AU; and that about 4.5×10⁸ years ago, all the objects in the Kuiper main belt exhibited a rather good normal distribution, without so many objects concentrated in the Neptune's 3:2 resonance region, as at present time.     

High albedos of low inclination Classical Kuiper belt objects

We present observations of thermal emission from fifteen transneptunian objects (TNOs) made using the Spitzer Space Telescope. Thirteen of the targets are members of the Classical population: six dynamically hot Classicals, five dynamically cold Classicals, and two dynamically cold inner Classical Kuiper belt objects (KBOs). We fit our observations using thermal models to determine the sizes and albedos of our targets finding that the cold Classical KBOs have distinctly higher visual albedos than the hot Classicals and other TNO dynamical classes. The cold Classicals are known to be distinct from other TNOs in terms of their color distribution, size distribution, and binarity fraction. The Classical objects in our sample all have red colors yet they show a diversity of albedos which suggests that there is not a simple relationship between albedo and color. As a consequence of high albedos, the mass estimate of the cold Classical Kuiper belt is reduced from approximately 0.01 M_⊕ to approximately 0.001 M_⊕. Our results also increase significantly the sample of small Classical KBOs with known albedos and sizes from 21 to 32 such objects.     

两个可能存在大质量类冥王星的区域

1992年以来，在海王星外的太阳系发现了近千个小天体，称为Kuiper带天体(KBO)或Edgeworth—Kuiper带天体，其中有一部分偏心率和倾角较大的小天体与海王星之间存在3：2平运动共振，轨道特征类似冥王星，命名为类冥王星，自KBO发现以来，天文学家们进行了多次小天区的搜索，发现了几个质量较大的KBO，通过数值计算，在轨道参数空间发现了两个和冥王星一样同时具有3种共振的区域，在这两个区域里的小天体既避免了海王星的强摄动又不会与冥王星密切交会，轨道非常稳定，因此有可能在其中发现质量较大的类冥王星。     

Kuiper带天体的轨道分布特性

1992年9月,夏威夷大学的D.Jewitt和加利福尼亚大学的J.Lun发现了海王星外绕太阳运行的第一个小天体1992QB1[1],开创了人类对于海王星外天体的实际观测的研究.近10年的接连不断发现,已经证实了海王星轨道外面存在着一个由大量的环绕太阳运动的小天体组成的环带[2].由于G.P.Kuiper曾在1951年的文章中提出过在冥王星的外边可能存在小天体的问题,因此人们一般把这个环带称为Kuiper带,你这些天体为“KuiperBelt　Objects”(KBOs),或从逻辑上称它们为“Trans-NeptunianObjects”(TNOs)[3]     

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.     

The luminosity function of the hot and cold Kuiper belt populations

We have performed an ecliptic survey of the Kuiper belt, with an areal coverage of 8.9 square degrees to a 50% limiting magnitude of , and have detected 88 Kuiper belt objects, roughly half of which received follow-up 1–2 months after detection. Using this survey data alone, we have measured the luminosity function of the Kuiper belt, thus avoiding any biases that might come from the inclusion of other observations. We have found that the Cold population defined as having inclinations less than 5° has a luminosity function slope α_Cold = 0.82 ± 0.23, and is different from the Hot population, which has inclinations greater than 5° and a luminosity function slope α_Hot = 0.35 ± 0.21. As well, we have found that those objects closer than 38 AU have virtually the same luminosity function slope as the Hot population. This result, along with similar findings of past surveys demonstrates that the dynamically Cold Kuiper belt objects likely have a steep size distribution, and are unique from all of the excited populations which have much shallower distributions. This suggests that the dynamically excited population underwent a different accretion history and achieved a more evolved state of accretion than the Cold population. As well, we discuss the similarities of the Cold and Hot populations with the size distributions of other planetesimal populations. We find that while the Jupiter family comets and the scattered disk exhibit similar size distributions, a power-law extrapolation to small sizes for the scattered disk cannot account for the observed influx of comets. As well, we have found that the Jupiter Trojan and Hot populations cannot have originated from the same parent population, a result that is difficult to reconcile with scattering models similar to the NICE model. We conclude that the similarity between the size distributions of the Cold population and the Jupiter Trojan population is a striking coincidence.     

Collisional velocities and rates in resonant planetesimal belts

We consider a belt of small bodies (planetesimals, asteroids, dust particles) around a star, captured in one of the external or 1:1 mean-motion resonances with a massive perturber (protoplanet, planet). The objects in the belt collide with each other. Combining methods of celestial mechanics and statistical physics, we calculate mean collisional velocities and mean collisional rates, averaged over the belt. The results are compared to collisional velocities and rates in a similar, but non-resonant belt, as predicted by the particle-in-a-box method. It is found that the effect of the resonant lock on the velocities is rather small, while on the rates more substantial. At low to moderate eccentricities and libration amplitudes of tens of degrees, which are typical of many astrophysical applications, the collisional rates between objects in an external resonance are by about a factor of two higher than those in a similar belt of objects not locked in a resonance. For Trojans under the same conditions, the collisional rates may be enhanced by up to an order of magnitude. The collisional rates increase with the decreasing libration amplitude of the resonant argument, depend on the eccentricity distribution of objects, and vary from one resonance to another. Our results imply, in particular, shorter collisional lifetimes of resonant Kuiper belt objects in the solar system and higher efficiency of dust production by resonant planetesimals in debris disks around other stars.     

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.     

Origin of scattered disk resonant TNOs: Evidence for an ancient excited Kuiper belt of 50 AU radius

Resonance occupation of trans-neptunian objects (TNOs) in the scattered disk (>48 AU) was investigated by integrating the orbits of 85 observed members for 4 Gyr. Twenty seven TNOs were locked in the 9:4, 16:7, 7:3, 12:5, 5:2, 8:3, 3:1, 4:1, 11:2, and 27:4 resonances. We then explored mechanisms for the origin of the resonant structure in the scattered disk, in particular the long-term 9:4, 5:2, and 8:3 resonant TNOs (median 4 Gyr), by performing large scale simulations involving Neptune scattering and planetary migration over an initially excited planetesimals disk (wide range of eccentricities and inclinations). To explain the formation of Gyr-resident populations in such distant resonances, our results suggest the existence of a primordial planetesimal disk of at least 45-50 AU radius that suffered a dynamical perturbation leading to 0.1-0.3 or greater eccentricities and a range of inclinations up to ∼20° during early stages of the Solar System history, before planetary migration.     

Kuiper带天体的轨道动力学

主要评述太阳系动力学研究的一个新方向——Kuiper带的轨道动力学。早期的研究是为了探讨短周期彗星的起源。在发现第一颗Kuiper带小天体之后，人们开始将注意力转到Kuiper带共振区的相空间结构上，Morbidelli和Malhotra分别采用不同的模型研究了这些共振区的大小。其中主要研究对象是3:2共振区。冥王星也处在这一共振区中。从冥王星的轨道特性来看，冥王星应是一颗较大的Kuiper带天体，它还拥有另外两种共振——Kozai共振和1：1超级共振。正是由于这些共振的存在，冥王星的运动才得以长期保持稳定。观测表明许多Kuiper带天体也处的海王星的平运动共振中。早期的理论认为这些平运动共振起源于灾难性事件，如碰撞。然而这都是一些小概率事件，无法对共振的形成进行合理的解释。Malhotra通过行星迁移成功地解释了冥王星被共振俘获的机制。这一机制的概率非常大，同样可以用来解释Kuiper带天体共振的形成。     

Origin of the structure of the Kuiper belt during a dynamical instability in the orbits of Uranus and Neptune

We explore the origin and orbital evolution of the Kuiper belt in the framework of a recent model of the dynamical evolution of the giant planets, sometimes known as the Nice model. This model is characterized by a short, but violent, instability phase, during which the planets were on large eccentricity orbits. It successfully explains, for the first time, the current orbital architecture of the giant planets [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461], the existence of the Trojans populations of Jupiter and Neptune [Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465], and the origin of the late heavy bombardment of the terrestrial planets [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466-469]. One characteristic of this model is that the proto-planetary disk must have been truncated at roughly 30 to 35 AU so that Neptune would stop migrating at its currently observed location. As a result, the Kuiper belt would have initially been empty. In this paper we present a new dynamical mechanism which can deliver objects from the region interior to ∼35 AU to the Kuiper belt without excessive inclination excitation. In particular, we show that during the phase when Neptune's eccentricity is large, the region interior to its 1:2 mean motion resonance becomes unstable and disk particles can diffuse into this area. In addition, we perform numerical simulations where the planets are forced to evolve using fictitious analytic forces, in a way consistent with the direct N-body simulations of the Nice model. Assuming that the last encounter with Uranus delivered Neptune onto a low-inclination orbit with a semi-major axis of ∼27 AU and an eccentricity of ∼0.3, and that subsequently Neptune's eccentricity damped in ∼1 My, our simulations reproduce the main observed properties of the Kuiper belt at an unprecedented level. In particular, our results explain, at least qualitatively: (1) the co-existence of resonant and non-resonant populations, (2) the eccentricity-inclination distribution of the Plutinos, (3) the peculiar semi-major axis—eccentricity distribution in the classical belt, (4) the outer edge at the 1:2 mean motion resonance with Neptune, (5) the bi-modal inclination distribution of the classical population, (6) the correlations between inclination and physical properties in the classical Kuiper belt, and (7) the existence of the so-called extended scattered disk. Nevertheless, we observe in the simulations a deficit of nearly-circular objects in the classical Kuiper belt.     

Inner Solar System dynamical analogs of plutinos

By studying orbits of asteroids potentially in 3:2 exterior mean motion resonance with Earth, Venus, and Mars, we have found plutino analogs. We identify at least 27 objects in the inner Solar System dynamically protected from encounter through this resonance. These are four objects associated with Venus, six with Earth, and seventeen with Mars. Bodies in the 3:2 exterior resonance (including those in the plutino resonance associated with Neptune) orbit the Sun twice for every three orbits of the associated planet, in such a way that with sufficiently low libration amplitude close approaches to the planet are impossible. As many as 15% of Kuiper Belt objects share the 3:2 resonance, but are poorly observed. One of several resonance sweeping mechanisms during planetary migration is likely needed to explain the origin and properties of 3:2 resonant Kuiper Belt objects. Such a mechanism likely did not operate in the inner Solar System. We suggest that scattering by the next planet out allows entry to, and exit from, 3:2 resonance for objects associated with Venus or Earth. 3:2 resonators of Mars, on the other hand, do not cross the paths of other planets, and have a long lifetime. There may exist some objects trapped in the 3:2 Mars resonance which are primordial, with our tests on the most promising objects known to date indicating lifetimes of at least tens of millions of years. Identifying 3:2 resonant systems in the inner Solar System permits this resonance to be studied on shorter timescales and with better determined orbits than has been possible to date, and introduces new mechanisms for entry into the resonant configuration.     

On the detectability of lightcurves of Kuiper belt objects

We present a statistical study of the detectability of lightcurves of Kuiper belt objects (KBOs). Some Kuiper belt objects display lightcurves that appear “flat”; i.e., there are no significant brightness variations within the photometric uncertainties. Under the assumption that KBO lightcurves are mainly due to shape, the lack of brightness variations may be due to (1) the objects having very nearly spherical shapes or (2) their rotation axes coinciding with the line of sight. We investigate the relative importance of these two effects and relate it to the observed fraction of “flat” lightcurves. This study suggests that the fraction of KBOs with detectable brightness variations may provide clues about the shape distribution of these objects. Although the current database of rotational properties of KBOs is still insufficient to draw any statistically meaningful conclusions, we expect that, with a larger dataset, this method will provide a useful test for candidate KBO shape distributions.     

On The Origin of The High-Perihelion Scattered Disk: The Role of The Kozai Mechanism And Mean Motion Resonances

We study the transfer process from the scattered disk (SD) to the high-perihelion scattered disk (HPSD) (defined as the population with perihelion distances q > 40 AU and semimajor axes a>50 AU) by means of two different models. One model (Model 1) assumes that SD objects (SDOs) were formed closer to the Sun and driven outwards by resonant coupling with the accreting Neptune during the stage of outward migration (Gomes 2003b, Earth, Moon, Planets 92, 29–42.). The other model (Model 2) considers the observed population of SDOs plus clones that try to compensate for observational discovery bias (Fernández et al. 2004, Icarus , in press). We find that the Kozai mechanism (coupling between the argument of perihelion, eccentricity, and inclination), associated with a mean motion resonance (MMR), is the main responsible for raising both the perihelion distance and the inclination of SDOs. The highest perihelion distance for a body of our samples was found to be q = 69.2 AU. This shows that bodies can be temporarily detached from the planetary region by dynamical interactions with the planets. This phenomenon is temporary since the same coupling of Kozai with a MMR will at some point bring the bodies back to states of lower-q values. However, the dynamical time scale in high-q states may be very long, up to several Gyr. For Model 1, about 10% of the bodies driven away by Neptune get trapped into the HPSD when the resonant coupling Kozai-MMR is disrupted by Neptune’s migration. Therefore, Model 1 also supplies a fossil HPSD, whose bodies remain in non-resonant orbits and thus stable for the age of the solar system, in addition to the HPSD formed by temporary captures of SDOs after the giant planets reached their current orbits. We find that about 12 – 15% of the surviving bodies of our samples are incorporated into the HPSD after about 4 – 5 Gyr, and that a large fraction of the captures occur for up to the 1:8 MMR (a ⋍ 120 AU), although we record captures up to the 1:24 MMR (a ≃ 260 AU). Because of the Kozai mechanism, HPSD objects have on average inclinations about 25°–50°, which are higher than those of the classical Edgeworth–Kuiper (EK) belt or the SD. Our results suggest that Sedna belongs to a dynamically distinct population from the HPSD, possibly being a member of the inner core of the Oort cloud. As regards to 2000 CR₁₀₅ , it is marginally within the region occupied by HPSD objects in the parametric planes (q,a) and (a,i), so it is not ruled out that it might be a member of the HPSD, though it might as well belong to the inner core.     

On the origin of the Kuiper belt

I review the work that has been done so far aiming at the understanding of the origin of the Kuiper belt. Three peculiar characteristics of the Kuiper belt are used as constraints for the formation models. These are the unexpected dynamical excitation of the orbits, the Kuiper belt outer edge near the 1:2 resonance with Neptune and the mass paucity of the belt. Among the various scenarios proposed, those based on a primordial planetary migration give the best results. In particular, the Nice model is analyzed with respect to its coherence with the present characteristics of the belt. Special attention is given to the controversy on the origin of the Kuiper belt cold population.     

Steady-state size distributions for collisional populations:: analytical solution with size-dependent strength

The steady-state population of bodies resulting from a collisional cascade depends on how material strength varies with size. We find a simple expression for the power-law index of the population, given a power law that describes how material strength varies with size. This result is extended to the case relevant for the asteroid belt and Kuiper belt, in which the material strength is described by 2 separate power laws—one for small bodies and one for larger bodies. We find that the power-law index of the small body population is unaffected by the strength law for the large bodies, and vice versa. Simple analytical expressions describe a wave that is superimposed on the large body population because of the transition between the two power laws describing the strength. These analytical results yield excellent agreement with a numerical simulation of collisional evolution. These results will help to interpret observations of the asteroids and KBOs, and constrain the strength properties of those objects.     

Thermal evolution of Kuiper belt objects, with implications for cryovolcanism

We investigate the internal thermal evolution of Kuiper belt objects (KBOs), small (radii <1000 km), icy (mean densities ) bodies orbiting beyond Neptune, focusing on Pluto's moon Charon in particular. Our calculations are time-dependent and account for differentiation. We review evidence for ammonia hydrates in the ices of KBOs, and include their effects on the thermal evolution. A key finding is that the production of the first melt, at the melting point of ammonia dihydrate, ≈176 K, triggers differentiation of rock and ice. The resulting structure comprises a rocky core surrounded by liquids and ice, enclosed within a >100-km thick undifferentiated crust of rock and ice. This structure is especially conducive to the retention of subsurface liquid, and bodies the size of Charon or larger (radii >600 km) are predicted to retain some subsurface liquid to the present day. We discuss the possibility that this liquid can be brought to the surface rapidly via self-propagating cracks. We conclude that cryovolcanism is a viable process expected to affect the surfaces of large KBOs including Charon.     

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.