Long-term evolution of the spin of Mercury: I. Effect of the obliquity and core-mantle friction

The present obliquity of Mercury is very low (less than 0.1°), which led previous studies to always adopt a nearly zero obliquity during the planet’s past evolution. However, the initial orientation of Mercury’s rotation axis is unknown and probably much different than today. As a consequence, we believe that the obliquity could have been significant when the rotation rate of the planet first encountered spin-orbit resonances. In order to compute the capture probabilities in resonance for any evolutionary scenario, we present in full detail the dynamical equations governing the long-term evolution of the spin, including the obliquity contribution.The secular spin evolution of Mercury results from tidal interactions with the Sun, but also from viscous friction at the core-mantle boundary. Here, this effect is also regarded with particular attention. Previous studies show that a liquid core enhances drastically the chances of capture in spin-orbit resonances. We confirm these results for null obliquity, but we find that the capture probability generally decreases as the obliquity increases. We finally show that, when core-mantle friction is combined with obliquity evolution, the spin can evolve into some unexpected configurations as the synchronous or the 1/2 spin-orbit resonance.     

The web of three-planet resonances in the outer Solar System: II. A source of orbital instability for Uranus and Neptune

The motion of the giant planets from Jupiter to Neptune is chaotic with Lyapunov time of approximately 10 Myr. A recent theory explains the presence of this chaos with three-planet mean-motion resonances, i.e. resonances among the orbital periods of at least three planets. We find that the distribution of these resonances with respect to the semi-major axes of all the planets is compatible with orbital instability. In particular, they overlap in a region of 10⁻³ AU with respect to the variation of the semi-major axes of Uranus and Neptune. Fictitious planetary systems with initial conditions in this region can undergo systematic variations of semi-major axes. The true Solar System is marginally in this region, and Uranus and Neptune undergo very slow systematic variations of semi-major axes with speed of order 10⁻⁴ AU/Gyr.     

Orbital resonances in the inner neptunian system: I. The 2:1 Proteus-Larissa mean-motion resonance

We investigate the orbital resonant history of Proteus and Larissa, the two largest inner neptunian satellites discovered by Voyager 2. Due to tidal migration, these two satellites probably passed through their 2:1 mean-motion resonance a few hundred million years ago. We explore this resonance passage as a method to excite orbital eccentricities and inclinations, and find interesting constraints on the satellites' mean density () and their tidal dissipation parameters (Qs>10). Through numerical study of this mean-motion resonance passage, we identify a new type of three-body resonance between the satellite pair and Triton. These new resonances occur near the traditional two-body resonances between the small satellites and, surprisingly, are much stronger than their two-body counterparts due to Triton's large mass and orbital inclination. We determine the relevant resonant arguments and derive a mathematical framework for analyzing resonances in this special system.     

Orbital resonances in the inner neptunian system: II. Resonant history of Proteus, Larissa, Galatea, and Despina

We investigate the orbital history of the small neptunian satellites discovered by Voyager 2. Over the age of the Solar System, tidal forces have caused the satellites to migrate radially, bringing them through mean-motion resonances with one another. In this paper, we extend our study of the largest satellites Proteus and Larissa [Zhang, K., Hamilton, D.P., 2007. Icarus 188, 386-399] by adding in mid-sized Galatea and Despina. We test the hypothesis that these moons all formed with zero inclinations, and that orbital resonances excited their tilts during tidal migration. We find that the current orbital inclinations of Proteus, Galatea, and Despina are consistent with resonant excitation if they have a common density . Larissa's inclination, however, is too large to have been caused by resonant kicks between these four satellites; we suggest that a prior resonant capture event involving either Naiad or Thalassa is responsible. Our solution requires at least three past resonances with Proteus, which helps constrain the tidal migration timescale and thus Neptune's tidal quality factor: 9000<QN<36,000. We also improve our determination of Qs for Proteus and Larissa, finding 36<QP<700 and 18<QL<200. Finally, we derive a more general resonant capture condition, and work out a resonant overlap criterion relevant to satellite orbital evolution around an oblate primary.     

Orbit determination with very short arcs: II. Identifications

When the observational data are not enough to compute a meaningful orbit for an asteroid/comet we can represent the data with an attributable, i.e., two angles and their time derivatives. The undetermined variables range and range rate span an admissible region of Solar System orbits, which can be sampled by a set of Virtual Asteroids (VAs) selected by means of an optimal triangulation [Milani, A., Gronchi, G.F., de' Michieli Vitturi, M., Kne?evi?, Z., 2004. Celest. Mech. Dyn. Astron. 90, 59-87]. The attributable 4 coordinates are the result of a fit and they have an uncertainty, represented by a covariance matrix. Two short arcs of observations, represented by two attributables, can be linked by considering for each VA (in the admissible region of the first arc) the covariance matrix for the prediction at the time of the second arc, and by comparing it with the attributable of the second arc with its own covariance. By defining an identification penalty we can select the VAs allowing to fit together both arcs and compute a preliminary orbit. Two attributables may not be enough to compute an orbit with convergent differential corrections. Thus the preliminary orbit is used in a constrained differential correction, providing solutions along the Line Of Variation which can be used as second generation VAs to further predict the observations at the time of a third arc. In general the identification with a third arc will ensure a well determined orbit, to which additional sets of observations can be attributed. To test these algorithms we use a large scale simulation and measure the completeness, the reliability and the efficiency of the overall procedure to build up orbits by accumulating identifications. Under the conditions expected for the next generation asteroid surveys, the methods developed in this and in the preceding papers are efficient enough to be used as primary identification methods, with very good results. One important property is that the completeness in finding the possible identifications is as good for comparatively rare orbits, such as the ones of Near-Earth Objects, as for main belt orbits.     

The jovian anticyclone BA: I. Motions and interaction with the GRS from observations and non-linear simulations

A study of the dynamics of the second largest anticyclone in Jupiter, Oval BA, and its red colour change that occurred in late 2005 is presented in a three part study. The first part, this paper, deals with its long-term kinematical and dynamical behaviour monitored since its formation in 2000 to September 2008 using ground-based observations archived at the public International Outer Planet Watch (IOPW) database. The vortex changed its zonal drift velocity from 1.8 m s⁻¹ in the period 2000-2002 to 0.8 m s⁻¹ in 2002-2003, and to 2.5 m s⁻¹ since late 2003. It also migrated southwards by 1.0 ± 0.5° in latitude between 2000 and 2004, remaining afterwards at an almost fixed latitude position. During the period 2000-2007, the oval also changed its triangular-like shape to a more symmetrical one. No latitudinal change was found in the months before the development of a red annulus in its interior. The colour change took place in less than 5 months in 2005-2006 and no red colour feature was observed to have been present or entrained by BA months before the annulus development. After detailed examination of the four encounters between BA and GRS that took place during this 9 year period, we did not detect any noticeable change in its drift rate or in apparent structure associated with the encounters at cloud level. Also, the area of BA did not significantly change in this period. Additionally, we found that BA displays a long-term oscillation of ∼160 days in its longitude position with peak to peak amplitude of 1.2°. Numerical experiments using the global circulation model EPIC reproduce accurately the shape, connecting it to its latitude migration, and morphology of the oval and confirm that no strong interaction between BA and the GRS is possible at least in the current situation.     

Modeling the 3-D secular planetary three-body problem: Discussion on the outer υ Andromedae planetary system

The three-dimensional secular behavior of a system composed of a central star and two massive planets is modeled semi-analytically in the frame of the general three-body problem. The main dynamical features of the system are presented in geometrical pictures allowing us to investigate a large domain of the phase space of this problem without time-expensive numerical integrations of the equations of motion and without any restriction on the magnitude of the planetary eccentricities, inclinations and mutual distance. Several regimes of motion of the system are observed. With respect to the secular angle Δ?, possible motions are circulations, oscillations (around 0° and 180°), and high-eccentricity/inclination librations in secular resonances. With respect to the arguments of pericenter, ω₁ and ω₂, possible motions are direct circulation and high-inclination libration around ±90° in the Lidov-Kozai resonance. The regions of transition between domains of different regimes of motion are characterized by chaotic behavior. We apply the analysis to the case of the two outer planets of the υ Andromedae system, observed edge-on. The topology of the 3-D phase space of this system is investigated in detail by means of surfaces of section, periodic orbits and dynamical spectra, mapping techniques and numerical simulations. We obtain the general structure of the phase space, and the boundaries of the spatial secular stability. We find that this system is secularly stable in a large domain of eccentricities and inclinations.     

Cassini imaging of Saturn's rings: II. A wavelet technique for analysis of density waves and other radial structure in the rings

We describe a powerful signal processing method, the continuous wavelet transform, and use it to analyze radial structure in Cassini ISS images of Saturn's rings. Wavelet analysis locally separates signal components in frequency space, causing many structures to become evident that are difficult to observe with the naked eye. Density waves, generated at resonances with saturnian satellites orbiting outside (or within) the rings, are particularly amenable to such analysis. We identify a number of previously unobserved weak waves, and demonstrate the wavelet transform's ability to isolate multiple waves superimposed on top of one another. We also present two wave-like structures that we are unable to conclusively identify. In a multi-step semi-automated process, we recover four parameters from clearly observed weak spiral density waves: the local ring surface density, the local ring viscosity, the precise resonance location (useful for pointing images, and potentially for refining saturnian astrometry), and the wave amplitude (potentially providing new constraints upon the masses of the perturbing moons). Our derived surface densities have less scatter than previous measurements that were derived from stronger non-linear waves, and suggest a gentle linear increase in surface density from the inner to the mid-A Ring. We show that ring viscosity consistently increases from the Cassini Division outward to the Encke Gap. Meaningful upper limits on ring thickness can be placed on the Cassini Division (3.0 m at r∼118,800 km, 4.5 m at r∼120,700 km) and the inner A Ring (10-15 m for r<127,000 km).     

Yarkovsky detection opportunities: II. Binary systems

We consider the possibility of detecting the Yarkovsky orbital perturbation acting on binary systems among the near-Earth asteroids. This task is significantly more difficult than for solitary asteroids because the Yarkovsky force affects both the heliocentric orbit of the system's center of mass and the relative orbit of the two components. Nevertheless, we argue these are sufficiently well decoupled so that the major Yarkovsky perturbation is in the simpler heliocentric motion and is observable with the current means of radar astrometry. Over the long term, the Yarkovsky perturbation in the relative motion of the two components is also detectable for the best observed systems. However, here we consider a simplified version of the problem by ignoring mutual non-spherical gravitational perturbations between the two asteroids. With the orbital plane constant in space and the components' rotation poles fixed (and assumed perpendicular to the orbital plane), we do not examine the coupling between Yarkovsky and gravitational effects. While radar observations remain an essential element of Yarkovsky detections, lightcurve observations, with their ability to track occultation and eclipse phenomena, are also very important in the case of binaries. The nearest possible future detection of the Yarkovsky effect for a binary system occurs for (66063) 1998 RO₁ in September 2006. Farther out, even more statistically significant detections are possible for several other systems including 2000 DP₁₀₇, (66391) 1999 KW₄ and 1996 FG₃.     

Non-gravitational force modeling of Comet 81P/Wild 2: II. Rotational evolution

In this paper, we have studied both the dynamical and the rotational evolution of an 81P/Wild 2-like comet under the effects of the outgassing-induced force and torque. The main aim is to study if it is possible to reproduce the non-gravitational orbital changes observed in this comet, and to establish the likely evolution of both orbital and rotational parameters. To perform this study, a simple thermophysical model has been used to estimate the torque acting on the nucleus. Once the torque is calculated, Euler equations are solved numerically considering a nucleus mass directly estimated from the changes in the orbital elements (as determined from astrometry). According to these simulations, when the water production rate and changes in orbital parameters for 1997, as well as observational rotational parameters for 2004 are imposed as constraints, the change in the orbital period of 81P/Wild 2, , will decrease so that to , which is similar to the actual tendency observed from 1988 up to 1997. This nearly constant decreasing can be explained as due to a slight drift of the spin axis orientation towards larger ecliptic longitudes. After studying the possible spin axis orientations proposed for 1997, simulations suggest that the spin obliquity and argument (I,Φ)=(56°,167°) is the most likely. As for rotational evolution, changes per orbit smaller than 10% of the actual spin velocity are probable, while the most likely value corresponds to a change between 2 and 7% of the spin velocity. Equally, net changes in the spin axis orientation of 4°-8° per orbit are highly expected.     

Magnetic aggregation: II. Laboratory and microgravity experiments

In a previous publication (Dominik and Nübold, 2002, Icarus 157, 173-186), we presented analytical expressions and theoretical considerations concerning preplanetary dust aggregation with magnetized grains in the solar nebula. The present work is dedicated to the experimental study of magnetic aggregation in a ground-based laboratory as well as under microgravity conditions on parabolic flights. We conducted aggregation experiments with dust analogues in order to study the temporal evolution and the structural outcome of grain growth processes dominated by or comprising exclusively magnetic grains. Within aggregation times ranging from a couple of seconds to a few minutes only, formation of huge chain-like and/or web-like dust aggregates was observed. After aggregate retrieval we were able to study the sizes and structures of the aggregates in great detail. We established the fractal dimension of the aggregates as D_fs=1.20±0.05 for single chains and D_fc=1.50±0.21 for inter-connected web-like structures. This is considerably lower than for non-magnetic grain growth. The dynamic exponent z for the mass increase with time according to t^z was found to be z=2.7 from in-situ video images of the microgravity aggregation runs. The results are compared with the theoretical considerations presented earlier as well as with previous experimental work on the same and on related topics, respectively.     

Orbital evolution and accretion of protoplanets tidally interacting with a gas disk: II. Solid surface density evolution with type-I migration

This paper investigates the surface density evolution of a planetesimal disk due to the effect of type-I migration by carrying out N-body simulation and through analytical method, focusing on terrestrial planet formation. The coagulation and the growth of the planetesimals take place in the abundant gas disk except for a final stage. A protoplanet excites density waves in the gas disk, which causes the torque on the protoplanet. The torque imbalance makes the protoplanet suffer radial migration, which is known as type-I migration. Type-I migration time scale derived by the linear theory may be too short for the terrestrial planets to survive, which is one of the major problems in the planet formation scenario. Although the linear theory assumes a protoplanet being in a gas disk alone, Kominami et al. [Kominami, J., Tanaka, H., Ida, S., 2005. Icarus 167, 231-243] showed that the effect of the interaction with the planetesimal disk and the neighboring protoplanets on type-I migration is negligible. The migration becomes pronounced before the planet's mass reaches the isolation mass, and decreases the solid component in the disk. Runaway protoplanets form again in the planetesimal disk with decreased surface density. In this paper, we present the analytical formulas that describe the evolution of the solid surface density of the disk as a function of gas-to-dust ratio, gas depletion time scale and semimajor axis, which agree well with our results of N-body simulations. In general, significant depletion of solid material is likely to take place in inner regions of disks. This might be responsible for the fact that there is no planet inside Mercury's orbit in our Solar System. Our most important result is that the final surface density of solid components (Σd) and mass of surviving planets depend on gas surface density (Σg) and its depletion time scale (τdep) but not on initial Σd; they decrease with increase in Σg and τdep. For a fixed gas-to-dust ratio and τdep, larger initial Σd results in smaller final Σd and smaller surviving planets, because of larger Σg. To retain a specific amount of Σd, the efficient disk condition is not an initially large Σd but the initial Σd as small as the specified final one and a smaller gas-to-dust ratio. To retain Σd comparable to that of the minimum mass solar nebula (MMSN), a disk must have the same Σd and a gas-to-dust ratio that is smaller than that of MMSN by a factor of 1.3×(τdep/1 Myr) at ∼1 AU. (Equivalently, type-I migration speed is slower than that predicted by the linear theory by the same factor.) The surviving planets are Mars-sized ones in this case; in order to form Earth-sized planets, their eccentricities must be pumped up to start orbit crossing and coagulation among them. At ∼5 AU, Σd of MMSN is retained under the same condition, but to form a core massive enough to start runaway gas accretion, a gas-to-dust ratio must be smaller than that of MMSN by a factor of 3×τdep/1 Myr.     

Impact evolution of asteroid shapes: 1. random mass redistribution

We explore whether the cumulative effect of small-scale meteoroid bombardment can drive asteroids into nonaxisymmetric shapes comparable to those of known objects (elongated prolate forms, twin-lobed binaries, etc). We simulate impact cratering as an excavation followed by the launch, orbit, and reimpact of ejecta. Orbits are determined by the gravity and rotation of the evolving asteroid, whose shape and spin change as cratering occurs repeatedly. For simplicity we consider an end-member evolution where impactors are all much smaller than the asteroid and where all ejecta remain bound. Given those assumptions, we find that cumulative small impacts on rotating asteroids lead to oblate shapes, irrespective of the chosen value for angle of repose or for initial angular momentum. The more rapidly a body is spinning, the more flattened the outcome, but oblateness prevails. Most actual asteroids, by contrast, appear spherical to prolate. We also evaluate the timescale for reshaping by small impacts and compare it to the timescale for catastrophic disruption. For all but the steepest size distributions of impactors, reshaping from small impacts takes more than an order of magnitude longer than catastrophic disruption. We conclude that small-scale cratering is probably not dominant in shaping asteroids, unless our assumptions are naive. We believe we have ruled out the end-member scenario; future modeling shall include angular momentum evolution from impacts, mass loss in the strength regime, and craters with diameters up to the disruption threshold. The ultimate goal is to find out how asteroids get their shapes and spins and whether tidal encounters in fact play a dominant role.     

Latitudinal transport by barotropic waves in Titan's stratosphere.: II. Results from a coupled dynamics-microphysics-photochemistry GCM

We present a 2D general circulation model of Titan's atmosphere, coupling axisymmetric dynamics with haze microphysics, a simplified photochemistry and eddy mixing. We develop a parameterization of latitudinal eddy mixing by barotropic waves based on a shallow-water, longitude-latitude model. The parameterization acts locally and in real time both on passive tracers and momentum. The mixing coefficient varies exponentially with a measure of the barotropic instability of the mean zonal flow. The coupled GCM approximately reproduces the Voyager temperature measurements and the latitudinal contrasts in the distributions of HCN and C₂H₂, as well as the main features of the zonal wind retrieved from the 1989 stellar occultation. Wind velocities are consistent with the observed reversal time of the North-South albedo asymmetry of 5 terrestrial years. Model results support the hypothesis of a non-uniform distribution of infrared opacity as the cause of the Voyager temperature asymmetry. Transport by the mean meridional circulation, combined with polar vortex isolation may be at the origin of the latitudinal contrasts of trace species, with eddy mixing remaining restricted to low latitudes most of the Titan year. We interpret the contrasts as a signature of non-axisymmetric motions.     

Cassini UVIS observations of the Io plasma torus: II. Radial variations

On January 14, 2001, shortly after the Cassini spacecraft's closest approach to Jupiter, the Ultraviolet Imaging Spectrometer (UVIS) made a radial scan through the midnight sector of Io plasma torus. The Io torus has not been previously observed at this local time. The UVIS data consist of 2-D spectrally dispersed images of the Io plasma torus in the wavelength range of 561-1912 Å. We developed a spectral emissions model that incorporates the latest atomic physics data contained in the CHIANTI database in order to derive the composition of the torus plasma as a function of radial distance. Electron temperatures derived from the UVIS torus spectra are generally less than those observed during the Voyager era. We find the torus ion composition derived from the UVIS spectra to be significantly different from the composition during the Voyager era. Notably, the torus contains substantially less oxygen, with a total oxygen-to-sulfur ion ratio of 0.9. The average ion charge state has increased to 1.7. We detect S(V) in the Io torus at the 3σ level. S(V) has a mixing ratio of 0.5%. The spectral emission model used can approximate the effects of a nonthermal distribution of electrons. The ion composition derived using a kappa distribution of electrons is identical to that derived using a Maxwellian electron distribution; however, the kappa distribution model requires a higher electron column density to match the observed brightness of the spectra. The derived value of the kappa parameter decreases with radial distance and is consistent with the value of κ=2.4 at 8R_J derived by the Ulysses URAP instrument (Meyer-Vernet et al., 1995). The observed radial profile of electron column density is consistent with a flux tube content, NL², that is proportional to r⁻².     

Corona-like atmospheric escape from KBOs: II. The behavior of aerosols

In Levi and Podolak (Levi, A., Podolak, M. [in press] Icarus) we applied the theory of coronal expansion to gas escape from a small, cold, object such as those found in the Kuiper belt. Here we extend the theory to include aerosols that are lifted off the surface by the escaping gas. Aerosols carried by the gas but still gravitationally bound, tend to be lifted to a height above the surface that is dependent on the aerosol radius, so that in steady state the variation of aerosol radius with height is well-defined. We develop an extension of Parker’s coronal flow theory to include the effect of aerosols carried along by the gas and use this to estimate the optical depth of such an atmosphere. For KBOs with CO evaporation from the surface and with radii in the range 245-334 km, line-of-site optical depths through the atmosphere can exceed one at heights of a few hundred kilometers above the surface. Such aerosol layers should be observable, and might be used to infer the flow proprieties of the escaping gas.     

Simulations of dense planetary rings: IV. Spinning self-gravitating particles with size distribution

Previous self-gravitating simulations of dense planetary rings are extended to include particle spins. Both identical particles as well as systems with a modest range of particle sizes are examined. For a ring of identical particles, we find that mutual impact velocity is always close to the escape velocity of the particles, even if the total rms velocity dispersion of the system is much larger, due to collective motions associated to wakes induced by near-gravitational instability or by viscous overstability. As a result, the spin velocity (i.e., the product of the particle radius and the spin frequency) maintained by mutual impacts is also of the order of the escape velocity, provided that friction is significant. For the size distribution case, smaller particles have larger impact velocities and thus larger spin velocities, particularly in optically thick rings, since small particles move rather freely between wakes. Nevertheless, the maximum ratio of spin velocities between the smallest and largest particles, as well as the ratio for translational velocities, stays below about 5 regardless of the width of the size distribution. Particle spin state is one of the important factors affecting the temperature difference between the lit and unlit face of Saturn's rings. Our results suggest that, to good accuracy, the spin frequency is inversely proportional to the particle size. Therefore, the mixing ratio of fast rotators to slow rotators on the scale of the thermal relaxation time increases with the width of the particle size distribution. This will offer means to constrain the particle size distribution with the systematic thermal infrared observations carried by the Cassini probe.     

On the Light-Absorbing Surface Layer of Cometary Nuclei: II. Thermal Modeling

The classical way to treat absorption of solar light in thermophysical modeling of cometary nuclei (and other ice-rich bodies such as jovian satellites) has been to assume complete opaqueness of the surface material. However, as shown by Davidsson and Skorov (2002, Icarus156, 223-248), substantial light penetration can occur in porous ice even if it is very dusty, implying that gradual absorption of energy in a surface layer should be accounted for.We present a thorough comparison between a surface energy absorption model and a layer energy absorption model, for various combinations of heliocentric distances, conductivities, opacities, pore sizes, and rotational periods relevant for cometary nuclei, by fully solving the coupled differential equations of heat transfer and gas diffusion. We find substantial differences between the models in terms of gas production rate, thermal lag angle, surface temperature, and the origin of coma molecules. For example, the surface energy absorption model overestimates the total gas production by a factor of 2-7, underestimates the lag angle by a factor of 2-3, and places the origin of coma molecules at the surface, instead of the near-surface interior.