Stable Chaos in High-Order Jovian Resonances

In a previous publication (Tsiganis et al. 2000, Icarus146, 240-252), we argued that the occurrence of stable chaos in the 12/7 mean motion resonance with Jupiter is related to the fact that there do not exist families of periodic orbits in the planar elliptic restricted problem and in the 3-D circular problem corresponding to this resonance. In the present paper we show that nonexistence of resonant periodic orbits, both for the planar and for the 3-D problem, also occurs in other jovian resonances—namely the 11/4, 22/9, 13/6, and 18/7—where cases of real asteroids on stable-chaotic orbits have been identified. This property may provide a “protection mechanism”, leading to semiconfinement of chaotic orbits and extremely slow migration in the space of proper elements, so that diffusion is practically unrelated to the value of the Lyapunov time, T_L, of chaotic orbits. However, we show that, in more complicated dynamical models, the long-term evolution of chaotic orbits initiated in the vicinity of these resonances may also be governed by secular resonances. Finally, we find that stable-chaotic orbits have a characteristic spectrum of autocorrelation times: for the action conjugate to the critical argument the autocorrelation time is of the order of the Lyapunov time, while for the eccentricity- and inclination-related actions the autocorrelation time may be longer than 10³T_L. This behavior is consistent with the trajectory being sticky around a manifold of lower-than-full dimensionality in phase space (e.g., a 4-D submanifold of the 5-D energy manifold in a three-degrees-of-freedom autonomus Hamiltonian system) and reflects the inability of these “flawed” resonances to modify secular motion significantly, at least for times of the order of 200 Myr.     

On the Inclination Distribution of the Jovian Irregular Satellites

Irregular satellites—moons that occupy large orbits of significant eccentricity e and/or inclination I—circle each of the giant planets. The irregulars often extend close to the orbital stability limit, about 1/3-1/2 of the way to the edge of their planet's Hill sphere. The distant, elongated, and inclined orbits suggest capture, which presumably would give a random distribution of inclinations. Yet, no known irregulars have inclinations (relative to the ecliptic) between 47 and 141°.This paper shows that many high-I orbits are unstable due to secular solar perturbations. High-inclination orbits suffer appreciable periodic changes in eccentricity; large eccentricities can either drive particles with ∼70°<I<110° deep into the realm of the regular satellites (where collisions and scatterings are likely to remove them from planetocentric orbits on a timescale of 10⁷-10⁹ years) or expel them from the Hill sphere of the planet.By carrying out long-term (10⁹ years) orbital integrations for a variety of hypothetical satellites, we demonstrate that solar and planetary perturbations, by causing particles to strike (or to escape) their planet, considerably broaden this zone of avoidance. It grows to at least 55°<I<130° for orbits whose pericenters freely oscillate from 0 to 360°, while particles whose pericenters are locked at ±90° (Kozai mechanism) can remain for longer times.We estimate that the stable phase space (over 10 Myr) for satellites trapped in the Kozai resonance contains ∼10% of all stable orbits, suggesting the possible existence of a family of undiscovered objects at higher inclinations than those currently known.     

Some peculiarities in the Asteroidal Belt

The analysis of the fine structure of the Asteroidal Belt evidenciates a group of asteroids next to the resonance 4/9 with Jupiter. In this group and in other groups associated to the Hirayama families there are indications that their orbital parameters can be represented by quantum numbers as defined here and in two of our previous works. Together with this the distribution of the eccentricities and inclinations of the orbital planes of short period comets and diverse type of asteroids indicates that they can be classified as objects with e > sin i and objects with e > sin i with a limit e = sin i which determinates geometrical properties of the orbits related with discrete states in the solar system. This study lets open the possibility of following studies in order to confirm the quantum characteristics of the Asteroidal Belt being these characteristics common to all the solar system and depending of the same fundamental constant of action per mass unit H ₀ = 1/2 ₀ × T ₀ (potential × time) because only a small part of all the available data in the Asteroid Belt is used here.     

Spectral Investigation of Two Asteroidal Fireballs

High resolution photographic spectra of two fireballs have been analyzed. The fireballs were produced by meteoroids of asteroidal origin of the mass of the order of 1 kg. Temperature, size, and mass of the vapor cloud around the meteoroid was derived at selected points along the trajectory. Abundances of 11 elements, including lithium, were determined. The abundances of refractory elements in the vapors of the first meteoroid indicate that only 90–95% of the ablated material was vaporized. The meteoroid was likely a chondritic body. Relative stability of the vapor cloud was disturbed for 0.1 s after a major fragmentation of the meteoroid at the height of 42 km. Size and mass of the cloud decreased after the fragmentation and this enabled more intensive heat transfer from the incoming airflow. Both the vapor temperature and the vaporization temperature of the ablated melt increased. A brief millisecond flare of the fireball was produced under these conditions by a violent vaporization of small amount of material. The composition of the vapors of the second meteoroid can be explained either by an anomalous meteoroid composition with severely depleted Al, Ca, and Mg or by highly incomplete evaporation of the ablated material reaching only about 50%.     

On the instability region around the 5 : 3 Jovian resonance

Variations in the dynamic parameters of Phobos have been determined after reaching critical value of the semi-major axis = 7247 km at which zero-gravity on the surface of Phobos near the equator will take place. The rate of the variations will increase significantly, e.g., in the tidal energy dissipation by one order in magnitude. The total dissipated mechanical energy during the whole tidal history of the system has been estimated as -5.5 × 10²¹ kg m² s^-2, the total decrease in the second zonal Stokes parameter of Phobos as -6.6 × 10^-2.     

Asteroidal source of L chondrite meteorites

Establishing connections between meteorites and their parent asteroids is an important goal of planetary science. Several links have been proposed in the past, including a spectroscopic match between basaltic meteorites and (4) Vesta, that are helping scientists understand the formation and evolution of the Solar System bodies. Here we show that the shocked L chondrite meteorites, which represent about two thirds of all L chondrite falls, may be fragments of a disrupted asteroid with orbital semimajor axis a=2.8 AU. This breakup left behind thousands of identified 1–15 km asteroid fragments known as the Gefion family. Fossil L chondrite meteorites and iridium enrichment found in an ≈467 Ma old marine limestone quarry in southern Sweden, and perhaps also ∼5 large terrestrial craters with corresponding radiometric ages, may be tracing the immediate aftermath of the family-forming collision when numerous Gefion fragments evolved into the Earth-crossing orbits by the 5:2 resonance with Jupiter. This work has major implications for our understanding of the source regions of ordinary chondrite meteorites because it implies that they can sample more distant asteroid material than was previously thought possible.     

On the level of h2 quadrupole absorption in the Jovian atmosphere

The hydrogen quadrupole absorption lines are uniquely characterized by the property of being collision narrowed. For the 3-0 and 4-0 bands the lines continue to narrow to below the pressure levels in the Jovian atmosphere where they appear to be formed. Since the collision narrowing is the reverse of the case for ordinary molecular absorptions the use of the Curtis-Godson approximation must be reconsidered. We have done this using the line shape for this process derived by Galatry and find that the Curtis-Godson approximation represents the absorption very well through the inhomogeneous Jovian atmosphere. The hydrogen quadrupole absorptions, 3-0 S (l) and 4-0 S (l), have been analysed by a procedure which has been shown to give self-consistent results for the methane 3v3 manifolds. The 3-0 S(1) line is strongly saturated and even the weak 4-0 S(l) line (equiv width ～ 8mÅ) exhibits a 10% saturation. We derive a mixing ratio (by volume) of approx 7 x 10^?4 for methane to hydrogen in agreement with earlier results.     

On penetration depth of the Shoemaker-Levy 9 fragments into the Jovian atmosphere

The actual penetration depth of the Shoemaker-Levy 9 fragments into the Jovian atmosphere is still an open question. From fundamental equations of meteoric physics with variable cross-section, a new analytic model of energy release of the fragments is presented. In use of reasonable parameters, a series of results are calculated for different initial mass of the fragments. The results show that the largest fragment explodes above pressure levels of 3 bars and does not penetrate into the H₂O cloud layer of the Jovian atmosphere, and that airburst of smaller fragments occur even above the upper cloud layer.     

On the nature of the blue and ultraviolet absorption in the Jovian atmosphere

Spatially resolved reflectivities from 3000 to 6600 Å of three positions from the center to the limb of the Jovian Equator, North Equatorial Belt, and North Tropical Zone are analyzed to determine the vertical distribution and wavelength dependence of various sources of blue and uv absorption. Six different models of the distribution of absorbing dust particles are examined. In each model, the variation of dust optical depth and cloud single-scattering albedo are determined. Only those models having dust above the upper NH₃ cloud layer will fit the data. The high altitude dust distribution is approximately uniform over the three regions examined. The contrast in reflectivity of the belts and zones may be modeled by a different cloud single-scattering albedo in the different regions.     

On the ortho-para equilibrium of H2 in the atmospheres of the Jovian planets

The ratio for the equivalent widths for the unsaturated H₂ quadrupole transitions observed in the Jovian planets is calculated and compared with a large number of observations. The comparison indicates that equilibrium hydrogen may be present in Jupiter and Saturn, while Uranus and Nepture exhibit ratios not in accord with equilibrium hydrogen. Observations which can differentiate among the possible states of H₂ are proposed.     

Location of the Jovian magnetic dipole

Measurements of the position of Jupiter's radio centroid at 11 cm were made using the Parkes telescope. They indicate that any systematic displacement of the Jovian magnetic dipole along the rotation axis is to the north of the center of the planet, contrary to a model proposed by Warwick. Any offset of the dipole normal to the rotation axis does not exceed 0.1 of a planetary radius.     

Sodium in the Jovian magnetosphere

Observations of sodium D-line emission from Io and the magnetosphere of Jupiter are reported. A disk-shaped cloud of sodium is found to exist in the Jovian magnetosphere with an inner edge at about 4R and an outer edge at about 10R . The gravitational scale height above the equatorial plane is a few Jovian radii. The data are interpreted in terms of a sputtering model, in which the sodium required to maintain the cloud is sputtered off the surface of Io by trapped energetic radiation-belt protons. Conditions on the atmospheric density are obtained. The Keplerian orbits attainable by such escaping sputtered atoms can provide the observed spatial distribution. The required 500-keV proton flux required to provide the 1–10 keV protons which will sputter the sodium at the surface of Io is consistent with the limiting trapped flux determined by ion-cyclotron turbulence.Publication No. 1410, Institute of Geophysics and Planetary Physics, University of California, Los Angeles 90024, Cal., U.S.A.     

Thermal structure of the Jovian plasmasphere

An equation of heat transport in the Jovian magnetosphere is formulated and solved in the L range between 2 and 7. Sources of thermal energy include the heating associated with inward radial diffusion and a hypothetical heat supply originating from Io's dynamo action. The principal sink of the thermal energy is charge exchange in Io's hydrogen torus. In order to explain the density and temperature profile reported by Frank et al. (1976), the presence of the heat source at Io is essential and the density of the torus hydrogen has to be considerably lower than the value inferred from L_α observations by Carlson and Judge (1975). Radial diffusion represents the principal heating mechanism for plasma at very low L values.     

Physical parameters of the Jovian atmosphere

The following physical parameters have been computed for the Jovian atmosphere between 270 and ?300 km: (1) Pressure, (2) Density, (3) Speed and sound, (4) Number density, (5) Density scale. It has considered that the top of the clouds is at 0 km. For the calculations of these parameters we have used:

1. for the altitudes 270-0 km data from Voyager I and II.
2. for the altitudes ?300–0 km data from Voyager II and spectroscopic observations.

     

On the production and interaction of planetary solitary waves: Applications to the Jovian atmosphere

We present further evidence that strengthens the case for our interpretation of many features in the Jovian atmosphere as solitary Rossby waves (solitons). These include: a mechanism whereby such waves can evolve from the instability of the basic shear flows; further interpretation of the interaction between observed features, and comparison with calculations of the interaction between planetary solitons of a restricted class; and calculations of the morphology for a type of shear flow other than the type considered originally by Maxworthy and Redekopp.     

The Jovian stratosphere in the ultraviolet

The center-of-disk reflectivity of Jupiter in the wavelength range from 1450 to 3150A?has been computed from 30 low-dispersion IUE spectra taken during solar maximum in 1978–1980. A vertically inhomogeneous radiative transfer program is used to compute model reflectivities of various stratospheric compositions for comparison. Ammonia and acetylene are well determined because they show narrow absorption bands in the ultraviolet. Above 1800A?, these two gases provide a good fit to the data, but not below. At shorter wavelengths the fit would be much improved by a small amount (5–15 ppb) of propadiene/allene (C₃H₄). Voyager IRIS spectra show that the IR bands of allene are not strong enough to be detected in such a small amount. Additional absorption around 1600A?can be reproduced best with the presence of cyclopropane (C₃H₆, <15ppb), although other absorbers (e.g., hydrocarbon molecules with more than three carbon atoms, oxygen- or nitrogen-containing molecules, or a high-attitude haze) could also explain the spectrum in this region. The data are too noisy to detect possible CO Cameron band absorption near 2000A?.     

Dust on the Outskirts of the Jovian System

The outer region of the jovian system between ∼50 and 300 jovian radii from the planet is found to be the host of a previously unknown dust population. We used the data from the dust detector aboard the Galileo spacecraft collected from December 1995 to April 2001 during Galileo's numerous traverses of the outer jovian system. Analyzing the ion amplitudes, calibrated masses and speeds of grains, and impact directions, we found about 100 individual events fully compatible with impacts of grains moving around Jupiter in bound orbits. These grains have moderate eccentricities and a wide range of inclinations—from prograde to retrograde ones. The radial number density profile of the micrometer-sized dust is nearly flat between about 50 and 300 jovian radii. The absolute number density level (∼10 km⁻³ with a factor of 2 or 3 uncertainty) surpasses by an order of magnitude that of the interplanetary background. We identify the sources of the bound grains with outer irregular satellites of Jupiter. Six outer tiny moons are orbiting the planet in prograde and fourteen in retrograde orbits. These moons are subject to continuous bombardment by interplanetary micrometeoroids. Hypervelocity impacts create ejecta, nearly all of which get injected into circumjovian space. Our analytic and numerical study of the ejecta dynamics shows that micrometer-sized particles from both satellite families, although strongly perturbed by solar tidal gravity and radiation pressure, would stay in bound orbits for hundreds of thousands of years as do a fraction of smaller grains, several tenths of a micrometer in radius, ejected from the prograde moons. Different-sized ejecta remain confined to spheroidal clouds embracing the orbits of the parent moons, with appreciable asymmetries created by the radiation pressure and solar gravity perturbations. Spatial location of the impacts, mass distribution, speeds, orbital inclinations, and number density of dust derived from the data are all consistent with the dynamical model.     

Dynamical Effects of Mars on Asteroidal Dust Particles

Asteroidal dust particles resulting from family-forming events migrate from their source locations in the asteroid belt inwards towards the Sun under the effect of Poynting-Robertson (PR) drag. Understanding the distribution of these dust particle orbits in the inner solar system is of great importance to determining the asteroidal contribution to the zodiacal cloud, the accretion rate by the Earth, and the threat that these particles pose to spacecraft and satellites in near-Earth space. In order to correctly describe this distribution of orbits in the inner solar system, we must track the dynamical perturbations that the dust particle orbits experience as they migrate inwards. In a seminal paper Öpik (1951) determines that very few of the μm-cm sized dust particles suffer a collision with the planet face as they decay inwards past Mars. Here we re-analyze this problem, considering additionally the likelihood that the dust particle orbits pass through the Hill sphere of Mars (to various depths) and experience potentially significant perturbations to their orbits. We find that a considerable fraction of dust particle orbits will enter the Hill sphere of Mars. Furthermore, we find that there is a bias with inclination, particle size, and eccentricity of the particle orbits that enter the Martian Hill sphere. In particular the bias with inclination may create a bias towards higher-inclination sources in the proportions of asteroid family particles that reach near-Earth space.     

Temperature anisotropy of the Jovian sulfur nebula

We discuss the apparent paradox between the reported observation of a 3-eV gyration energy of Jupiter's ionized sulfur nebula and its observed thickness. We present an observation of the thickness of the cloud taken nearly edge on and show that this implies a large bounce-averaged anisotropy of the sulfur in temperature, T₆ ? T_⊥. From these observations, we construct a self-consistent model of the sulfur nebula in which the sulfur ions are injected by Io as ions and remain sufficiently collisionless in the magnetosphere to maintain the anisotropy for a time longer than a characteristic diffusion time. We also show that the proton-electron plasma is collisionally thermalized and provides an adequate means of tapping the rotational energy of the planet to provide the power radiated in the sulfur lines.     

A theory of the Jovian hydrogen torus

The Jovian hydrogen torus associated with Io, that was observed by Judge and Carlson, has been found by them to be a third of a torus rather than a complete torus. It is shown that the energetic particles observed by Pioneer 10 do not ionize atomic hydrogen sufficiently fast to erode the torus as observed. It is proposed that the reason an incomplete torus exists is the presence of a corotating cold magnetospheric plasma. If this explanation is correct, the angular extent of the fractional torus is a measure of the density of the magnetospheric plasma near Io's orbit, which is found to be ～10²cm^?3. It is shown that such a plasma may provide an adequate input to Io, where it can recombine and escape, to form enough hydrogen atoms to explain the number of observed torus atoms. Thus the magnetospheric plasma may serve as both the source and the sink of the torus. However, while it is not difficult to make the plasma be the sink of the toroidal hydrogen, it is difficult (although perhaps possible) to self-consistently make it the source. It may be necessary to invoke some other mechanism to generate the hydrogen.