On the migration of a system of protoplanets

The evolution of a system consisting of a protoplanetary disc with two embedded Jupiter-sized planets is studied numerically. The disc is assumed to be flat and non-self-gravitating; this is modelled by the planar (two-dimensional) Navier–Stokes equations. The mutual gravitational interaction of the planets and the star, and the gravitational torques of the disc acting on the planets and the central star are included. The planets have an initial mass of one Jupiter mass M _Jup each, and the radial distances from the star are one and two semimajor axes of Jupiter, respectively.
During the evolution a joint wide annular gap is created by the planets. Both planets increase their mass owing to accretion of gas from the disc: after about 2500 orbital periods of the inner planet it has reached a mass of 2.3  M _Jup, while the outer planet has reached a mass of 3.2  M _Jup. The net gravitational torques exerted by the disc on the planets result in an inward migration of the outer planet on time-scales comparable to the viscous evolution time of the disc. The semimajor axis of the inner planet remains constant as there is very little gas left in its vicinity to induce any migration. When the distance of close approach eventually becomes smaller than the mutual Hill radius, the eccentricities increase strongly and the system may become unstable.
If disc depletion occurs rapidly enough before the planets come too close to each other, a stable system similar to our own Solar system may remain. Otherwise the orbits may become unstable and produce systems like υ And.     

Nonlocal density wave theory for gravitational instability of protoplanetary disks without sharp boundaries

The stability of a self‐gravitating infinitesimally thin gaseous disk rotating around a central mass is studied. Our global linear analysis concerns marginal stability, i.e. it yields the critical temperature for the onset of instability for any given ratio of the disk mass to the central mass. Both axisymmetric and low‐m nonaxisymmetric excitations are analysed. When the fractional disk mass increases, the symmetry character of the instability changes from rings (m = 0) to one‐armed trailing spirals (m = 1). The distribution of the surface density along the spiral arms is not uniform, but describes a sequence of maxima that might be identified with forming planets. The number of the mass concentrations decreases with increasing fractional disk mass. We also obtain solutions in the form of global nonaxisymmetric vortices, which are, however, never excited.     

Final tidal evolution of orbit-orbit resonances

In this paper we describe a model for the tidal evolution of an orbit-orbit resonance between two satellites of the same planet. We let the system evolve till infinity or until the resonance is destroyed. We find that there are asymptotic values for the eccentricities and inclinations. We list the possible final stages that a resonance can achieve, we give a few examples, and finally we discuss the limitations of the model and its possible applications to real systems.     

Microwave observations of Saturn's rings: anisotropy in directly transmitted and scattered saturnian thermal emission

We present a new Very Large Array (VLA) image of Saturn, made from data taken in October 1998 at a wavelength of λ3.6 cm. The moderate ring opening angle (B≈15°) allows us to explore direct transmission of microwave photons through the A and C rings. We find a strong asymmetry of photons transmitted through the A ring, but not in the C ring, a new diagnostic of wake structure in the ring particles. We also find a weak asymmetry between east and west for the far side of the ansae. To facilitate quantitative comparison between dynamic models of the A ring and radio observations, we extend our Monte Carlo radiative transfer code (described in Dunn et al., 2002, Icarus 160, 132-160) to include idealized wakes. We show the idealized model can reproduce the properties of dynamic simulations in directly transmitted light. We examine the model behavior in directly transmitted and scattered light over a range of physical and geometric wake parameters. Finally, we present a wake model with a plausible set of physical parameters that quantitatively reproduces the observed intensity and asymmetry of the A ring both across the planet and in the ansae.     

First observations of the Na exosphere of Mercury with the high-resolution spectrograph of the 3.5M Telescopio Nazionale Galileo

Analysis of three spectra of the exosphere of Mercury in the Na-D lines are presented. Spectra were secured with the high-resolution spectrograph (SARG) of the 3.5 M Telescopio Nazionale Galileo (TNG, located on the Roque de los Muchachos, Canaries) on the evenings of August 23 and 24, 2002. Spectra have resolution ; the slit length was 26.7”. The Na column abundances range from 4.3 to with the highest abundances being close to the illuminated limb. Our observations at true anomaly angles (TAA) from 171°to 174°show the traces of the emission lines to be strongly peaked at the illuminated limb, supportive of recent modeling that shows thermal desorption to be a strong factor in determining the distribution of Na about the planet.     

Dynamics of Two Planets in the 2/1 Mean-Motion Resonance

The dynamics of two planets near a first-order mean-motion resonance is modeled in the domain of the general three-body planar problem. The system studied is the pair Uranus-Neptune (2/1 resonance). The phase space of the resonance and near-resonance regions is studied by means of surfaces of section and spectral analysis techniques. After a thorough investigation of the topology of the phase space, we find that several regimes of motion are possible for the Uranus-Neptune system, and the regions of transition between the regimes of motion are the seats of chaotic motion. This revised version was published online in July 2006 with corrections to the Cover Date.     

A landscape pattern analysis method based on boundaries and nodes: A case study in upper Minjiang River, China

Traditionally,patch-based analysis at the landscape scale fragmentation has been used in the study of landscape ecology while the study of boundary and node has not been considered as much detail until recently.This study investigated the possibility of applying boundary-and node-based methods in landscape pattern analysis to the upper reaches of the Minjiang River in the southwestern China.Boundary-based and node-based landscape indices were selected to be used in analyzing changes in landscape patterns,and the results were compared with analysis using traditional pattern indices.We compared the responses of patch-area-based,boundary-length-based and node-number-based indices,and concluded that boundary-based and node-based indices are more sensitive to disturbance than patch-based indices with various patterns,and node-based indices are even more sensitive than boundary-based ones.Thus,the results suggest that boundary-based and node-based pattern analysis methods provide helpful supplementary information to traditional patch-based pattern analysis methods.The results about pattern dynamics of landscapes in the upper reaches of the Minjiang River based on boundaries and nodes showed that with human disturbance,the dominance of forest landscape was weakened by other landscape types; thus the landscape pattern of the study area became more homogeneous and the boundary network became more complex.These changes further augmented disturbance interfaces in the landscape and increased the possibilities of further landscape fragmentation.     

Changes in Land Use and Agricultural Production Structure Before and After the Implementation of Grain for Green Program in Western China–Taking Two Typical Counties as Examples

Soil erosion becomes a serious environmental problem in the world, especially in western China. An effective management practice called the Grain for Green Program （GGP）, which was launched in 1999, aims to reduce soil and water loss and alleviate the ecological environment problem in western China. Two typical counties in western China, the Zhongxian （in Chongqing Municipality） and Ansai （in Shaanxi Province） were chosen to evaluate the dynamic changes of land use and agricultural production structure before and after the implementation of the Program in this paper. The results showed that the cultivated land area was reduced by 7.08% from 1989 to 2003. The cultivated land per person was decreased by 8.42% during 1999-2003. Moreover, the stability index of the secondary sector of the economy was increased from 0.91 in the period 1990-1999 to 0.94 in the following ten years. In addition, the stability index of tertiary economic sector increased from 0.88 to 0.92 in Zhongxian county. Meanwhile, the cultivated land area was reduced by 15.48% from 1990 to 1999. The soil erosion modulus was decreased by 33.33% from 1999 to 2006. Also, the stability index of secondary and tertiary economic sectors was 0.86 in the period 1998-2002. However, it decreased by 77% during 2002 to 2007 in Ansai County. These results imply that the Grain for Green Program had different impact on the two regions. Several effective strategies of soil and water conservation have been carried out to ameliorate the sustainable development of ecological environment and economy in these two counties of western China.