Galilean satellites: Evolutionary paths in deep resonance

The Laplace resonance among the inner three Galilean satellites (mean motions n₁ − 3n₂ + 2n₃ = 0) has stable configurations in “deep resonance,” i.e., where mean motions taken by pairs are in ratios very close to 2:1. The present satellite configuration, with the resonance variable φ ≡ λ₁ − 3λ₂ + 2λ₃ stable at 180°, is unstable near this exact commensurability. But there is a continuous path of stable conditions branching from φ = 180° to higher and lower values of φ and toward very deep resonance, according to a theory extended to third order in orbital eccentricity. This path provides a track for tidal evolution of the system. Thus, scenarios involving evolution (probably episodic) from deep resonance are viable, and eliminate the requirement by the alternative equilibrium hypothesis for rapid tidal dissipation in Jupiter. Evolution out from deep resonance is consistent with the free eccentricity of Ganymede, the free libration of φ, and observational constraints on Io's secular acceleration. Also, the relatively large forced eccentricities in deep resonance may have controlled geophysical processes in the satellites by much greater tidal heating and global stress than at present.     

Chaotic motion of comets in near-parabolic orbit: Mapping approaches

There exist many comets with near-parabolic orbits in the Solar System. Among various theories proposed to explain their origin, the Oort cloud hypothesis seems to be the most reasonable (Oort, 1950). The theory assumes that there is a cometary cloud at a distance 10³ – 10⁵ AU from the Sun and that perturbing forces from planets or stars make orbits of some of these comets become of near-parabolic type. Concerning the evolution of these orbits under planetary perturbations, we can raise the question: Will they stay in the Solar System forever or will they escape from it? This is an attractive dynamical problem. If we go ahead by directly solving the dynamical differential equations, we may encounter the difficulty of long-time computation. For the orbits of these comets are near-parabolic and their periods are too long to study on their long-term evolution. With mapping approaches the difficulty will be overcome. In another aspect, the study of this model has special meaning for chaotic dynamics. We know that in the neighbourhood of any separatrix i.e. the trajectory with zero frequency of the unperturbed motion of an Hamiltonian system, some chaotic motions have to be expected. Actually, the simplest example of separatrix is the parabolic trajectory of the two body problem which separates the bounded and unbounded motion. From this point of view, the dynamical study on near-parabolic motion is very important. Petrosky's elegant but more abstract deduction gives a Kepler mapping which describes the dynamics of the cometary motion (Petrosky, 1988). In this paper we derive a similar mapping directly and discuss its dynamical characters.     

Secular Dynamics of Asteroids in the Inner Solar System

In the last three years we have carried out numerical and semi-analytical studies on the secular dynamical mechanisms in the region (semimajor axis a < 2 AU) where the NEA orbits evolve. Our numerical integrations (over a time span of a few Myr) have shown that: (i) the linear secular resonances with both the inner and the outer planets may play an important role in the dynamical evolution of NEAs; (ii) the apsidal secular resonance with Mars could provide an important dynamical transport mechanism by which asteroids in the Mars-crossing region eventually achieve Earth-crossing orbits; (iii) in this region, due to the interaction with the terrestrial planets, the Kozai resonance can occur at small inclinations, with the argument of perihelion ω librating around 0° or 180°, providing a temporary protection mechanism against close approaches to the planets. The location of the linear secular resonances in this zone has also been obtained by an automatic procedure using a semi-numerical method valid for all values of the inclinations and eccentricities of the small bodies, and also in the case of libration of the argument of perihelion. A map of the secular resonances in the (a, i) plane shows — in agreement with the numerical integrations — that all the resonances with the terrestrial and giant planets are present, and also that some of them overlap. Thus the way is now open to fully take into account secular resonances in modelling the dynamical evolution of NEAs. This revised version was published online in July 2006 with corrections to the Cover Date.     

Uranus and Neptune: Shape and rotation

Both Uranus and Neptune are thought to have strong zonal winds with velocities of several 100 m s⁻¹. These wind velocities, however, assume solid-body rotation periods based on Voyager 2 measurements of periodic variations in the planets’ radio signals and of fits to the planets’ magnetic fields; 17.24 h and 16.11 h for Uranus and Neptune, respectively. The realization that the radio period of Saturn does not represent the planet’s deep interior rotation and the complexity of the magnetic fields of Uranus and Neptune raise the possibility that the Voyager 2 radio and magnetic periods might not represent the deep interior rotation periods of the ice giants. Moreover, if there is deep differential rotation within Uranus and Neptune no single solid-body rotation period could characterize the bulk rotation of the planets. We use wind and shape data to investigate the rotation of Uranus and Neptune. The shapes (flattening) of the ice giants are not measured, but only inferred from atmospheric wind speeds and radio occultation measurements at a single latitude. The inferred oblateness values of Uranus and Neptune do not correspond to bodies rotating with the Voyager rotation periods. Minimization of wind velocities or dynamic heights of the 1 bar isosurfaces, constrained by the single occultation radii and gravitational coefficients of the planets, leads to solid-body rotation periods of ∼16.58 h for Uranus and ∼17.46 h for Neptune. Uranus might be rotating faster and Neptune slower than Voyager rotation speeds. We derive shapes for the planets based on these rotation rates. Wind velocities with respect to these rotation periods are essentially identical on Uranus and Neptune and wind speeds are slower than previously thought. Alternatively, if we interpret wind measurements in terms of differential rotation on cylinders there are essentially no residual atmospheric winds.     

Orbital evolution of a planet with tidal dissipation in a restricted three-body system

The angle between planetary spin and the normal direction of an orbital plane is supposed to reveal a range of information about the associated planetary formation and evolution. Since the orbit's eccentricity and inclination oscillate periodically in a hierarchical triple body and tidal friction makes the spin parallel to the normal orientation of the orbital plane with a short timescale in an isolated binary system, we focus on the comprehensive effect of third body perturbation and tidal mechanism on the angle. Firstly, we extend the Hut tidal model(1981) to the general spatial case, adopting the equilibrium tide and weak friction hypothesis with constant delay time, which is suitable for arbitrary eccentricity and any angle ? between the planetary spin and normal orientation of the orbital plane. Furthermore, under the constraint of angular momentum conservation, the equations of orbital and ratational motion are given. Secondly, considering the coupled effects of tidal dissipation and third body perturbation, and adopting the quadrupole approximation as the third body perturbation effect, a comprehensive model is established by this work. Finally, we find that the ultimate evolution depends on the timescales of the third body and tidal friction. When the timescale of the third body is much shorter than that of tidal friction, the angle ? will oscillate for a long time,even over the whole evolution; when the timescale of the third body is observably larger than that of the tidal friction, the system may enter stable states, with the angle ? decaying to zero ultimately, and some cases may have a stable inclination beyond the critical value of Lidov-Kozai resonance. In addition, these dynamical evolutions depend on the initial values of the orbital elements and may aid in understanding the characteristics of the orbits of exoplanets.     

Yarkovsky origin of the unstable asteroids in the 2/1 mean motion resonance with Jupiter

The 2/1 mean motion resonance with Jupiter, intersecting the main asteroid belt at ≈3.27  au, contains a small population of objects. Numerical investigations have classified three groups within this population: asteroids residing on stable orbits (i.e. Zhongguos), those on marginally stable orbits with dynamical lifetimes of the order of 100 Myr (i.e. Griquas), and those on unstable orbits. In this paper, we reexamine the origin, evolution and survivability of objects in the 2/1 population. Using recent asteroid survey data, we have identified 100 new members since the last search, which increases the resonant population to 153. The most interesting new asteroids are those located in the theoretically predicted stable island A, which until now had been thought to be empty. We also investigate whether the population of objects residing on the unstable orbits could be resupplied by material from the edges of the 2/1 resonance by the thermal drag force known as the Yarkovsky effect (and by the YORP effect, which is related to the rotational dynamics). Using N -body simulations, we show that test particles pushed into the 2/1 resonance by the Yarkovsky effect visit the regions occupied by the unstable asteroids. We also find that our test bodies have dynamical lifetimes consistent with the integrated orbits of the unstable population. Using a semi-analytical Monte Carlo model, we compute the steady-state size distribution of magnitude   H < 14  asteroids on unstable orbits within the resonance. Our results provide a good match with the available observational data. Finally, we discuss whether some 2/1 objects may be temporarily captured Jupiter-family comets or near-Earth asteroids.     

Vesta fragments from v6 and 3:1 resonances: Implications for V-type near-Earth asteroids and howardite,eucrite and diogenite meteorites

Abstract— A large body of evidence, including the presence of a dynamical family associated with 4 Vesta, suggests that this asteroid might be the ultimate source of both the V-type near-Earth asteroids (NEAs) and howardite, eucrite and diogenite (HED) meteorites. Dynamical routes from Vesta to the inner regions of the solar system are provided by both the 3:1 mean-motion resonance with Jupiter and the V₆, secular resonance. For this reason, numerical integrations of the orbits of fictitious Vesta fragments injected in both of these resonances have been performed. At the same time, the orbital evolution of the known V-type NEAs has been investigated. The results indicate that the dynamical half lifetimes of Vesta fragments injected in both the 3:1 and the V₆, resonances are rather short ('2 Ma). The present location of the seven known V-type NEAs is better explained by orbital evolutions starting from the v₆ secular resonance. The most important result of the present investigation, however, is that we now face what we call the “Vesta paradox.” Roughly speaking, the paradox consists of the fact that the present V-type NEAs appear to be too dynamically young to have originated in the event that produced the family, but they are too big to be plausible second-generation fragments from the family members. The cosmic-ray exposure (CRE) age distribution of HED meteorites also raises a puzzle, since we would expect an overabundance of meteorites with short CRE ages. We propose different scenarios to explain these paradoxes.     

双黑洞系统的不同起源及其参数分布

双黑洞组成的近密双星系统并合是激光干涉仪引力波天文台等地基引力波探测器的主要探测对象。随着探测器灵敏度的提高,大量该类信号的探测将成为进一步研究黑洞物理的有效工具。但是目前对双黑洞系统的起源机制和内禀参数分布等物理问题的研究还不够深入,例如由引力波探测得到的黑洞质量分布与X射线双星观测的结果存在较大差异,还未有很好的理论模型可解释该结果。目前普遍认为双黑洞系统主要有两种起源:大质量双星演化机制和动力学起源机制。基于这两类起源的双黑洞系统在质量、自旋分布等方面存在差异。因此可在贝叶斯理论框架下,利用引力波信号携带的波源质量和自旋等信息,推断波源起源,计算不同起源的双黑洞系统所占比例,以及检验质量自旋等参数分布的差异。     

Two dynamical classes of Centaurs

The Centaurs are a transient population of small bodies in the outer Solar System whose orbits are strongly chaotic. These objects typically suffer significant changes of orbital parameters on timescales of a few thousand years, and their orbital evolution exhibits two types of behaviors described qualitatively as random walk and resonance-sticking. We have analyzed the chaotic behavior of the known Centaurs. Our analysis has revealed that the two types of chaotic evolution are quantitatively distinguishable: (1) the random walk type behavior is well described by so-called generalized diffusion in which the rms deviation of the semimajor axis grows with time t as ∼t^H, with Hurst exponent H in the range 0.22-0.95, however (2) orbital evolution dominated by intermittent resonance sticking, with sudden jumps from one mean motion resonance to another, has poorly defined H. We further find that these two types of behavior are correlated with Centaur dynamical lifetime: most Centaurs whose dynamical lifetime is less than ∼22 Myr exhibit generalized diffusion, whereas most Centaurs of longer dynamical lifetimes exhibit intermittent resonance sticking. We also find that Centaurs in the diffusing class are likely to evolve into Jupiter-family comets during their dynamical lifetimes, while those in the resonance-hopping class do not.     

On the implications of the shape of Mars

Determinations of the ellipticity of the surface of Mars reveal a large discrepancy with the dynamical value obtained from the precession of the orbits of the satellites. Because the dynamical value is in accordance with that expected on the basis of hydrostatic theory, assuming the density of Mars was almost uniform, the optical value was doubted. However, the discrepancy might be explained by solid state convection in the deep interior of Mars. Observations from occultations of the Mariner spacecraft have confirmed the existence of the discrepancy between the ellipticities; thus, the role of convection in the Martian interior may be a key to its evolution.     

Angular momentum and tidal evolution of Saturn's system

It has been demonstrated that dynamically the Saturnian system is analogous to the Jovian system; however, it is not an analogue of the Solar system as a whole. The departures in the figure parameters of the tri-axial Saturnian satellites orbiting in 1 : 1 resonance, from equilibrium figure parameters are not large in general, and the tidal and centrifugal distorting forces can be supposed to be responsible for the actual figures. The estimates for different dynamical parameters of the system support the hypothesis that the tri-axial satellites in 1 : 1 resonance were formed from the same protoplanetary nebula that gave rise to Saturn.     

Extragalactic novae

Novae are expected to form in all stellar systems with a binary population. Detection of extragalactic novae provides direct evidence of close binary populations and possible spatial variations in those populations. Comparison of extragalactic novae with their local counterparts can yield valuable tests of close binary evolution theory. I report early results from surveys of globular clusters, the Large Magellanic Cloud and M81 for classical novae in eruption and in quiescence. T Sco, the nova of 1860 A.D. in the globular cluster M80, has now been recovered. It is three magnitudes fainter than canonical old novae, though this might be an inclination effect. Seven quiescent old novae in the Large Magellanic Cloud have been recovered (at brightnesses comparable to their Galactic counterparts). Their orbital periods are now within reach. Twenty-three novae have been detected on archival 5 meter Palomar plates of M81. The spatial distribution of these novae strongly suggests that most come from the spiral arm population.     

Temporal changes in the flux of meteorites in the recent past

The depth variations of the fossil cosmic ray tracks and agglutinates have been examined in the (0.6–0.7)m deep Apollo 12 and 16 drive cores, in the 2.4 m Apollo 15 deep drill core and in a 0.6 m long section of the Apollo 17 deep drill core. These data indicate Moon-wide short duration episodes of impacts of meteorites of size 10 cm^–1m on the lunar surface. Based on the longest continuous Apollo 15 deep drill core record, these impact episodes occurred about 150, 400 and 700 m.y. ago. The enhancements in the meteorite flux may be due to solar dynamical processes or they may be related to excursions of the solar system, once in each orbit, through a certain dusty region of the galaxy.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978.     

Dense and diffuse gas in dynamically active clouds

We investigate the chemical and observational implications of repetitive transient dense core formation in molecular clouds. We allow a transient density fluctuation to form and disperse over a period of 1 Myr, tracing its chemical evolution. We then allow the same gas immediately to undergo further such formation and dispersion cycles. The chemistry of the dense gas in subsequent cycles is similar to that of the first, and a limit cycle is reached quickly (2–3 cycles). Enhancement of hydrocarbon abundances during a specific period of evolution is the strongest indicator of previous dynamical history. The molecular content of the diffuse background gas in the molecular cloud is expected to be strongly enhanced by the core formation and dispersion process. Such enhancement may remain for as long as 0.5 Myr. The frequency of repetitive core formation should strongly determine the level of background molecular enhancement.
We also convolve the emission from a synthesized dark cloud, comprised of ensembles of transient dense cores. We find that the dynamical history of the gas, and therefore the chemical state of the diffuse intercore medium, may be determined if a sufficient sample of cores is present in an ensemble. Molecular ratios of key hydrocarbons with SO and SO₂ are crucial to this distinction. Only surveys with great enough angular resolution to resolve individual cores, or very small groupings, are expected to show evidence of repetitive dynamical processing. The existence of non-equilibrium chemistry in the diffuse background may have implications for the initial conditions used in chemical models. Observed variations in the chemistries of diffuse and translucent regions may be explained by lines of sight which intersect a number of molecular cloud cores in various stages of evolution.     

A simple mapping for comets in resonance

The dynamical evolution of a low inclination, intermediate period comet in mean-motion resonance with a giant planet can be described by a simple mapping giving the comet's heliocentric energy and ecliptic longitude at successive aphelia. Provided that the energy oscillations produced by the resonance are not too large, this mapping is linear. When the amplitude of the oscillations is close to the maximum possible within the resonance, the mapping can be improved by adding non-linear terms.     

Influence of periodic orbits on the formation of giant planetary systems

The late-stage formation of giant planetary systems is rich in interesting dynamical mechanisms. Previous simulations of three giant planets initially on quasi-circular and quasi-coplanar orbits in the gas disc have shown that highly mutually inclined configurations can be formed, despite the strong eccentricity and inclination damping exerted by the disc. Much attention has been directed to inclination-type resonance, asking for large eccentricities to be acquired during the migration of the planets. Here we show that inclination excitation is also present at small to moderate eccentricities in two-planet systems that have previously experienced an ejection or a merging and are close to resonant commensurabilities at the end of the gas phase. We perform a dynamical analysis of these planetary systems, guided by the computation of planar families of periodic orbits and the bifurcation of families of spatial periodic orbits. We show that inclination excitation at small to moderate eccentricities can be produced by (temporary) capture in inclination-type resonance and the possible proximity of the non-coplanar systems to spatial periodic orbits contributes to maintaining their mutual inclination over long periods of time.     

Long-term variations in the microwave brightness temperature of the Uranus atmosphere

We present a self-consistent, 36-year record of the disk-averaged radio brightness of Uranus at wavelengths near 3.5 cm. It covers nearly half a uranian year, and includes both equatorial and polar viewing geometries (corresponding to equinox and solstice, respectively). We find large (greater than 30 K) changes over this time span. In agreement with analyses made of more limited microwave data sets, our observations suggest the changes are not caused by geometric effects alone, and that temporal variations may exist in the deep uranian troposphere down to pressures of tens of bars. Our data also support an earlier suggestion that a rapid, planetary-scale change may have occurred in late 1993 and early 1994. The seasonal record presented here will be useful for constraining dynamical models of the deep atmosphere, and for interpreting observations made during Uranus' 2007 equinox passage. As part of a multi-wavelength observing campaign for this event, the Goldstone-Apple Valley Radio Telescope (GAVRT) project will continue to make frequent, single-dish observations near 3.5 cm.     

小天体离散元仿真软件的搭建与测试

小天体探测是当今太阳系探测的一大热点, 对小行星演化的研究有助于人们了解太阳系的起源. 演化研究的一项重要内容是小天体结构的演化, 即小天体在多种力学机制作用下自身形状与结构的演化. 在小天体碎石堆结构的假设之下, 一种比较常见的模拟小天体结构演化的方法是离散元仿真算法(Discrete Element Method, DEM), 目前国内外有数个团队开发了相关算法软件. 本文介绍了团队开发的《基于DEM仿真算法的多粒子系统模拟软件》的基础理论、实现方法以及加速算法, 并使用二体接触模型、声速传播仿真、小行星内部压强、小行星旋转稳定性仿真算例验证了算法的可靠性.     

Effects of Planetary Migration on Natural Satellites of the Outer Planets

Numerous studies in the past few years have analyzed possible effects of planetary migration on the small bodies of the Solar System (mainly asteroids and KBOs), with the double aim of explaining certain dynamical structures in these systems, as well as placing limits on the magnitude of the radial migration of the planets. Here we undertake a similar aim, only this time concentrating on the dynamical stability of planetary satellites in a migration scenario. However, different from previous works, the strongest perturbations on satellite systems are not due to the secular variation of the semimajor axes of the planets, but from the planetesimals themselves. These perturbations result from close approaches between the planetesimals and satellites.We present results of several numerical simulations of the dynamical evolution of real and fictitious satellite systems around the outer planets, under the effects of multiple passages of a population of planetesimals representing the large-body component of a residual rocky disk. Assuming that this component dominated the total mass of the disk, our results show that the present systems of satellites of Uranus and Neptune do not seem to be compatible with a planetary migration larger than even one quarter that suggested by previous studies, unless these bodies were originated during the late stage of evaporation of the planetesimal disk. For larger variations of the semimajor axes of the planets, most of the satellites would either be ejected from the system or suffer mutual collisions due to excitation in their eccentricities. For the systems of Jupiter and Saturn, these perturbations are not so severe, and even large migrations do not introduce large instabilities.Nevertheless, even a small number of 1000-km planetesimals in the region may introduce significant excitation in the eccentricities and inclinations of satellites. Adequate values of this component may help explain the present dynamical distribution of distant satellites, including the highly peculiar orbit of Nereid.     

Photometric monitoring of the ROSAT selected late type stars

We monitored the light variations of 16 solar-type stars recently discovered in the X-ray wave-length range during the ROSAT all-sky survey. We find that 9 out of 16 stars showed appreciable light variability with amplitudes of a few hundredths of a magnitude. They are all proved to be in periodic variations. Using the methods of the phase dispersion minimization (PDM) and Fourier Analysis (PERIOD04), we derive the photometric periods for these stars. The rotational periods are found range from 0.471 to 17.31 days and the period of stars most (of 7 stars) being shorter than 3 days. Apart from binaries system, the results give further evidence for the spin up of solar-type stars as predicted by models of angular momentum evolution of pre-main sequence stars.