On corotation torques, horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration

We study the torque on low-mass protoplanets on fixed circular orbits, embedded in a protoplanetary disc in the isothermal limit. We consider a wide range of surface density distributions including cases where the surface density increases smoothly outwards. We perform both linear disc response calculations and non-linear numerical simulations. We consider a large range of viscosities, including the inviscid limit, as well as a range of protoplanet mass ratios, with special emphasis on the co-orbital region and the corotation torque acting between disc and protoplanet.
For low-mass protoplanets and large viscosity, the corotation torque behaves as expected from linear theory. However, when the viscosity becomes small enough to enable horseshoe turns to occur, the linear corotation torque exists only temporarily after insertion of a planet into the disc, being replaced by the horseshoe drag first discussed by Ward. This happens after a time that is equal to the horseshoe libration period reduced by a factor amounting to about twice the disc aspect ratio. This torque scales with the radial gradient of specific vorticity, as does the linear torque, but we find it to be many times larger. If the viscosity is large enough for viscous diffusion across the co-orbital region to occur within a libration period, we find that the horseshoe drag may be sustained. If not, the corotation torque saturates leaving only the linear Lindblad torques. As the magnitude of the non-linear co-orbital torque (horseshoe drag) is always found to be larger than the linear torque, we find that the sign of the total torque may change even for mildly positive surface density gradients. In combination with a kinematic viscosity large enough to keep the torque from saturating, strong sustained deviations from linear theory and outward or stalled migration may occur in such cases.     

Astrometric observations of the Uranian satellites with the Faulkes Telescope North in 2007 September

The results of astrometric observations of the main Uranian satellites taken with the Faulkes Telescope North are presented. A median filter algorithm was applied to subtract a scattered-light halo caused by Uranus. The Two-Micron All-Sky Survey (2MASS) and USNO-B1.0 were used as reference catalogues. The mean value of the differences between the equatorial coordinates of the satellites determined with 2MASS and USNO-B1.0 is close to 200 mas. A comparison of the observed equatorial coordinates of the satellites and their relative positions with ephemerides based on different combinations of theories of motion of Uranus and its satellites (DE405+GUST86, DE405+GUST06, INPOP+GUST86, INPOP+GUST06) was performed. The satellites' positions obtained with respect to 2MASS are in better agreement with theories. The values of (O−C) of the equatorial coordinates determined with the 2MASS are mainly less than 100 mas. The majority of (O−C) of relative positions are within ±50 mas. The mean values of the standard errors of (O−C) are within 20 to 60 mas.     

中国历代荧惑守列宿与四星聚、五星聚考查

利用授时历法和现代天文计算方法,对中国历代天文志记录的荧惑(火星)守列宿、四星聚、五星聚进行分析研究,结果表明:65条荧惑守列宿,正误率分别为49%和51%.如果把荧惑留、留守、在某宿等运动形态也考虑为守的范围,共有95条,其正误率分别为56%和44%.12条四星聚正误率各占一半,即50%.11条五星聚正误率分别为82%和18%(其中含五星并见).并对错误记录的原因做了初步探讨.     

Normal forms for the epicyclic approximations of the perturbed Kepler problem

We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the tidal expansion of the potential, the equations of motion take the form of perturbed harmonic oscillators in a rotating frame. In the unperturbed, purely Keplerian case, the post-epicyclic solutions produced with the normal form coincide with those obtained from the expansion of the solution of the Kepler equation. In all cases where the perturbed problem can be cast in autonomous form, the solution is easily obtained as a perturbation series. The generalization to the spatial problem and/or the non-autonomous case is straightforward.     

Ultraviolet observations of Phoebe from the Cassini UVIS

Observations of Saturn's distant moon Phoebe were made at far-ultraviolet (FUV) (1100-1900 Å) and extreme-ultraviolet (EUV) (600-1100 Å) wavelengths by the Cassini Ultraviolet Imaging Spectrograph (UVIS) during the Cassini spacecraft flyby on June 11, 2004. These are the first UV spectra of Phoebe and the first detection of water ice on a Solar System surface using FUV wavelengths. The characteristics of water ice in the FUV are presented, and Hapke models are used to interpret the spectra in terms of composition and grain size; the use of both areal and intimate mixing models is explored. Non-ice species used in these models include carbon, ice tholin, Triton tholin, poly-HCN and kerogen. Satisfactory disk-integrated fits are obtained for intimate mixtures of ∼10% H₂O plus a non-ice species. Spatially resolved regions of higher (∼20%) and lower (∼5%) H₂O ice concentrations are also detected. Phoebe does not display any evidence of volatile activity. Upper limits on atomic oxygen and carbon are 5×¹⁰¹¹ and 2×¹⁰¹² atoms/cm², respectively, for solar photon scattering. The UVIS detection of water ice on Phoebe, and the ice amounts detected, are consistent with IR measurements and contribute to the evidence for a Phoebe origin in the outer Solar System rather than in the main asteroid belt.     

The albedo dichotomy of Iapetus measured at UV wavelengths

The dramatic hemispheric dichotomy in albedo displayed by Saturn's moon Iapetus has intrigued astronomers for centuries. Here we report on far-ultraviolet observations of Iapetus' bright and dark terrains from Cassini. We compare the reflectance spectra of Iapetus's dark terrain, Hyperion and Phoebe and find that both Phoebe and Hyperion are richer in water ice than Iapetus' dark terrain. Spectra of the lowest latitudes of the dark terrain display the diagnostic water ice absorption feature; water ice amounts increase within the dark material away from the apex (at 90° W longitude, the center of the dark leading hemisphere), consistent with thermal segregation of water ice. The water ice in the darkest, warmest low latitude regions is not expected to be stable and may be a sign of ongoing or recent emplacement of the dark material from an exogenic source.     

Thermal convection in ice-I shells of Titan and Enceladus

Cassini-Huygens observations have shown that Titan and Enceladus are geologically active icy satellites. Mitri and Showman [Mitri, G., Showman, A.P., 2005. Icarus 177, 447-460] and McKinnon [McKinnon, W.B., 2006. Icarus 183, 435-450] investigated the dynamics of an ice shell overlying a pure liquid-water ocean and showed that transitions from a conductive state to a convective state have major implications for the surface tectonics. We extend this analysis to the case of ice shells overlying ammonia-water oceans. We explore the thermal state of Titan and Enceladus ice-I shells, and also we investigate the consequences of the ice-I shell conductive-convective switch for the geology. We show that thermal convection can occur, under a range of conditions, in the ice-I shells of Titan and Enceladus. Because the Rayleigh number Ra scales with δ³/ηb, where δ is the thickness of the ice shell and ηb is the viscosity at the base of the ice-I shell, and because ammonia in the liquid layer (if any) strongly depresses the melting temperature of the water ice, Ra equals its critical value for two ice-I shell thicknesses: for relatively thin ice shell with warm, low-viscosity base (Onset I) and for thick ice shell with cold, high-viscosity base (Onset II). At Onset I, for a range of heat fluxes, two equilibrium states—corresponding to a thin, conductive shell and a thick, convective shell—exist for a given heat flux. Switches between these states can cause large, rapid changes in the ice-shell thickness. For Enceladus, we demonstrate that an Onset I transition can produce tectonic stress of ∼500 bars and fractures of several tens of km depth. At Onset II, in contrast, we demonstrate that zero equilibrium states exist for a range of heat fluxes. For a mean heat flux within this range, the satellite experiences oscillations in surface heat flux and satellite volume with periods of ∼50-800 Myr even when the interior heat production is constant or monotonically declining in time; these oscillations in the thermal state of the ice-I shell would cause repeated episodes of extensional and compressional tectonism.     

Energetic electron signatures of Saturn's smaller moons: Evidence of an arc of material at Methone

We present several energetic charged particle microsignatures of two Lagrange moons, Telesto and Helene, measured by the MIMI/LEMMS instrument. These small moons absorb charged particles but their effects are usually obscured by Tethys and Dione, the two larger saturnian satellites that occupy the same orbits. The scales and structures of these microsignatures are consistent with standard models for electron absorption from asteroid-sized moons in Saturn's radiation belts. In the context of these observations, we also examine the possibility that the 3 km Satellite Methone is responsible for two electron microsignatures detected by Cassini close to this moon's orbit. We infer that a previously undetected arc of material exists at Methone's orbit (R/2006 S5), we speculate how such a structure could form and what its physical characteristics and location could be. The origin of this arc could be linked to a possible presence of a faint ring produced by micrometeoroid impacts on Methone's surface, to E-ring dust clump formation at that distance or to temporary dust clouds produced by enceladian activity that spiral inwards under the effect of non-gravitational forces.     

The topography of Iapetus' leading side

We have used Cassini stereo images to study the topography of Iapetus' leading side. A terrain model derived at resolutions of 4-8 km reveals that Iapetus has substantial topography with heights in the range of −10 km to +13 km, much more than observed on the other middle-sized satellites of Saturn so far. Most of the topography is older than 4 Ga [Neukum, G., Wagner, R., Denk, T., Porco, C.C., 2005. Lunar Planet. Sci. XXXVI. Abstract 2034] which implies that Iapetus must have had a thick lithosphere early in its history to support this topography. Models of lithospheric deflection by topographic loads provide an estimate of the required elastic thickness in the range of 50-100 km. Iapetus' prominent equatorial ridge [Porco, C.C., and 34 colleagues, 2005. Science 307, 1237-1242] reaches widths of 70 km and heights of up to 13 km from their base within the modeled area. The morphology of the ridge suggests an endogenous origin rather than a formation by collisional accretion of a ring remnant [Ip, W.-H., 2006. Geophys. Res. Lett. 33, doi:10.1029/2005GL025386. L16203]. The transition from simple to complex central peak craters on Iapetus occurs at diameters of 11±3 km. The central peaks have pronounced conical shapes with flanking slopes of typically 11° and heights that can rise above the surrounding plains. Crater depths seem to be systematically lower on Iapetus than on similarly sized Rhea, which if true, may be related to more pronounced crater-wall slumping (which widens the craters) on Iapetus than on Rhea. There are seven large impact basins with complex morphologies including central peak massifs and terraced walls, the largest one reaches 800 km in diameter and has rim topography of up to 10 km. Generally, no rings are observed with the basins consistent with a thick lithosphere but still thin enough to allow for viscous relaxation of the basin floors, which is inferred from crater depth-to-diameter measurements. In particular, a 400-km basin shows up-domed floor topography which is suggestive of viscous relaxation. A model of complex crater formation with a viscoplastic (Bingham) rheology [Melosh, H.J., 1989. Impact Cratering. Oxford Univ. Press, New York] of the impact-shocked icy material provides an estimate of the effective cohesion/viscosity at . The local distribution of bright and dark material on the surface of Iapetus is largely controlled by topography and consistent with the dark material being a sublimation lag deposit originating from a bright icy substrate mixed with the dark components, but frost deposits are possible as well.