Eccentricity Generation in Hierarchical Triple Systems with Non-coplanar and Initially Circular Orbits

In a previous paper, we developed a technique for estimating the inner eccentricity in coplanar hierarchical triple systems on initially circular orbits, with comparable masses and with well-separated components, based on an expansion of the rate of change of the Runge-Lenz vector. Now, the same technique is extended to non-coplanar orbits. However, it can only be applied to systems with I ₀ < 39.23° or I ₀ > 140.77°, where I is the inclination of the two orbits, because of complications arising from the so-called ‘Kozai effect’. The theoretical model is tested against results from numerical integrations of the full equations of motion. This revised version was published online in July 2006 with corrections to the Cover Date.     

The geomorphic dynamics and environmental history of an upper deltaic floodplain tract in the Sacramento–San Joaquin Delta,California, USA

A multi‐proxy approach was used to examine the geomorphic dynamics and environmental history of an upper deltaic ?oodplain tract in the Sacramento–San Joaquin Delta, California. Three long cores were collected from the McCormack–Williamson Tract (MWT) and these cores were analyzed for bulk density, loss‐on‐ignition, ?ne (clay and silt) content, Al concentration, magnetic susceptibility, pollen, and charcoal. Radiocarbon dates obtained for the cores were converted into calendar years and an age–depth model was constructed. Long‐term vertical accretion and sedimentation rates were estimated from the age–depth model. Cross‐core relations show that coarse sediment generally accumulates more rapidly and has greater magnetic susceptibility compared to ?ne sediment. Percentage ?ne and LOI data show a strong linear relationship that indicates ?ooding is the primary mechanism for the deposition of particular organic matter on the ?oodplain and that landscape wash load has contributed a highly consistent fraction of persistent organic matter averaging 5·5 per cent to the site. Down‐core grain size pro?les show two hydrological domains in the cores, namely millennial ?ne–coarse ?uctuations superimposed on general up‐core ?ning. Coarse sediment is viewed as channel or near‐channel overbank deposits, whereas ?ne deposits are considered to be distal overbank ?ood deposits. The coarse–?ne ?uctuations are indicative of changing depositional settings as channels migrated laterally across MWT, whereas the upward ?ning trend re?ects a combination of self‐limiting overbank deposition as ?oodplain elevation increased and decreasing competence as sea‐level rise reduced ?ood‐pulse energy slopes. MWT has been cross‐cut and incised numerous times in the past, only to have the channels abandoned and subsequently ?lled by ?ne sediment. The channels around MWT attained their modern con?guration about 4000 years ago. MWT likely came under tidal in?uence at about 2500 cal BP. Wetlands have recently developed on MWT, but they are inorganic sediment dominated. Copyright © 2004 John Wiley & Sons, Ltd.     

Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field

We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is caused by its inhomogeneous potential. We begin by truncating the equations of motion at second order, that is, incorporating the zonal and the tesseral harmonics up to order two. The system is formulated as an autonomous Hamiltonian and has three degrees of freedom. After three successive Lie transformations, the system is normalised with respect to two angular co-ordinates up to order five in a suitable small parameter given by the quotient between the angular velocity of the planet and the mean motion of the satellite. Our treatment is free of power expansions of the eccentricity and of truncated Fourier series in the anomalies. Once these transformations are performed, the truncated Hamiltonian defines a system of one degree of freedom which is rewritten as a function of two variables which generate a phase space which takes into account all of the symmetries of the problem. Next an analysis of the system is achieved obtaining up to six relative equilibria and three types of bifurcations. The connection with the original system is established concluding the existence of various families of invariant 3-tori of it, as well as quasiperiodic and periodic trajectories. This is achieved by using KAM theory techniques.     

Is Ursa Major II the progenitor of the Orphan Stream?

Prominent in the 'Field of Streams'– the Sloan Digital Sky Survey map of substructure in the Galactic halo – is an 'Orphan Stream' without obvious progenitor. In this numerical study, we show a possible connection between the newly found dwarf satellite Ursa Major II (UMa II) and the Orphan Stream. We provide numerical simulations of the disruption of UMa II that match the observational data on the position, distance and morphology of the Orphan Stream. We predict the radial velocity of UMa II as −100 km s⁻¹, as well as the existence of strong velocity gradients along the Orphan Stream. The velocity dispersion of UMa II is expected to be high, though this can be caused both by a high dark matter content or by the presence of unbound stars in a disrupted remnant. However, the existence of a gradient in the mean radial velocity across UMa II provides a clear-cut distinction between these possibilities. The simulations support the idea that some of the anomalous, young halo globular clusters like Palomar 1 or Arp 2 or Ruprecht 106 may be physically associated with the Orphan Stream.     

Dynamical friction force exerted on spherical bodies

We present a rigorous calculation of the dynamical friction force exerted on a spherical massive perturber moving through an infinite homogenous system of field stars. By calculating the shape and mass of the polarization cloud induced by the perturber in the background system, which decelerates the motion of the perturber, we recover Chandrasekhar's drag force law with a modified Coulomb logarithm. As concrete examples, we calculate the drag force exerted on a Plummer sphere or a sphere with the density distribution of a Hernquist profile. It is shown that the shape of the perturber only affects the exact form of the Coulomb logarithm. The latter converges on small scales because encounters of the test and field stars with impact parameters less than the size of the massive perturber become inefficient. We confirm in this way the earlier results based on the impulse approximation of small angle scatterings.