Irregular Satellites of Jupiter: a study of the capture direction

The irregular satellites of Jupiter are believed to be captured asteroids or planetesimals. In the present work is studied the direction of capture of these objects as a function of their orbital inclination. We performed numerical simulations of the restricted three-body problem, Sun-Jupiter-particle, taking into account the growth of Jupiter. The integration was made backward in time. Initially, the particles have orbits as satellites of Jupiter, which has its present mass. Then, the system evolved with Jupiter losing mass and the satellites escaping from the planet. The reverse of the escape direction corresponds to the capture direction. The results show that the Lagrangian points L1 and L2 mainly guide the direction of capture. Prograde satellites are captured through these two gates with very narrow amplitude angles. In the case of retrograde satellites, these two gates are wider. The capture region increases as the orbital inclination increases. In the case of planar retrograde satellites the directions of capture cover the whole 360° around Jupiter. We also verified that prograde satellites are captured earlier in actual time than retrograde ones. This paper was presented at the Asteriods, Comets and Meteors meeting held at Búzios, Rio de Janeiro, Brazil in August 2005 and could not be included in the special issue related to that conference.     

Three-body capture of irregular satellites: Application to Jupiter

We investigate a new theory of the origin of the irregular satellites of the giant planets: capture of one member of a ∼100-km binary asteroid after tidal disruption. The energy loss from disruption is sufficient for capture, but it cannot deliver the bodies directly to the observed orbits of the irregular satellites. Instead, the long-lived capture orbits subsequently evolve inward due to interactions with a tenuous circumplanetary gas disk.We focus on the capture by Jupiter, which, due to its large mass, provides a stringent test of our model. We investigate the possible fates of disrupted bodies, the differences between prograde and retrograde captures, and the effects of Callisto on captured objects. We make an impulse approximation and discuss how it allows us to generalize capture results from equal-mass binaries to binaries with arbitrary mass ratios.We find that at Jupiter, binaries offer an increase of a factor of ∼10 in the capture rate of 100-km objects as compared to single bodies, for objects separated by tens of radii that approach the planet on relatively low-energy trajectories. These bodies are at risk of collision with Callisto, but may be preserved by gas drag if their pericenters are raised quickly enough. We conclude that our mechanism is as capable of producing large irregular satellites as previous suggestions, and it avoids several problems faced by alternative models.     

Deciphering the origin of the regular satellites of gaseous giants - Iapetus: The Rosetta ice-moon

Ever since their discovery the regular satellites of Jupiter and Saturn have held out the promise of providing an independent set of observations with which to test theories of planet formation. Yet elucidating their origins has proven elusive. Here we show that Iapetus can serve to discriminate between satellite formation models. Its accretion history can be understood in terms of a two-component gaseous subnebula, with a relatively dense inner region, and an extended tail out to the location of the irregular satellites, as in the SEMM model of Mosqueira and Estrada (2003a,b) (Mosqueira, I., Estrada, P.R. [2003a]. Icarus 163, 198-231; Mosqueira, I., Estrada, P.R. [2003b]. Icarus 163, 232-255). Following giant planet formation, planetesimals in the feeding zone of Jupiter and Saturn become dynamically excited, and undergo a collisional cascade. Ablation and capture of planetesimal fragments crossing the gaseous circumplanetary disks delivers enough collisional rubble to account for the mass budgets of the regular satellites of Jupiter and Saturn. This process can result in rock/ice fractionation as long as the make up of the population of disk crossers is non-homogeneous, thus offering a natural explanation for the marked compositional differences between outer solar nebula objects and those that accreted in the subnebulae of the giant planets. For a given size, icy objects are easier to capture and to ablate, likely resulting in an overall enrichment of ice in the subnebula. Furthermore, capture and ablation of rocky fragments become inefficient far from the planet for two reasons: the gas surface density of the subnebula is taken to drop outside the centrifugal radius, and the velocity of interlopers decreases with distance from the planet. Thus, rocky objects crossing the outer disks of Jupiter and Saturn never reach a temperature high enough to ablate either due to melting or vaporization, and capture is also greatly diminished there. In contrast, icy objects crossing the outer disks of each planet ablate due to the melting and vaporization of water-ice. Consequently, our model leads to an enhancement of the ice content of Iapetus, and to a lesser degree those of Titan, Callisto and Ganymede, and accounts for the (non-stochastic) compositions of these large, low-porosity outer regular satellites of Jupiter and Saturn. For this to work, the primordial population of planetesimals in the Jupiter-Saturn region must be partially differentiated, so that the ensuing collisional cascade produces an icy population of ?1 m size fragments to be ablated during subnebula crossing. We argue this is likely because the first generation of solar nebula ∼10 km planetesimals in the Jupiter-Saturn region incorporated significant quantities of ²⁶Al. This is the first study successfully to provide a direct connection between nebula planetesimals and subnebulae mixtures with quantifiable and observable consequences for the bulk properties of the regular satellites of Jupiter and Saturn, and the only explanation presently available for Iapetus’ low density and ice-rich composition.     

Photometric properties of outer planetary satellites

We present optical broadband photometry for the satellites J6, J7, J8, S7, S9, U3, U4, N1, and polarimetry for J6, obtained between 1970 and 1979. The outer Jovian satellites resemble C-type asteroids; J6 has a rotational lightcurve with period ～9.5 hr. The satellites beyond Jupiter also show C-like colors with the exception of S7 Hyperion. S9 Phoebe has a rotational lightcurve with period near either 11.25 or 21.1 hr. For U4 and N1 there is evidence for a lightcurve synchronous with the orbital revolution. The seven brighter Saturnian satellites show a regular relation between the ultraviolet dropoff and distance to the planet, probably related with differences in the rock component on their surfaces.     

Gas drag in primordial circumplanetary envelopes: A mechanism for satellite capture

Some natural satellites may have been captured due to the gas drag they experienced in passing through primordial circumplanetary nebulas. This paper models such an encounter and derives the testable parameters from the known properties of current solar system objects and Bodenheimer's (1977, Icarus 31) model of the earliest phases of Jupiter's evolution. We propose that the clusters of prograde and retrograde irregular satellites of Jupiter originated when two parent bodies were decelerated and fragmented as they passed through an extended primordial Jovian nebula. Fragmentation occured because the gas dynamic pressure exceeded the parent bodies' strengths. These events must have occurred only shortly before the primordial nebula experienced hydrodynamical collapse so that subsequently the fragments underwent only limited orbital evolution. Because self-gravity exceeded the relative drag force, the fragments initially remained together, only to be dispersed at a later time by a collision with a stray body. Predictions of this hypothesis, such as orbital distance of the irregular satellites and size of the parent bodies, are found to be consistent with the observed properties of Jupiter's irregular satellites. In addition nebular drag at a later time may have caused the inner three Galilean satellites to undergo a modest amount of orbital evolution, accounting for their present orbital resonance. Gas drag capture of Saturn's Phoebe and Iapetus and Neptune's Nereid and Triton may also be possible. Reasonable differences in properties could explain why these satellites, in contrast to the Jovian ones, did not fracture upon capture. The current irregular satellites represent only a tiny fraction of the bodies captured by primordial nebulas. The dominant fraction would have spiraled into the center of the nebula as a result of continued gas drag and thus offer one source for the heavy element cores of the outer planets. If one is willing to postulate the presence of a massive gaseous nebula around primordial Mars, then gas drag capture could account for the origin of the Martian moons. We hypothesize that a single parent body was captured in a region of the nebula where the gas velocity approached the Keplerian value, that it fragmented upon deceleration into at least two bodies, Phobos and Deimos, and that continued nebular drag led to the low eccentricity and inclination that characterize the satellites' current orbits. Following the dissipation of this nebula, the more massive Phobos tidally evolved to its current position.     

Some remarks on the capture of Triton and the origin of Pluto

Harrington and Van Flandern (1979, Icarus39, 131–136) suggests that the irregular features of the Neptunian satellite system and Pluto's escape were caused by an encounter with a massive external body. They rule out the alternative mechanism based on the capture of Triton (which seems more plausible because it does not appeal to any unobserved object) on the basis of an incorrect deduction from McCord's (1966, Astron. J.71, 585–590) analysis on the tidal decay of Triton's orbit. As a matter of fact, many recent results show that satellite captures are possible, and in the case of Triton several arguments support this interpretation.     

An Upper Limit of Mass for a Stable Minor Planet in the Main Asteroid Belt

The stability of an imaginary planet located in the present main asteroid belt is studied with a 7-body model (Sun, Mars, Jupiter, Saturn, Uranus, Neptune and the imaginary planet). The fourth-order Hermite algorithm P(EC)³ is used, which has a very small secular energy error for the integration of periodic orbits with a constant time-step. The evolution of orbits is followed up to 10⁸ years. Our numerical results show that the low-order resonances with Jupiter can enhance the stability of the imaginary planet in some cases. The survival probability of the imaginary planet decreases with the planet mass. The upper limit of the imaginary planet's mass that can survive in the main belt is around 10²⁵ kg, i.e., about the Earth's mass.     

Exploring the 7:4 mean motion resonance—II: Scattering evolutionary paths and resonance sticking

In our preliminary study, we have investigated basic properties and dynamical evolution of classical TNOs around the 7:4 mean motion resonance with Neptune (a∼43.7 AU), motivated by observational evidences that apparently present irregular features near this resonance (see [Lykawka and Mukai, 2005a. Exploring the 7:4 mean motion resonance—I. Dynamical evolution of classical trans-Neptunian objects (TNOs). Space Planet. Sci. 53, 1175-1187]; hereafter “Paper I”). In this paper, we aim to explore the dynamical long-term evolution in the scattered disk (but not its early formation) based on the computer simulations performed in Paper I together with extra computations. Specifically, we integrated the orbital motion of test particles (totalizing a bit more than 10,000) placed around the 7:4 mean motion resonance under the effect of the four giant planets for the age of the Solar System. In order to investigate chaotic diffusion, we also conducted a special simulation with on-line computation of proper elements following tracks in phase space over 4-5 Gyr. We found that: (1) A few percent (1-2%) of the test particles survived in the scattered disk with direct influence of other Neptunian mean motion resonances, indicating that resonance sticking is an extremely common phenomenon and that it helps to enhance scattered objects longevity. (2) In the same region, the so-called extended scattered TNOs are able to form via very long resonance trapping under certain conditions. Namely, if the body spends more than about 80% of its dynamical lifetime trapped in mean motion resonance(s) and there is the action of a k+1 or (k+2)/2 mean motion resonance (e.g., external mean motion resonances with Neptune described as (j+k)/j with j=1 and 2, respectively). According to this hypothetical mechanism, 5-15% of current scattered TNOs would possess thus probably constituting a significant part of the extended scattered disk. (3) Moreover, considering hot orbital initial conditions, it is likely that the trans-Neptunian belt (or Edgeworth-Kuiper belt) has been providing members to the scattered disk, so that scattered TNOs observed today would consist of primordial scattered bodies mixed with TNOs that came from unstable regions of the trans-Neptunian belt in the past.Considering the three points together, our results demonstrated that the scattered disk has been evolving continuously since early times until present.     

Dynamical capture in the Pluto–Charon system

This paper explores the possibility that the progenitors of the small satellites of Pluto got captured in the Pluto?CCharon system from the massive heliocentric planetesimal disk in which Pluto was originally embedded into. We find that, if the dynamical excitation of the disk is small, temporary capture in the Pluto?CCharon system can occur with non- negligible probability, due to the dynamical perturbations exerted by the binary nature of the Pluto?CCharon pair. However, the captured objects remain on very elliptic orbits and the typical capture time is only ~ 100?years. In order to explain the origin of the small satellites of Pluto, we conjecture that some of these objects got disrupted during their Pluto-bound phase by a collision with a planetesimal of the disk. This could have generated a debris disk, which damped under internal collisional evolution, until turning itself into an accretional disk that could form small satellites on circular orbits, co-planar with Charon. Unfortunately, we find that objects large enough to carry a sufficient amount of mass to generate the small satellites of Pluto have collisional lifetimes orders of magnitude longer than the capture time. Thus, this scenario cannot explain the origin of the small satellites of Pluto, which remains elusive.     

An efficient, low-velocity, resonant mechanism for capture of satellites by a protoplanet

Numerical simulations of the gravitational scattering of planetesimals by a protoplanet reveal that a significant fraction of scattered planetesimals can become trapped as so-called quasi-satellites in heliocentric 1:1 co-orbital resonance with the protoplanet. While trapped, these resonant planetesimals can have deep low-velocity encounters with the protoplanet that result in temporary or permanent capture onto highly eccentric prograde or retrograde circumplanetary orbits. The simulations include solar nebula gas drag and use planetesimals with diameters ranging from ∼1 to ∼1000 km. Initial protoplanet eccentricities range from ep=0 to 0.15 and protoplanet masses range from 300 Earth-masses (M_⊕) down to 0.1M_⊕. This mass range effectively covers the final masses of all planets currently thought to be in possession of captured satellites—Jupiter, Saturn, Neptune, Uranus, and Mars. For protoplanets on moderately eccentric orbits (ep?0.1) most simulations show from 5-20% of all scattered planetesimals becoming temporarily trapped in the quasi-satellite co-orbital resonance. Typically, 20-30% of the temporarily trapped quasi-satellites of all sizes came within half the Hill radius of the protoplanet while trapped in the resonance. The efficiency of the resonance trapping combined with the subsequent low-velocity circumplanetary capture suggests that this trapped-to-captured transition may be important not only for the origin of captured satellites but also for continued growth of protoplanets.     

The Scattered Disk Population and the Oort Cloud

The trans-Neptunian belt has been subject to a strong depletion that has reduced its primordial population by a factor of one hundred over the solar system's age. One by-product of such a depletion process is the existence of a scattered disk population in transit from the belt to other places, such as the Jupiter zone, the Oort cloud or interstellar space. We have integrated the orbits of the scattered disk objects (SDOs) so far discovered by 2500 Myr to study their dynamical time scales and the probability of falling in each of the end states mentioned above, paying special attention to their contribution to the Oort cloud. We found that their dynamical half-time is close to 2.5 Gyr and that about one third of the SDOs end up in the Oort cloud.     

Model consideration of the bombardment event of the asteroidal belt by the planetesimals scattered from the Jupiter zone

The temporal evolutions of the planetesimals scattered from the Jupiter zone for different masses of the proto-Jupiter [(a) 0.1 and (b) 1.0 of the present mass] are investigated. Due to the combined effects of the orbital evolution of the planetesimals and the elimination of these projectiles either via impact capture or injection into escape velocity by the outer planets, the whole scattering process lasts about 10⁸ yr for case (a) and about 10⁷ yr for case (b). The longer time scale may be a good estimate for the accretion time interval of Jupiter while the shorter one (10⁷) gives the upper time limit of the late heavy-bombardment epoch of the terrestrial planets due to planetesimals scattered from the Jupiter zone. The limiting value of the encounter velocity U at the end of the scattering process is ≈0.6. Consideration of the collisional interaction of these projectiles with the asteroids indicates that the corresponding bombardment effect could be rather appreciable. Also, the asteroids on the inner edge of the main asteroid belt would have been bombarded more severely than those on the outer edge. From this point of view, the structure of the asteroidal belt could be affected significantly not only by Jupiter's gravitational perturbation effect but also by its early scattering process.     

Production of organic molecules in the outer solar system by proton irradiation: Laboratory simulations

In the past few years considerable attention has been given to the determination of likely compounds that could account for the various colors observed in the outer solar system: and to possible formation mechanisms for these compounds. Many experiments have been done using electrical discharges (Chadha, M. S., et al., 1971, Icarus15, 39) and ultraviolet light (Khare, B. N., and Sagan, C., 1973, Icarus20, 311) on mixtures of CH₄, NH₃, and H₂S, which are most likely the dominant minor constituents of the atmospheres of Jupiter, Saturn, Titan, and possibly the other satellites early in their histories. Colored polymers, usually brownish-red, have been produced in these experiments. With the passage of Pioneer 10 around Jupiter, there is another source of energy worthy of consideration, energetic protons (and electrons). Preliminary experiments to investigate the formation of colored polymers and other interesting molecules by the irradiation of gas mixtures by protons are discussed. Two to four Mev protons were used, with corresponding beam fluxes (as measured at 6R_J from the planet) equivalent to approximately 80 Earth years at Jupiter per hour of exposure. As in the other types of experiments, colored polymers have been produced. An important feature of this work is the presence or absence of absorption at 5 μm in the different materials produced; Titan is quite dark at this wavelength and Io is fairly bright. Such features may provide criteria for accepting or rejecting various materials produced in these experiments as reasonable coloring agents for the outer solar system.     

Tidally Induced Volcanism

The dissipation of tidal energy causes the ongoing silicate volcanism on Jupiter's satellite, Io, and cryovolcanism almost certainly has resurfaced parts of Saturn's satellite, Enceladus, at various epochs distributed over the latter's history. The maintenance of tidal dissipation in Io and the occurrence of the same on Enceladus depends crucially on the maintenance of the respective orbital eccentricities by the existence of mean motion resonances with nearby satellites. A formation of the resonances among the Galilean satellites by differential expansion of the satellite orbits from tides raised on Jupiter by the satellites means the onset of the volcanism on Io could be relatively recent. If, on the other hand, the resonances formed by differential migration from resonant interactions of the satellites with the disk of gas and particles from which they formed, Io would have been at least intermittently volcanically active throughout its history. Either means of assembling the Galilean satellite resonances lead to the same constraint on the dissipation function of Jupiter Q _J 10⁶, where the currently high heat flux from Io seems to favor episodic heating as Io's eccentricity periodically increases and decreases. Either of the two models might account for sufficient tidal dissipation in the icy satellite Enceladus to cause at least occasional cryovolcanism over much of its history. However, both models are assumption-dependent and not secure, so uncertainty remains on how tidal dissipation resurfaced Enceladus.     

Orbital evolution of the Galilean satellites: Capture into resonance

C.F. Yoder's scenario 1979 for the capture into resonance of the first three Galilean satellites is reexamined. A more refined dynamical model for the resonance and for the tidal effects is proposed and analyzed. The results agree qualitatively with those of Yoder but differ numerically by 10 to 20%.     

When and where were the satellites of uranus formed?

Uranus exhibits an unusually large obliquity compared to other planets of the solar system; its equator is inclined by 98° to the plane of its orbit. However its five satellites are remarkably regular, with eccentricities and inclinations very nearly zero, but of course with orbit planes that are tilted by ～98° to the plane of the ecliptic. This circumstance is used here to relate the formation of satellites to planet formation. Six different cases are discussed, of which two can be ruled out and two others are highly improbable. In the analysis, use is made of the fact that satellites in near-equatorial orbits could not follow a rapid (“non-adiabatic”) change of the planet's obliquity. We assume, also, that the observed obliquity is the result of the last stages of planet accumulation. We can therefore exclude contemporaneous formation of planet and satellites, and conclude instead that the satellites were formed or acquired after the planet's axis had been tilted. A plausible scenario involves the tidal capture of a body having 5% to 10% of the planet's mass—sufficient to account for the tilt—followed by its accretion. However, tidal forces break up the body into chunks, slow the accretion, and allow ～1% of the chunks to form the satellites through interaction with a temporary dense atmosphere. The same reasoning may apply also for Saturn and Jupiter. It should be noted that the synchronous orbit it well within the Roche limit for all three planets.     

Formation of the regular satellites of giant planets in an extended gaseous nebula II: satellite migration and survival

For a satellite to survive in the disk the time scale of satellite migration must be longer than the time scale for gas dissipation. For large satellites (∼1000 km) migration is dominated by the gas tidal torque. We consider the possibility that the redistribution of gas in the disk due to the tidal torque of a satellite with mass larger than the inviscid critical mass causes the satellite to stall and open a gap (W.R. Ward, 1997, Icarus 26, 261-281). We adapt the inviscid critical mass criterion to include gas drag, and m-dependent nonlocal deposition of angular momentum. We find that such a model holds promise of explaining the survival of satellites in the subnebula, the mass versus distance relationship apparent in the saturnian and uranian satellite systems, the concentration of mass in Titan, and the observation that the satellites of Jupiter get rockier closer to the planet whereas those of Saturn become increasingly icy. It is also possible that either weak turbulence (close to the planet) or gap-opening satellite tidal torque removes gas on a similar time scale (10⁴-10⁵ years) as the orbital decay time of midsized (200-700 km) regular satellites forming in the inner disk (inside the centrifugal radius (I. Mosqueira and P.R. Estrada, 2003, Icarus, this issue)). We argue that Saturn’s satellite system bridges the gap between those of Jupiter and Uranus by combining the formation of a Galilean-sized satellite in a gas optically thick subnebula with a strong temperature gradient, and the formation of smaller satellites, closer to the planet, in a disk with gas optical depth ?1, and a weak temperature gradient.Using an optically thick inner disk (given gaseous opacity), and an extended, quiescent, optically thin outer disk, we show that there are regions of the disk of small net tidal torque (even zero) where satellites (Iapetus-sized or larger) may stall far from the planet. For our model these outer regions of small net tidal torque correspond roughly to the locations of Callisto and Iapetus. Though the precise location depends on the (unknown) size of the transition region between the inner and outer disks, the result that Saturn’s is found much farther out (at ∼3rcS, where rcS is Saturn’s centrifugal radius) than Jupiter’s (at ∼ 2rcJ, where rcJ is Jupiter’s centrifugal radius) is mostly due to Saturn’s less massive outer disk and larger Hill radius. However, despite the large separation between Ganymede and Callisto and Titan and Iapetus, the long formation and migration time scales for Callisto and Iapetus (I. Mosqueira and P.R. Estrada, 2003, Icarus, this issue) makes it possible (depending on the details of the damping of acoustic waves) that the tidal torque of Ganymede and Titan clears the gas disk out to their location, thus stranding Callisto and Iapetus far from the planet. Either way, our model provides an explanation for the presence of regular satellites outside the centrifugal radii of Jupiter and Saturn, and the absence of such a satellite for Uranus.     

Capture of dust grains in exterior resonances with planets

The temporary capture of the dust grains in the exterior resonances with planets is studied in the frames of the planar circular three-body problem with Poynting-Robertson (PR) drag. For the Earth and particles ~ 10 Μm the resonances 4/5, 5/6, 6/7, 7/8 are shown to be most effective. The capture is only temporary (of order 10⁵ years) and the position of resonance may be calculated from semi-analytical model using averaged disturbing function. These semi-analytical results are confirmed by numerical integration. For various planet this picture changes as with increasing planetary mass the more exterior resonances become more important. We showed that for Jupiter (at least in the space between Jupiter and Saturn) the resonance 1/2 plays the dominant role. The capture time is here several myr but again eccentricity is evolving to eccentricity e ₀ ~ 0.48 of libration point for this resonance.     

On the C/H and D/H ratios in the atmospheres of Jupiter and Saturn

Using a method defined in a previous paper [M. Combes and T. Encrenaz, Icarus39 1–27 (1979)], we reestimated the C/H ratio in the atmospheres of Jupiter and Saturn by the measurements of the weak visible CH₄ bands, the CH₄ 3ν₃ band, and the (3-0) and (4-0) quadrupole bands of H₂. In the case of Jupiter we conclude that the C/H ratio is enriched by a factor ranging from 1.7 to 3.6 relative to the solar value. In the case of Saturn, our derived C/H value ranges from 1.2 to 3.2 times the solar value. The Jovian D/H ratio derived from this study is 1.2 × 10^?5 < D/H < 3.1 × 10^?5. The value derived for the D/H ratio on Saturn is not precise enough to be conclusive.     

Resonance sticking in the scattered disk

We investigate the dynamical evolution of trans-neptunian objects (TNOs) in typical scattered disk orbits (scattered TNOs) by performing simulations using several thousand particles lying initially on Neptune-encountering orbits. We explore the role of resonance sticking in the scattered disk, a phenomenon characterized by multiple temporary resonance captures (‘resonances’ refers to external mean motion resonances with Neptune, which can be described in the form r:s, where the arguments r and s are integers). First, all scattered TNOs evolve through intermittent temporary resonance capture events and gravitational scattering by Neptune. Each scattered TNO experiences tens to hundreds of resonance captures over a period of 4 Gyr, which represents about 38% of the object's lifetime (mean value). Second, resonance sticking plays an important role at semimajor axes , where the great majority of such captures occurred. It is noteworthy that the stickiest (i.e., dominant) resonances in the scattered disk are located within this distance range and are those possessing the lowest argument s. This was evinced by r:1, r:2 and r:3 resonances, which played the greatest role during resonance sticking evolution, often leading to captures in several of their neighboring resonances. Finally, the timescales and likelihood of temporary resonance captures are roughly proportional to resonance strength. The dominance of low s resonances is also related to the latter. In sum, resonance sticking has an important impact on the evolution of scattered TNOs, contributing significantly to the longevity of these objects.