Formation of the Kuiper Belt by Long Time-Scale Migration of Jovian Planets

The orbital migration of Jovian planets is believed to have played an important role in shaping the Kuiper Belt. We investigate the effects of the long time-scale (2×107 yr) migration of Jovian planets on the orbital evolution of massless test particles that are initially located beyond 28 AU. Because of the slowness of the migration, Neptune's mean motion resonances capture test particles very efficiently. Taking into account the stochastic behavior during the planetary migration and for proper parameter values, the resulting concentration of objects in the 3:2 resonance is prominent, while very few objects enter the 2:1 resonance, thus matching the observed Kuiper Belt objects very well. We also find that such a long time-scale migration is favorable for exciting the inclinations of the test particles, because it makes the secular resonance possible to operate during the migration. Our analyses show that the v8 secular resonance excites the eccentricities of some test particles, so decreasing their perihelion distances, leading to close encounters with Neptune, which can then pump the inclinations up to 20℃.     

Formation of the resonant populations in the Kuiper belt: gas-drag-induced resonant capture

On the basis of their orbital elements, present-day Kuiper belt objects can be grouped into distinct dynamical classes: classical, resonant and scattered ones. Jiang & Yeh have proposed gas-drag-induced resonant capture in a protostellar disc analogous to the primordial solar nebula as a mechanism able to explain the dominant 3:2 resonant population observed in Kuiper belt objects. de la Fuente Marcos & de la Fuente Marcos further investigated the drag-induced mechanism numerically. Our significant contribution is a hydrodynamic theory derivation of results obtained in the Jiang & Yeh and de la Fuente Marcos & de la Fuente Marcos numerical simulations.     

The origin of the Kuiper Belt high-inclination population

I simulate the orbital evolution of the four major planets and a massive primordial planetesimal disk composed of 10⁴ objects, which perturb the planets but not themselves. As Neptune migrates by energy and angular momentum exchange with the planetesimals, a large number of primordial Neptune-scattered objects are formed. These objects may experience secular, Kozai, and mean motion resonances that induce temporary decrease of their eccentricities. Because planets are migrating, some planetesimals can escape those resonances while in a low-eccentricity incursion, thus avoiding the return path to Neptune close encounter dynamics. In the end, this mechanism produces stable orbits with high inclination and moderate eccentricities. The population so formed together with the objects coming from the classical resonance sweeping process, originates a bimodal distribution for the Kuiper Belt orbits. The inclinations obtained by the simulations can attain values above 30° and their distribution resembles a debiased distribution for the high-inclination population coming from the real classical Kuiper Belt.     

The dynamical stability of a Kuiper Belt-like region

The dynamics of the Kuiper Belt region between 33 and 63 au is investigated just taking into account the gravitational influence of Neptune. Indeed the aim is to analyse the information which can be drawn from the actual exoplanetary systems, where typically physical and orbital data of just one or two planets are available. Under this perspective we start our investigation using the simplest three-body model (with Sun and Neptune as primaries), adding at a later stage the eccentricity of Neptune and the inclinations of the orbital planes to evaluate their effects on the Kuiper Belt dynamics. Afterwards we remove the assumption that the orbit of Neptune is Keplerian by adding the effect of Uranus through the Lagrange–Laplace solution or through a suitable resonant normal form. Finally, different values of the mass ratios of the primary to the host star are considered in order to perform a preliminary analysis of the behaviour of exoplanetary systems. In all cases, the stability is investigated by means of classical tools borrowed from dynamical system theory, like Poincaré mappings and Lyapunov exponents.     

The Kuiper Belt luminosity function from mR= 22 to 25

In summer 1999, we performed a survey optimized for the discovery of irregular satellites of Uranus and Neptune. We imaged 11.85 deg² of sky and discovered 66 new outer Solar system objects (not counting the three new Uranian satellites). Given the very short orbital arcs of our observations, only the heliocentric distance can be reliably determined. We were able to model the radial distribution of trans-Neptunian objects (TNOs). Our data support the idea of a strong depletion in the surface density beyond 45 au.
After fully characterizing this survey's detection efficiency as a function of object magnitude and rate of motion, we find that the apparent luminosity function of the trans-Neptunian region in the range   m_R = 22–25  is steep with a best-fitting cumulative power-law index of  α≃ 0.76  with one object per deg² estimated at magnitude   R _o= 23.3  . This steep slope, corresponding to a differential size index of   q ≃ 4.8  , agrees with other older and more recent analyses for the luminosity function brighter than 25 mag. A double power-law fit to the new data set turns out to be statistically unwarrented; this large and homogeneous data set provides no evidence for a break in the power-law slope, which must eventually occur if the Bernstein et al. sky density measurements are correct.     

A stability study of Kuiper Belt binaries

The dynamical structure of the orbital element space of seven Kuiper Belt binary systems is studied by numerical methods in the model of the spatial elliptic restricted three‐body problem. It is shown that three systems have an extended region of stability where additional satellites could exist. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

长期共振迁移对经典Kuiper带的影响

太阳星云气体的耗散可以引起长期共振迁移(secular resonance sweeping,SRS),当长期共振的位置扫过经典Kuiper带小天体(Kuiper Belt objects,KBOs),就会激发其轨道倾角.详细研究了在太阳系紧致构形中(指四个大行星轨道彼此相距较小的状态)SRS对经典KBOs轨道倾角的激发过程,发现KBOs轨道倾角受激发的程度敏感地依赖于星云气体中面与太阳系不变平面1的夹角δ:当星云气体中面与不变平面重合,即δ=0时,经典KBOs倾角受到的激发很小;而当星云气体中面与黄道面重合,即δ≈1.6°时,在合理的初始条件下,经典KBOs的倾角最高可以被激发到30°以上.另外,通过模拟木星具有较大轨道倾角的情形以及SRS和大行星轨道迁移同时发生的情形,发现对于经典KBOs倾角的受激发程度而言,它们两者的影响都远弱于δ.     

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 effect on the Edgeworth–Kuiper Belt of a large distant tenth planet

We investigate the orbital evolution of both real and hypothetical Edgeworth–Kuiper Objects in order to determine whether any conclusions can be drawn regarding the existence, or otherwise, of the tenth planet postulated by Murray. We find no qualitative difference in the orbital evolution, and so conclude that the hypothetical planet has been placed on an orbit at such a large heliocentric distance that no evidence for the existence, or non-existence, can be found from a study of the known Edgeworth–Kuiper Objects.     

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。     

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.     

The history of the Solar system's debris disc: observable properties of the Kuiper belt

The Nice model of Gomes et al. suggests that the migration of the giant planets caused a planetesimal clearing event, which led to the late heavy bombardment (LHB) at 880 Myr. Here, we investigate the infrared emission from the Kuiper belt during the history of the Solar system as described by the Nice model. We describe a method for easily converting the results of N -body planetesimal simulations into observational properties (assuming blackbody grains and a single size distribution) and further modify this method to improve its realism (using realistic grain properties and a three-phase size distribution). We compare our results with observed debris discs and evaluate the plausibility of detecting an LHB-like process in extrasolar systems. Recent surveys have shown that 4 per cent of stars exhibit 24 μm excess and 16 per cent exhibit 70 μm excess. We show that the Solar system would have been amongst the brightest of these systems before the LHB at both 24 and 70 μm. We find a significant increase in 24 μm emission during the LHB, which rapidly drops off and becomes undetectable within 30 Myr, whereas the 70 μm emission remains detectable until 360 Myr after the LHB. Comparison with the statistics of debris disc evolution shows that such depletion events must be rare occurring around less than 12 per cent of Sun-like stars and with this level of incidence we would expect approximately one of the 413 Sun-like field stars so far detected to have a 24 μm excess to be currently going through an LHB. We also find that collisional processes are important in the Solar system before the LHB and that parameters for weak Kuiper belt objects are inconsistent with the Nice model interpretation of the LHB.     

Dynamical determination of the mass of the Kuiper Belt from motions of the inner planets of the Solar system

In this paper we determine dynamically the mass of the Kuiper Belt Objects by exploiting the latest least-squares determinations of the extra rates of perihelia of the inner planets of the Solar system. By modelling classical Kuiper Belt Objects as an ecliptic ring of finite thickness, we obtain 0.033 ± 0.115 in units of terrestrial masses. For resonant Kuiper Belt Objects, a two-ring model yields 0.018 ± 0.063. These values are consistent with recent determinations obtained using ground- and space-based optical techniques. Some implications for precise tests of Einsteinian and post-Einsteinian gravity are briefly discussed.     

Possible patterns in the distribution of planetary formation regions

Eris, an object larger than Pluto, is known to reside in the transneptunian region further away than Pluto. One can wonder whether its semimajor orbital axis fits in a generalized Titius–Bode law, in the same way as Pluto does. We performed a new least-squares fit to a generalized Titius–Bode law including Eris and found that not only does Eris fit in the trend, but also the correlation coefficient improves. In addition, there is a remarkable symmetry of the location of the planetary formation regions with respect to Jupiter when the natural logarithm of the heliocentric distance is used as the metric. The issue of whether the observed patterns have some physical meaning or are due to mere chance is addressed using a Monte Carlo approach identical to that of Lynch. Although the probability of chance occurrence is highly dependent on the way in which the random configurations of synthetic planetary systems are selected, we find that in all reasonable scenarios of random planetary systems the probability of chance occurrence of the observed patterns is small (below 1 per cent in most cases). If the trend were used as a prediction tool, one might expect another planet or dwarf planet or a swarm of bodies with semimajor orbital axis of 120 ± 20 au. Simple calculations show that the protoplanetary nebula most likely had enough mass to allow the accretion of at least a dwarf planet at that distance. We also found that if the surface density of the nebula decayed with heliocentric distance ( r ) as a power of −2, the regular spacing in ln  r in the Solar system could be a natural consequence of the existence of a threshold mass for planetary formation.