Models of the collisional damping scenario for ice-giant planets and Kuiper belt formation

Chiang et al. [Chiang, E., Lithwick, Y., Murray-Clay, R., Buie, M., Grundy, W., Holman, M., 2007. In: Protostars and Planets V, pp. 895-911] have recently proposed that the observed structure of the Kuiper belt could be the result of a dynamical instability of a system of ∼5 primordial ice-giant planets in the outer Solar System. According to this scenario, before the instability occurred, these giants were growing in a highly collisionally damped environment according to the arguments in Goldreich et al. [Goldreich, P., Lithwick, Y., Sari, R., 2004. Astrophys. J. 614, 497-507; Annu. Rev. Astron. Astrophys. 42, 549-601]. Here we test this hypothesis with a series of numerical simulations using a new code designed to incorporate the dynamical effects of collisions. We find that we cannot reproduce the observed Solar System. In particular, Goldreich et al. [Goldreich, P., Lithwick, Y., Sari, R., 2004. Astrophys. J. 614, 497-507; Annu. Rev. Astron. Astrophys. 42, 549-601] and Chiang et al. [Chiang, E., Lithwick, Y., Murray-Clay, R., Buie, M., Grundy, W., Holman, M., 2007. In: Protostars and Planets V, pp. 895-911] argue that during the instability, all but two of the ice giants would be ejected from the Solar System by Jupiter and Saturn, leaving Uranus and Neptune behind. We find that ejections are actually rare and that instead the systems spread outward. This always leads to a configuration with too many planets that are too far from the Sun. Thus, we conclude that both Goldreich et al.'s scheme for the formation of Uranus and Neptune and Chiang et al.'s Kuiper belt formation scenario are not viable in their current forms.     

The edge of the Kuiper belt: the Planet X scenario

Our goal is to determine whether or not the observed sudden termination of the Edgeworth-Kuiper belt can be the result of perturbations from a hypothetical planet. We investigate the effects that such an object would produce on the primordial orbital distribution if the trans-neptunian objects, for a range of masses and orbital parameters of the hypothetical planet. In this numerical investigation, the motion of the hypothetical planet was influenced by the existing planets but not by its interaction with the disk. We find that no set of parameters produce results that match the observed data. Dynamical interaction with the disk is likely to be important so that the orbit of the hypothetical planet changes significantly during the integration interval. This is also discussed. The overall conclusion is that none of the models for the hypothetical planet that were investigated can reproduce the observed features of the Edgeworth-Kuiper belt starting from any probable primordial distribution.     

The color of the Kuiper belt Core

Recent dynamical analyses of the Kuiper belt have introduced a rigorous classification scheme, determined the mean orbital plane, and identified “Core” and “Halo” populations as a function of inclination with respect to this plane (Elliot, J.L., Kern, S.D., Clancy, K.B., Gulbis, A.A.S., Millis, R.L., Buie, M.W., Wasserman, L.H., Chiang, E.I., Jordan, A.B., Trilling, D.E., Meech, K.J., 2005. Astron. J. 129, 1117-1162). Here, we use new observations and existing data to investigate the colors of Kuiper belt objects (KBOs) within this framework. With respect to the bulk KBO color distribution (all objects for which we have B-V and V-R colors; median B-R=1.56), we find that the population of objects classified following (Elliot, J.L., Kern, S.D., Clancy, K.B., Gulbis, A.A.S., Millis, R.L., Buie, M.W., Wasserman, L.H., Chiang, E.I., Jordan, A.B., Trilling, D.E., Meech, K.J., 2005. Astron. J. 129, 1117-1162) as Classical tends to be red (B-R>1.56) while the Scattered Near population is mostly neutral (B-R<1.56). Colors of Scattered Extended and Resonant objects are consistent with the bulk distribution. Separating objects into specific resonances demonstrates that the color of the Resonant sample is dominated by KBOs in the 3:2 resonance, which is consistent with previous findings. Unlike the objects in the 3:2 resonance, however, the majority of objects in the 5:2 resonance are neutral and all but one of the objects in the 4:3, 5:3, 7:4, 2:1, and 7:3 resonances are red. In particular, the objects in the 7:4 resonance are remarkably red. We find that the colors of KBOs in the Core (low-inclination) and Halo (high-inclination) are statistically different, with Core objects being primarily red and Halo objects having a slight tendency to be neutral. Notably, virtually all of the non-Resonant Core objects are red. This combination of low inclination, unperturbed orbits and red colors in the Core may be indicative of a relic grouping of objects.     

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.     

Accurate absolute magnitudes for Kuiper belt objects and Centaurs

Accurate absolute optical magnitude values (HV and HR) for Kuiper belt objects (KBOs) and Centaurs are becoming increasingly important as observations in other wavelengths, particularly SIRTF thermal infrared measurements, become available for large samples of objects. We present accurate HV and HR values for 90 KBOs and Centaurs, based on our published optical photometry. We find that our HV values are in good agreement with those available from the European photometric survey of minor bodies in the outer Solar System. Comparison with HV values from the JPL Horizons database and the Minor Planet Center database shows that these sources are systematically brighter than ours by about 0.3 mag.     

Shaping the Kuiper belt size distribution by shattering large but strengthless bodies

The observed size distribution of Kuiper belt objects (KBOs)—small icy and rocky Solar System bodies orbiting beyond Neptune—is well described by a power law at large KBO sizes. However, recent work by Bernstein et al. (2004, Astron. J. 128, 1364-1390) indicates that the size distribution breaks and becomes shallower for KBOs smaller than about 70 km in size. Here we show that we expect such a break at KBO radius ∼40 km since destructive collisions are frequent for smaller KBOs. Specifically, we assume that KBOs are gravity-dominated bodies with negligible material strength. This gives a power-law slope q?3 where the number N>r of KBOs larger than a size r is given by N>r∝r1−q; the break location follows from this slope through a self-consistent calculation. The existence of this break, the break's location, and the power-law slope we expect below the break are consistent with the findings of Bernstein et al. (2004, Astron. J. 128, 1364-1390). The agreement with observations indicates that KBOs as small as ∼40 km are effectively strengthless.     

Discovery and characteristics of the Kuiper belt binary 2003QY90

We present photometric and astrometric results from four epochs of ground-based observations at the Magellan telescopes of the Kuiper belt binary 2003QY90. Resolved observations show both components to be highly variable and often of nearly equal brightness, causing difficulty in distinguishing between the primary and secondary components for observations spaced widely in time. Resolved lightcurve observations on one night show one component to have a single-peaked rotation period of 3.4±1.1 h and a peak-to-peak amplitude of 0.34±0.12 mag. The other component exhibits a less constrained lightcurve, with a single-peaked rotation period of 7.1±2.9 h and a peak-to-peak amplitude of 0.90±0.36 mag. Under the assumption of equal albedos, the diameter ratio is 1.25±0.11 in the Sloan i^′ filter. While we cannot determine an orbit from our four distinct epochs of observation (due to ambiguity in component identification), we place limits on the orbital period of the system of 300-600 days, we find a minimum semi-major axis of 13,092 km for a circular orbit and a system mass range of (2.3-18.0)×¹⁰¹⁷ kg depending on the identification of components in our observations.     

On the collisional disruption of porous icy targets simulating Kuiper belt objects

We present results from 27 impact experiments using porous (porosity ranging from 0.39 to 0.54) ice targets and solid ice projectiles at impact speeds ranging from 90 to 155 m/s. These targets were designed to simulate Kuiper Belt Objects (KBOs) in structure. We measured a specific energy for shattering, , of 2.1×¹⁰⁵ erg/g for those snowball targets hit by intact ice projectiles; this is of the same order as that measured for solid ice targets. The fragment mass distribution follows a power law, although the exponent is not simply related to the largest fragment size as assumed by fragmentation models. We provide the first measurement of the three-dimensional mass-velocity distribution for disrupted ice targets and find that fragment speeds range from ∼2 to ∼20 m/s. The fraction of collisional kinetic energy that is partitioned into ejecta speeds is between 1 and 15% (although it should be noted that the lower limit is more reliable than the upper).     

Visible and infrared photometry of Kuiper Belt objects: searching for evidence of trends

We present new visible-infrared (V−J) observations of 17 Kuiper Belt objects, of which 14 were observed in the visible and infrared wavebands simultaneously to limit the effects of lightcurve variations. Combining these data with our previously published visible-infrared data provides a dataset of 29 objects, 25 of which offer simultaneous V−J colors. We examine the resulting dataset for evidence of relationships between physical properties and orbital characteristics. We find no evidence of a color-size relationship (as previously suspected), at least over the size range sampled. The dataset supports the trend, reported elsewhere, that there is a predominance of red material on the surfaces of objects having perihelia beyond 40 AU. Our data are also supportive, albeit weakly, of a reported correlation between inclination and color in the classical Kuiper Belt — although it is perhaps more correct to say that our data show that there appears to be a lack of low inclination blue objects. Our V−J colors appear broadly correlated with published optical colors, thus suggesting that the surfaces of Kuiper Belt objects are subject to a single reddening agent.     

The CFEPS Kuiper Belt Survey: Strategy and presurvey results

We present the data acquisition strategy and characterization procedures for the Canada-France Ecliptic Plane Survey (CFEPS), a sub-component of the Canada-France-Hawaii Telescope Legacy Survey. The survey began in early 2003 and as of summer 2005 has covered 430 square degrees of sky within a few degrees of the ecliptic. Moving objects beyond the orbit of Uranus are detected to a magnitude limit of mR=23-24 (depending on the image quality). To track as large a sample as possible and avoid introducing followup bias, we have developed a multi-epoch observing strategy that is spread over several years. We present the evolution of the uncertainties in ephemeris position and orbital elements of a small 10-object sample of objects tracked through these epochs as part of a preliminary presurvey starting a year before the main CFEPS project. We describe the CFEPS survey simulator, to be released in 2006, which allows theoretical models of the Kuiper belt to be compared with the survey discoveries. The simulator utilizes the well-documented pointing history of CFEPS, with characterized detection efficiencies as a function of magnitude and rate of motion on the sky. Using the presurvey objects we illustrate the usage of the simulator in modeling the classical Kuiper belt. The primary purpose of this paper is to allow a user to immediately exploit the CFEPS data set and releases as they become available in the coming months.     

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.     

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.     

Resolution of the kuiper belt object color controversy: two distinct color populations

Four years ago, we reported that the surface colors of ancient, icy bodies at and beyond the orbit of Neptune—Kuiper belt objects— divide into two distinct color populations. Our report has proven quite controversial. Specifically, every other research group looking with large telescopes at Kuiper belt objects finds a continuous range of colors rather than two distinct populations. Here we report new color measurements of 18 objects, primarily from the Keck I 10-m telescope, that confirm the existence of two populations. We have combined the color measurements of the other groups to create a data set comparable in size to our data set. We have carried out a Monte Carlo statistical analysis and found that both data sets are consistent with two color populations and our data set, which has smaller uncertainties, rules out a continuum of colors. In addition, our new observations and those in the literature confirm our earlier report that classical KBOs with perihelion distances beyond 40 AU exhibit extremely red surface colors. Our results rule out a continuous color distribution for both our complete sample and subsamples with perihelion distances greater than or less than 40 AU. We suspect the color patterns will result in a better understanding of the formation and evolution of the outer Solar System.     

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.     

Drag-induced resonant capture in a multiplanet scenario: An application to 55 Cancri A

The binary star 55 Cancri harbors at least five giant planets. The discovery of a possible dust disk around the primary of the system was announced in 1998 although it was later dismissed as an observational artifact induced by the presence of three background galaxies. However, the possible existence of an asteroid belt beyond 6 AU from the primary could not be excluded. The actual properties of a hypothetical outer asteroid belt around 55 Cancri A are likely to be the result of the gravitational influence of the outermost planets and gas drag during the late stages of the formation of the planetary system. Gaseous drag within a protoplanetary disk in a multiplanet context can induce resonant capture of solid material rather easily, triggering the formation of asteroid belts similar to our own transneptunian belt. In this paper we investigate this scenario using numerical simulations within the framework of the planar restricted four-body problem to find possible stable debris locations or additional planets around 55 Cancri A. Our results indicate that, beyond 55 Cancri d, only the 1:2 and 1:3 mean-motion resonances may be possible although the details of gas drag-induced resonant trapping depend strongly on the size of the particles, with larger particles being preferentially trapped farther away from the host star. For a primary of mass 0.94 M and i=53° we find solid particles submitted to confined chaos at 10.14 and 13.22 AU with average eccentricities 0.14 and 0.20, respectively. The argument of pericentre of the trapped particles is found to librate around π/2 with the pericentres of the two resonant structures nearly aligned. The resonance responsible for the inner ring effectively halts the migration of the particles. The outer structure resembles a rosette or separatrix orbit. Our calculations suggest that hypothetical planets or asteroid belts in these locations would be, in principle, dynamically stable.     

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.     

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.     

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.     

The plane of the Edgeworth-Kuiper belt

We examine possible locations for the primordial disk of the Edgeworth-Kuiper Belt (EKB), using several subsets of the known objects as markers of the total mass distribution. Using a secular perturbation theory, we find that the primordial plane of the EKB could have remained thin enough to escape detection only if it is clustered very closely about the invariable plane of the Solar System.