Mapping the stability field of Jupiter Trojans

Jupiter Trojans are a remnant of outer solar system planetesimals captured into stable or quasistable libration about the 1:1 resonance with the mean motion of Jupiter. The observed swarms of Trojans may provide insight into the original mass of condensed solids in the zone from which the Jovian planets accumulated, provided that the mechanisms of capture can be understood. As the first step toward this understanding, the stability field of Trojans were mapped in the coordinate proper eccentricity, e(sub p), and libration amplitude, D. To accomplish this mapping, the orbits of 100 particles with e(sub p) in the range of 0 to 0.8 and D in the range 0 to 140 deg were numerically integrated. Orbits of the Sun, the four Jovian planets, and the massless particles were integrated as a full N-body system, in a barycentric frame using fourth order symplectic scheme

An Oort cloud origin for the high-inclination, high-perihelion Centaurs

We analyse the origin of three Centaurs with perihelia in the range 15 AU to 30 AU, inclinations above 70 deg and semi-major axes shorter than 100 AU. Based on long-term numerical simulations we conclude that these objects most likely originate from the Oort cloud rather than the Kuiper Belt or Scattered Disc. We estimate that there are currently between 1 and 200 of these high-inclination, high-perihelion Centaurs with absolute magnitude H<8.Comment: Accepted for publication in MNRA

Reassessing the formation of the inner Oort cloud in an embedded star cluster

We re-examine the formation of the inner Oort comet cloud while the Sun was in its birth cluster with the aid of numerical simulations. This work is a continuation of an earlier study (Brasser et al., 2006) with several substantial modifications. First, the system consisting of stars, planets and comets is treated self-consistently in our N-body simulations, rather than approximating the stellar encounters with the outer Solar System as hyperbolic fly-bys. Second, we have included the expulsion of the cluster gas, a feature that was absent previously. Third, we have used several models for the initial conditions and density profile of the cluster -- either a Hernquist or Plummer potential -- and chose other parameters based on the latest observations of embedded clusters from the literature. {These other parameters result in the stars being on radial orbits and the cluster collapses.} Similar to previous studies, in our simulations the inner Oort cloud is formed from comets being scattered by Jupiter and Saturn and having their pericentres decoupled from the planets by perturbations from the cluster gas and other stars. We find that all inner Oort clouds formed in these clusters have an inner edge ranging from 100 AU to a few hundred AU, and an outer edge at over 100\,000 AU, with little variation in these values for all clusters. All inner Oort clouds formed are consistent with the existence of (90377) Sedna, an inner Oort cloud dwarf planetoid, at the inner edge of the cloud: Sedna tends to be at the innermost 2% for Plummer models, while it is 5% for Hernquist models. We emphasise that the existence of Sedna is a generic outcome. We define a `concentration radius' for the inner Oort cloud and find that its value increases with increasing number of stars in the cluster, ranging from 600 AU to 1500 AU for Hernquist clusters and from 1500 AU to 4000 AU for Plummer clusters...Comment: Accepted Icarus 201

Simulations of the Population of Centaurs I: The Bulk Statistics

Large-scale simulations of the Centaur population are carried out. The evolution of 23328 particles based on the orbits of 32 well-known Centaurs is followed for up to 3 Myr in the forward and backward direction under the influence of the 4 massive planets. The objects exhibit a rich variety of dynamical behaviour with half-lives ranging from 540 kyr (1996 AR20) to 32 Myr (2000 FZ53). The mean half-life of the entire sample of Centaurs is 2.7 Myr. The data are analyzed using a classification scheme based on the controlling planets at perihelion and aphelion, previously given in Horner et al (2003). Transfer probabilities are computed and show the main dynamical pathways of the Centaur population. The total number of Centaurs with diameters larger than 1 km is estimated as roughly 44300, assuming an inward flux of one new short-period comet every 200 yrs. The flux into the Centaur region from the Edgeworth-Kuiper belt is estimated to be 1 new object every 125 yrs. Finally, the flux from the Centaur region to Earth-crossing orbits is 1 new Earth-crosser every 880 yrsComment: 15 pages, 2 figures, MNRAS in pres

The formation of Uranus and Neptune among Jupiter and Saturn

The outer giant planets, Uranus and Neptune, pose a challenge to theories of planet formation. They exist in a region of the Solar System where long dynamical timescales and a low primordial density of material would have conspired to make the formation of such large bodies ($\sim$ 15 and 17 times as massive as the Earth, respectively) very difficult. Previously, we proposed a model which addresses this problem: Instead of forming in the trans-Saturnian region, Uranus and Neptune underwent most of their growth among proto-Jupiter and -Saturn, were scattered outward when Jupiter acquired its massive gas envelope, and subsequently evolved toward their present orbits. We present the results of additional numerical simulations, which further demonstrate that the model readily produces analogues to our Solar System for a wide range of initial conditions. We also find that this mechanism may partly account for the high orbital inclinations observed in the Kuiper belt.Comment: Submitted to AJ; 38 pages, 16 figure

Colors and taxonomy of Centaurs and Trans-Neptunian Objects

The study of the surface properties of Centaurs and Trans-Neptunian Objects (TNOs) provides essential information about the early conditions and evolution of the outer Solar System. Due to the faintness of most of these distant and icy bodies, photometry currently constitutes the best technique to survey a statistically significant number of them. Our aim is to investigate color properties of a large sample of minor bodies of the outer Solar System, and set their taxonomic classification. We carried out visible and near-infrared photometry of Centaurs and TNOs, making use, respectively, of the FORS2 and ISAAC instruments at the Very Large Telescope (European Southern Observatory). Using G-mode analysis, we derived taxonomic classifications according to the Barucci et al. (2005a) system. We report photometric observations of 31 objects, 10 of them have their colors reported for the first time ever. 28 Centaurs and TNOs have been assigned to a taxon. We combined the entire sample of 38 objects taxonomically classified in the framework of our programme (28 objects from this work; 10 objects from DeMeo et al. 2009a) with previously classified TNOs and Centaurs, looking for correlations between taxonomy and dynamics. We compared our photometric results to literature data, finding hints of heterogeneity for the surfaces of 4 objects.Comment: 7 pages, 4 figures. To be published in Astronomy and Astrophysic

Convex Shape and Rotation Model of Lucy Target (11351) Leucus from Lightcurves and Occultations

We report new photometric lightcurve observations of the Lucy Mission target (11351) Leucus acquired during the 2017, 2018, and 2019 apparitions. We use these data in combination with stellar occultations captured during five epochs to determine the sidereal rotation period, the spin axis orientation, a convex shape model, the absolute scale of the object, its geometric albedo, and a model of the photometric properties of the target. We find that Leucus is a prograde rotator with a spin axis located within a sky-projected radius of 3° (1σ) from J2000 Ecliptic coordinates (λ = 208°, β = +77°) or J2000 Equatorial Coordinates (R.A. = 248°, decl. = +58°). The sidereal period is refined to P_(sid) = 445.683 ± 0.007 h. The convex shape model is irregular, with maximum dimensions of 60.8, 39.1, and 27.8 km. The convex model accounts for global features of the occultation silhouettes, although minor deviations suggest that local and global concavities are present. We determine a geometric albedo of p_V = 0.043 ± 0.002. The derived phase curve supports a D-type classification for Leucus

Symplectic integrators with adaptive time steps

In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper we identify the causes for this lack of performance, and find that they fall into two categories. In the first, the time step is considered a function of time alone, \Delta=\Delta(t). In this case, backwards error analysis shows that while the algorithms remain symplectic, parametric instabilities arise because of resonance between oscillations of \Delta(t) and the orbital motion. In the second category the time step is a function of phase space variables \Delta=\Delta(q,p). In this case, the system of equations to be solved is analyzed by introducing a new time variable \tau with dt=\Delta(q,p) d\tau. The transformed equations are no longer in Hamiltonian form, and thus are not guaranteed to be stable even when integrated using a method which is symplectic for constant \Delta. We analyze two methods for integrating the transformed equations which do, however, preserve the structure of the original equations. The first is an extended phase space method, which has been successfully used in previous studies of adaptive time step symplectic integrators. The second, novel, method is based on a non-canonical mixed-variable generating function. Numerical trials for both of these methods show good results, without parametric instabilities or spurious growth or damping. It is then shown how to adapt the time step to an error estimate found by backward error analysis, in order to optimize the time-stepping scheme. Numerical results are obtained using this formulation and compared with other time-stepping schemes for the extended phase space symplectic method.Comment: 23 pages, 9 figures, submitted to Plasma Phys. Control. Fusio