Rotating convection in f-boxes: Faster rotation

Results based on 36 cases of f-box computations for different latitudes and rotation rates are summarized. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constraints on the C ring parameters of Saturn at the Titan −1:0 resonance

A one-armed spiral bending wave in Saturn's rings excited by Titan's −1:0 inner vertical resonance is one of the most prominent oscillatory features observed by Voyager 1 . We study detailed dynamics of the particles inside the ring, and show that one of the main causes of the complete dissipation of the bending wave within a distance of ∼85 km from the resonance site could be as a result of the presence of a strong shear caused by radial velocity variation along the vertical direction. Assuming this to be the only source, Voyager data would suggest that if the surface density of matter is around 0.45 g cm⁻² and the amplitude of the bending wave is around 1200 m, then the upper limit of total vertical thickness of the C ring near this resonance is around 40 m.     

Migration of giant planets in a time-dependent planetesimal accretion disc

In this paper we develop further the model for the migration of planets introduced in Del Popolo et al. We first model the protoplanetary nebula as a time-dependent accretion disc, and find self-similar solutions to the equations of the accretion disc that give us explicit formulae for the spatial structure and the temporal evolution of the nebula. These equations are then used to obtain the migration rate of the planet in the planetesimal disc, and to study how the migration rate depends on the disc mass, on its time evolution and on some values of the dimensionless viscosity parameter α . We find that planets that are embedded in planetesimal discs, having total mass of  10^-4-0.1 M_⊙  , can migrate inward a large distance for low values of α (e.g.,   α ≃10^-3-10^-2)  and/or large disc mass, and can survive only if the inner disc is truncated or because of tidal interaction with the star. Orbits with larger a are obtained for smaller values of the disc mass and/or for larger values of α . This model may explain several orbital features of the recently discovered giant planets orbiting nearby stars.     

The evolution of bodies orbiting in the trans-Neptunian region on to intermediate-type orbits

We investigate the dynamical evolution of 210 hypothetical massless bodies initially situated between 10 and 30 au from the Sun in order to determine the general characteristics of the evolved system. This is of particular relevance to the understanding of the origin of Edgeworth–Kuiper belt objects on scattered intermediate orbits, such as 1996 TL ₆₆, which have high eccentricity and semimajor axis but nevertheless have perihelion in the region between 30 and 50 au from the Sun.     

火星上游离子回旋波的观测研究

离子回旋波(Ion Cyclotron Wave, ICW)是指频率接近离子回旋频率的一种等离子体波,它在火星上游广泛存在,卫星观测到的频率多在质子回旋频率附近. ICW是拾起离子时的副产物,成为新生行星质子存在的间接标志.火星上游ICW自1990年首次报道以来,受到广泛的关注.总结了火星上游ICW的研究进展,包括ICW事件的观测、ICW的产生机制、统计性质以及将来的研究趋势.     

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.     

Exoplanet's Figure and Its Interior

Along with the development of the observing technology, the observation and study on the exoplanets’ oblateness and apsidal precession have achieved significant progress. The oblateness of an exoplanet is determined by its interior density profile and rotation period. Between its Love number k₂ and core size exists obviously a negative correlation. So oblateness and k₂ can well constrain its interior structure. Starting from the Lane-Emden equation, the planet models based on different polytropic indices are built. Then the flattening factors are obtained by solving the Wavre's integro-differential equation. The result shows that the smaller the polytropic index, the faster the rotation, and the larger the oblateness. We have selected 469 exoplanets, which have simultaneously the observed or estimated values of radius, mass, and orbit period from the NASA (National Aeronautics and Space Administration) Exoplanet Archive, and calculated their flattening factors under the two assumptions: tidal locking and fixed rotation period of 10.55 hours. The result shows that the flattening factors are too small to be detected under the tidal locking assumption, and that 28% of exoplanets have the flattening factors larger than 0.1 under the fixed rotation period of 10.55 hours. The Love numbers under the different polytropic models are solved by the Zharkov's approach, and the relation between k₂ and core size is discussed.     

内日冕的绿线强度分布研究

日冕是太阳大气活动的关键区域,是日地空间天气的源头.受观测限制,对日冕低层大气等离子体结构和磁场状态的研究非常欠缺,国际上对于可见光波段日冕低层大气的亮度分层研究很少.利用丽江日冕仪YOGIS(Yunnan Green-line Imaging System)的日冕绿线(Fe_ⅩⅣ5303?)观测资料,对内日冕区域(1.03R_☉-1.25R_☉,R_☉表示太阳半径)亮结构及其中冕环进行了有效的强度衰减分析.对亮结构的强度在太阳径向高度上进行了指数衰减拟合,比较这些拟合结果发现所得到的静态内冕环的衰减指数在一固定值附近.然后将比较明显的冕环提取出来,通过对不同高度的绿线强度进行指数拟合,得出的衰减指数与亮结构中也比较相近,这对进一步研究日冕中的各项物理参数演化提供了参考.     

Dynamical friction of bodies orbiting in a gaseous sphere

The dynamical friction experienced by a body moving in a gaseous medium is different from the friction in the case of a collisionless stellar system. Here we consider the orbital evolution of a gravitational perturber inside a gaseous sphere using three-dimensional simulations, ignoring however self-gravity. The results are analysed in terms of a 'local' formula with the associated Coulomb logarithm taken as a free parameter. For forced circular orbits, the asymptotic value of the component of the drag force in the direction of the velocity is a slowly varying function of the Mach number in the range 1.0–1.6. The dynamical friction time-scale for free decay orbits is typically only half as long as in the case of a collisionless background, which is in agreement with E. C. Ostriker's recent analytic result. The orbital decay rate is rather insensitive to the past history of the perturber. It is shown that, similarly to the case of stellar systems, orbits are not subject to any significant circularization. However, the dynamical friction time-scales are found to increase with increasing orbital eccentricity for the Plummer model, whilst no strong dependence on the initial eccentricity is found for the isothermal sphere.     

Practical SPH models for major planets

Modelling planets is done for two main reasons – the first to further understanding of their internal structure and the second to provide models to explore astrophysical situations in which planets play a role. For the latter reason, the requirements on accuracy are less severe, although the planet must be realistic in its major features. A numerical model of a layered giant planet is developed with an iron core, a silicate mantle, an ice region and a hydrogen–helium atmosphere. The Tillotson equation of state is used and examples of two model planets are given, one reproducing the mass and radius of Jupiter quite closely and the other with two Jupiter masses. Transferring these results into a smoothed particle hydrodynamics (SPH) model presents two main difficulties. A uniform distribution of SPH points leads to too few points representing the non-atmospheric component. It is shown that using a distorted lattice enables the core + silicate + ice to be represented by several hundred points so that the evolution of these regions can be followed in detail. Another difficulty concerns the density discontinuities attendant on a layered structure. Density estimates of SPH points are either too large or too small near material interfaces leading to unrealistic pressure gradients and, consequently, to large and unphysical local forces. Algorithms are described for avoiding this difficulty both at material interfaces and near the surface of the planet. In some astrophysical situations involving SPH-modelled planets, the main bulk of the planet is so opaque that internal heat transfer can be neglected. However, surface regions should radiate and a convenient way for including radiation from a planetary surface is described.