Search

It has been claimed (Canup and Ward 2002; Ward 2003) that a long-lived massive (compared to the mass of the Galilean satellites) circumplanetary gas disk is inconsistent with Jupiter's low obliquity. Such a constraint could be downplayed on the basis that it deals with a single observation. Here we argue that this argument is flawed because it assumes a solar system much like that of the present day with the one exception of a circumjovian disk which is then allowed to dissipate on a long timescale (10^6-10^7 yrs). Given that the sequence of events in solar-system history that fit known constraints is non-unique, we choose for the sake of clarity of exposition the orbital architecture framework of Tsiganis et al. (2005), in which Jupiter and Saturn were once in closer, less inclined orbits than they are at present, and show that Jupiter's low obliquity is consistent with the SEMM (solids-enhanced minimum mass) satellite formation model of Mosqueira and Estrada (2003a,b)., Comment: 8 pages, 1 figure. Submitted note to Icarus

Assuming that an unknown mechanism (e.g., gas turbulence) removes most of the subnebula gas disk in a timescale shorter than that for satellite formation, we develop a model for the formation of regular (and possibly at least some of the irregular) satellites around giant planets in a gas-poor environment. In this model, which follows along the lines of the work of Safronov et al. (1986), heliocentric planetesimals collide within the planet's Hill sphere and generate a circumplanetary disk of prograde and retrograde satellitesimals extending as far out as $\sim R_H/2$. At first, the net angular momentum of this proto-satellite swarm is small, and collisions among satellitesimals leads to loss of mass from the outer disk, and delivers mass to the inner disk (where regular satellites form) in a timescale $\lesssim 10^5$ years. This mass loss may be offset by continued collisional capture of sufficiently small $< 1$ km interlopers resulting from the disruption of planetesimals in the feeding zone of the giant planet. As the planet's feeding zone is cleared in a timescale $\lesssim 10^5$ years, enough angular momentum may be delivered to the proto-satellite swarm to account for the angular momentum of the regular satellites of Jupiter and Saturn.(abridged), Comment: 45 pages, 11 figures, 3 appendices, uses rgfmacro.tex, accepted for publication to Icarus

Given our presently inadequate understanding of the turbulent state of the solar and planetary nebulae, we believe the way to make progress in satellite formation is to consider two end member models that avoid over-reliance on specific choices of the turbulence (alpha), which is essentially a free parameter. The first end member model postulates turbulence decay once giant planet accretion ends. If so, Keplerian disks must eventually pass through the quiescent phases, so that the survival of satellites (and planets) ultimately hinges on gap-opening. In this scenario, the criterion for gap-opening itself sets the value for the gas surface density of the satellite disk.

Current models of planet and satellite formation are marred by our lack of understanding regarding the turbulent state of accretion disks. According to the Rayleigh criterion, Keplerian disks are hydrodynamically stable. Indeed, it has been argued that a carefully designed Taylor Couette experiment shows stability in the case of positive radial gradients in specific angular momentum even for high Reynolds numbers [1], in agreement with numerical simulations which consistently show turbulence decay [2]. Other possible sources of turbulence may fail due to low ionization, may decay as the optical depth decreases due to dust coagulation, may involve unrealistic boundary conditions, or result in limited transport. The difficulty stems not only from the degree of turbulence, but also from the kind of turbulence, and whether it may be characterized by an alpha parameter.

A long-popular model for producing Ganymede s bright terrain involves flooding of low-lying graben with liquid water, slush, or warm, soft ice. The model suffers from major problems, however, including the absence of obvious near-surface heat sources, the negative buoyancy of liquid water, and the lack of a mechanism for confining the flows to graben floors. We show that topography - such as a global set of graben - causes subsurface (a hydrostatic) pressure gradients that can "suck" subsurface liquid water upward onto the floors of topographic lows (graben). As the low areas become full, the pressure gradients disappear and the resurfacing ceases. This provides an explanation for the observed straight dark-bright terrain boundaries: water cannot overflow the graben, so surfacing rarely embays craters and other rough topography. Subsurface liquid water must exist for the scenario to exist, of course, and is plausibly provided by tidal heating during an ancient orbital resonance. This abstract is a summary of Showman et al. recently submitted to Icarus.

Here we investigate a scenario in which cores as small as a few Earth masses stall in the terrestrial planet region, but continue to grow as a result of the Type I migration of other Earth sized objects, taking place in a timescale approx. 10(exp 6) years similar to the disk clearing timescale (such migration may thus significantly reduce the accretion efficiency, particularly in the terrestrial planet region). Since the core may intercept such inwardly migrating objects (possibly by altering the surface density to the point that the object stalls within the core's feeding zone) or coalesce with neighboring cores, its growth may continue until it reaches a CCM. The question then arises whether such a core can accrete enough gas to become a Jovian-sized giant planet. In the limit of low opacity (such that the protoplanet s tidal torque fails to clear gas from its feeding zone in time to prevent its accretion), the final mass of the planet is given by the gaseous isolation mass (provided alpha is < or approx. = 10(exp -4) and that the gas component dominates the planet's mass).

In the core accretion model of giant planet formation, when the core reaches critical mass, hydrostatic equilibrium is no longer possible and gas accretion ensues. If the envelope is radiative, the critical core mass is nearly independent of the boundary conditions and is roughly M(sub crit) ~ 10Mass of the Earth (with weak dependence on the rate of planetesimal accretion M(sub core) and the disk opacity k). Given that such a core may form at the present location of Jupiter in a time comparable to its Type I migration time (10(exp 5) - 10(exp 6) years) provided that the nebula was significantly enhanced in solids with respect to the MMSN and stall at this location in a weakly turbulent (alpha approximately less than 10(exp -4) disk, it may be appropriate to assume that such objects inevitably form and drive the evolution of late-phase T Tauri star disks. Here we investigate the final masses of giant planets in disks with one or more than one such cores. Although the presence of several planets would lead to Type II migration (due to the effective viscosity resulting from the planetary tidal torques), we ignore this complication for now and simply assume that each core has stalled at its location in the disk. Once a core has achieved critical mass, its gaseous accretion is governed by the given Kelvin-Helmholtz timescale.

In order to create a coherent scenario of satellite formation. the source of the solids (rock-metal and ice) that will eventually make up the satellites must be considered. While it is customary to use a solar composition mixture with a gas/solid mass ratio of about 100, at the tail end of the formation of the giant planet (when satellite formation is thought to have taken place) the fraction of solids entrained in the gas (particles with sizes lower than the decoupling size about 1 m for typical nebula parameters) is likely to be significantly lower than cosmic. In particular, in the core accretion model of giant planet formation one expects low dust and rubble content at late times due to particle coagulation leading to a collisional distribution of particle sizes with most of the mas residing in objects 1 km or larger, which are not coupled to the gas and whose dynamics must be followed independently. As a result, flow of gas into circumplanetary orbits is not sufficient to constrain the mas available to form satellites.

It is only recently that the theory of disk-companion interactions yields migration rates due to the gas tidal torque that are in agreement with numerical simulations and up to an order of magnitude slower than previous estimates. Also, for a weakly turbulent disk, the gap size is controlled primarily by the damping length of acoustic waves launched by the secondary at Lindblad resonances, which in turn depends on whether the waves are 2D or 3D. At least for small azimuthal wavenumbers this damping length is of the order of the radial location of the Lindblad resonance. This may have important consequences for disk dispersal in satellite systems. In the case of Jupiter, it means that the inner Galilean satellites may have jointly opened a gap. On the other hand, in Saturn's system the satellites inside of Titan are probably too small to have opened gaps in the gas disk at the time of their formation; but the possibility exists that, by effectively clearing the gas disk inside its own orbit, Titan may have allowed smaller satellites to survive, depending on whether Titan can clear the disk in a timescale comparable to the migration rates due to gas drag and gas tidal torque for these objects.

We look into the possibility that Callisto's accretional history straddled the time during which Jupiter opened a gap in the solar nebula and occurred over an extended period from a very extended very low density disk. Additional information is contained in the original extended abstract.

We model the subnebulae of Jupiter and Saturn wherein satellite accretion took place. We expect a giant planet subnebula to be composed of an optically thick (given gaseous opacity) inner region inside of the planet's centrifugal radius (located at r(sub c, sup J) = l5R(sub J) for Jupiter and r(sub c, sup S) = 22R(sub S) for Saturn), and an optically thin, extended outer disk out to a fraction of the planet's Roche lobe, which we choose to be R(sub roche)/5 (located at approximately 150R(sub J) near the inner irregular satellites for Jupiter, and approximately 200R(sub S) near Phoebe for Saturn). This places Titan and Ganymede in the inner disk, Callisto and Iapetus in the outer disk, and Hyperion in the transition region. The inner disk is the leftover of the gas accreted by the protoplanet. The outer disk results from the solar torque on nebula gas flowing into the protoplanet during the time of giant planet gap opening. For the sake of specificity, we use a cosmic mixture 'minimum mass' model to constrain the gas densities of the inner disks of Jupiter and Saturn (and also Uranus). For the total mass of the outer disk we use the simple scaling M(sub disk) = M(sub P)tau(sub gap)/tau(sub acc), where M(sub P) is the mass of the giant planet, tau(sub gap) is the gap opening timescale, and tau(sub acc) is the giant planet accretion time. This gives a total outer disk mass of approximately 100M(sub Callisto) for Jupiter and possibly approximately 200M(sub Iapetus) for Saturn (which contain enough condensables to form Callisto and Iapetus respectively). Our model has Ganymede at a subnebula temperature of approximately 250 K and Titan at approximately 100 K. The outer disks of Jupiter and Saturn have constant temperatures of 130 K and 90 K respectively.

An explanation of the dynamical mechanism for apse-alignment of the eccentric Uranian rings is necessary before observations can be used to determine properties such as ring masses, particle sizes, and elasticities. The leading model relies on the ring self-gravity to accomplish this task, yet it yields equilibrium masses which are not in accord with Voyager radio measurements. We explore possible solutions such that the self-gravity and the collisional terms are both involved in the process of apse-alignment. We consider limits that correspond to a hot and a cold ring, and show that pressure terms may play a significant role in the equilibrium conditions for the narrow Uranian rings. In the cold ring case, where the scale height of the ring near periapse is comparable to the ring particle size, we introduce a new pressure correction pertaining to a region of the ring where the particles are locked in their relative positions and jammed against their neighbors, and the velocity dispersion is so low that the collisions are nearly elastic. In this case, we find a solution such that the ring self-gravity maintains apse-alignment against both differential precession (m = 1 mode) and the fluid pressure. We apply this model to the Uranian alpha ring, and show that, compared to the previous self-gravity model, the mass estimate for this ring increases by an order of magnitude. In the case of a hot ring, where the scale height can reach a value as much as fifty times larger than a particle size, we find velocity dispersion profiles that result in pressure forces which act in such a way as to alter the ring equilibrium conditions, again leading to a ring mass increase of an order of magnitude; however, such a velocity dispersion profile would require a different mechanism than is currently envisioned for establishing heating/cooling balance in a finite-sized, inelastic particle ring. Finally, we introduce an important correction to the model of Chiang and Goldreich.

Using an optically thick inner disk and an extended, optically thin outer disk as described in Mosqueira and Estrada, we compute the torque as a function of position in the subnebula, and show that although the torque exerted on the satellite is generally negative, which leads to inward migration as expected, there are regions of the disk where the torque is positive. For our model these regions of positive torque correspond roughly to the locations of Callisto and Iapetus. Though the outer location of zero torque 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 approximately 3r(sub c, sup S) where r(sub c, sup S) is Saturn's centrifugal radius) than Jupiter's (at approximately 2r(sub c, sup J), where r(sub c, sup J) is Jupiter's centrifugal radius) is mostly due to Saturn's less massive outer disk, and larger Hill radius. For a satellite to survive in the disk the timescale of satellite migration must be longer than the timescale for gas dissipation. For large satellites (approximately 1000 km) migration is dominated by the gas torque. We consider the possibility that the feedback reaction of the gas disk caused by the redistribution of gas surface density around satellites with masses larger than the inertial mass causes a large drop in the drift velocity of such objects, thus improving the likelihood that they will be left stranded following gas dissipation. We adapt the inviscid inertial mass criterion to include gas drag, and m-dependent non-local deposition of angular momentum.