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.     

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.     

Population of the Scattered Kuiper Belt

We study how the internal structure of dark halos is affected if cold dark matter particles are assumed to have a large cross section for elastic collisions. We identify a cluster halo in a large cosmological N-body simulation and resimulate its formation with progressively increasing resolution. We compare the structure found in the two cases in which dark matter is treated as collisionless or as a fluid. For the collisionless case, the overall ellipticity of the cluster, the central density cusp, and the amount of surviving substructure are all similar to those found in earlier high-resolution simulations. Collisional dark matter results in a cluster that is more nearly spherical at all radii, has a steeper central density cusp, and has less-but still substantial-surviving substructure. As in the collisionless case, these results for a "fluid" cluster halo are expected to carry over approximately to smaller mass systems. The observed rotation curves of dwarf galaxies then argue that self-interacting dark matter can only be viable if intermediate cross sections produce structure that does not lie between the extremes we have simulated.     

Extrasolar Analogues to the Kuiper Belt

Debris disks are found around some 15% of main sequencestars and their dust is thought to be continuallyreplenished in collisions between planetesimals inextrasolar Kuiper belts.While they were discovered in 1984 by IRAS, it is onlywith more recent imaging that their true nature has beenrevealed. This paper discusses recent debris disk images andtheir impact on our understanding of extrasolar systems.Importantly these images confirm the extrasolar Kuiper belthypothesis for most (but not all) debris diskcandidates and show that the planetesimals within thesedisks must have grown to at least a few km.Asymmetries in imaged disk structures also provide informationabout the planetary systems orbiting inside these planetesimalbelts. The impact of debris disk studies on our understandingof the evolution of our own Kuiper belt, as well as theirpotential to solve puzzles such as the origin of the missingmass and the outer edge of the Kuiper belt, is alsodiscussed.     

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。     

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.     

柯伊伯带结构形成动力学

柯伊伯带是指位于海王星轨道外的小天体构成的盘状区域.一般认为柯伊伯带小天体是早期太阳系物质凝聚成各大行星后的残留物,因此这些小天体能够为研究外太阳系的形成与演化提供很多重要的线索.该文首先介绍了柯伊伯带的发现历史及它的主要观测特征,然后回顾了近年来提出的形成这些特征的机制,最后讨论了柯伊伯带中有待解释的主要问题.     

Kuiper带小天体动力演化

Kuiper带是指太阳系内位于离太阳 30～ 50AU一个区域。 1 992年该区域陆续发现了一群半径在几十到几百公里的小天体。这些小天体在Kuiper带的分布是极其不均匀的。Kuiper带小天体的发现对人们认识太阳系的形成与演化有重要的意义。本文回顾了近年来国际上在Kuiper带小天体动力演化方面的研究 ,着重分析了目前国际上几种用以解释其非均匀分布的动力学机制 ,并提出目前该领域的一些尚未解决的问题。     

The Kuiper Belt and its Primordial Sculpting

We discuss the structure of the Kuiper belt as it can be inferred from the first decade of observations. In particular, we focus on its most intriguing properties – the mass deficit, inclination distribution, the apparent existence of an outer edge and of a correlation among inclinations, colours and sizes – which clearly show that the belt has lost its pristine structureof a dynamically cold proto-planetary disk. Understanding how the Kuiperbelt acquired its present structure will provide insight into the formationof the outer planetary system and on its early evolution. We outline ascenario of primordial sculpting – issued from a combination of mechanismsproposed by various authors – that seems to explain most of the observedproperties of the Kuiper belt. Several aspects are not yet totallyclear. But, for the first time, we have a view – if not of the detailedsculpture – at least of its rough cast.     

Spectral Models of Kuiper Belt Objects and Centaurs

We present models of the spectral reflectances of groups of outer Solar System objects defined primarily by their colors in the spectral region 0.4–1.2 mu;m, and which have geometric albedo ～0.04 at wavelength 0.55 μm. Our models of the groups with the strongest reflectance gradients (reddest colors) use combinations of organic tholins. We test the hypothesis that metal-reddened igneous rock-forming minerals contribute to the red colors of Centaurs and KBOs by using the space-weathered lunar soil as one of the components of our models. We find that our models can admit the presence of moderate amounts of space-weathered (metal-reddened) minerals, but that they do not require this material to achieve the red colors of the reddest outer Solar System bodies. Our models with organic tholins are consistent with the results of other investigators.     

Planetary Embryos Never Formed in the Kuiper Belt

We study the orbital evolutions of various systems of planetary embryos in the transneptunian region, undergoing mutual scattering and perturbations from the giant planets. We show that about 15-20% of the original embryos should survive in the transneptunian region at the current epoch. The orbital dispersion of the surviving embryos depends on their individual mass, so that only lunar mass embryos could survive with semimajor axis smaller than 50 AU. In all cases, we show by a Monte Carlo model that at least one of the surviving embryos should have already been discovered by one of the most effective Kuiper-belt surveys. This implies that planetary embryos did not form in the transneptunian region (or have been removed by some external and unknown mechanism). Therefore, we conclude that the Kuiper belt was not excited by resident planetary embryos, unlike the asteroid belt. We also compute with the Monte Carlo model that a significant number (order 10) of Pluto-size bodies could exist only on very eccentric and long-periodic orbits, typical of the scattered disk, while the existence of about 30 bodies brighter than absolute magnitude 4 in the classical belt is compatible with the discovery of Varuna by the Spacewatch survey.     

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)     

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 Shape Distribution Of Kuiper Belt Objects

If we assume that the periodic brightness variations ina Kuiper Belt lightcurve are determined only by theiraspherical shapes and the observing geomtry, the fractionof detectable Kuiper Belt lightcurves and the lightcurveamplitude distribution can be used to constrain the shapesof Kuiper Belt objects. The results indicate that most KuiperBelt objects (～85%) have shapes that are close to spherical(a/b ≤ 1.5$), but there is a small but significant fraction(～12%) possessing highly aspherical shapes (a/b ≥ 1.7).The distribution cannot be well fitted by a gaussian and is betterapproximated by a power law.     

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.     

Hawaii Kuiper Belt Variability Project: An Update

We have been systematically monitoring a large sample of bright Kuiper Beltobjects for possible light variations due to rotational and phase angle effects.Here we report on three objects, 2003 AZ₈₄, (24835) 1995 SM₅₅and (55636) 2002 TX₃₀₀ observed to have measurable rotational lightcurveswith peak-to-peak amplitudes of 0.14 ± 0.03, 0.19 ± 0.05 and 0.08 ± 0.02magnitudes and single-peaked periods of 6.71 ± 0.05, 4.04 ± 0.03 and8.12 ± 0.08 hours, respectively. We observed a further ten objects whichshowed no rotational photometric variation within measurement uncertainties.In addition, we find that the lightcurve of 1995 SM₅₅ may have a variableamplitude. We discuss this peculiar object as well as our observations of the reportedlyvariable Kuiper Belt object (19308) 1996 TO₆₆. Finally, we continue to find the phase functions of the Kuiper Belt objects to be very steep and linear, to firstorder, with a median slope of 0.16 ± 0.01 magnitudes per degree in the phaseangle range 0 to 2 degrees.     

The Study of Kuiper Belt Objects With ESO and ISO

Amajor objective of the Infrared Space Observatory (ISO) is the determination of the sized and albedoes of several objects in the "Kuiper disc".The method by which this will be achieved is described.It is shown that the unknown shapes and surface thermal properties proviede additional complications to the interpretation of ISO data.The requirement for ground-based measurements of the visual light curves of these objects is demonstrated and the implications of the results of the ISO observ Vations is discussed.     

Near-Infrared Colors of the Binary Kuiper Belt Object 1998 WW 31

We have measured near-infrared colorsof the binary Kuiper Belt object (KBO)1998 WW₃₁ using the Subaru Telescope withadaptive optics. The satellite was detectednear its perigee and apogee(0.18“ and 1.2” apart from the primary).The primary and the satellite have similar H–Kcolors, while the satellite is redder thanthe primary in J–H. Combined with the Rband magnitude previously published byVeillet et al., 2002, the color of the primaryis consistent with that of optically red KBOs. Thesatellite's R-, J-, H-colors suggest thepresence of ～1 μm absorption band dueto rock-forming minerals. If the surface of thesatellite is mainly composed by olivine, thesatellite's albedo is higher value than the canonicallyassumed value of 4%.     

Research of Small Kuiper Belt Objects by Stellar Occultations

Fast photometric observations of target stars in the ecliptic are a powerful tool to detect small objects in the Kuiper Belt. The various parameters involved in such observations are described. Meter-sized telescopes are able to detect sub-kilometer KBO (Kuiper Belt Objects). A campaign of research of KBO by stellar occultations, organized at the Pic du Midi Observatory is presented. These observations bring the first constraint on the small end of the size distribution of the KBOs.