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a Planetary mass. b semimajor axis. c Hill sphere radius from Equation (23). d apparent angular radius of the Hill sphere from Earth.

a Planetary mass. b semimajor axis. c Hill sphere radius from Equation (23). d apparent angular radius of the Hill sphere from Earth.

where a is the planet semimajor axis, mp is the planet mass, and Mq is the Solar mass (Table 7). The irregular satellites are interesting in the context of the Saas Fee workshop from the point of view of their possible origin. They cannot have been formed like the regular satellites within accretion disks surrounding the planets. Instead, they must have been captured. It is not known from where they were captured, but there are two broad possibilities. First, they might have had a local source. The irregular satellites could be planetesimals that were initially in heliocentric orbits and were captured by the planets as a result of their sudden growth (we will discuss the "standard models" for satellite capture in a moment). In this case, the irregulars are interesting because they are surviving samples of the kinds of solid bodies most of which were accreted into the cores of the giant planets, or which were scattered out of the Solar system soon after the giant planets attained their final masses. A second possibility is that the irregular satellites are captured comets or, equivalently, captured KBOs. In this case, the irregulars would take on new significance as (relatively) local examples of objects from the much more distant Kuiper Belt.

Research into the irregular satellites is in the midst of a sudden burst of new work, driven by the application of large-format CCD detectors to the problem of their detection. Less than a dozen irregular satellites were discovered in the entire twentieth Century. Most of these were chance detections made by observers using photographic plates and long exposures on large telescopes. Within the past ^half-decade, nearly 100 new irregulars have been identified, most as the result of surveys conducted using various telescopes and large cameras on Mauna Kea [133,135]; an updated summary of the data may be found at http://www.ifa.hawaii.edu/~jewitt/irregulars.html. These surveys continue, and more irregular satellites discoveries are anticipated, but we already are beginning to see new patterns in the distribution of the satellites that raise problems concerning the mechanisms of capture.

The central problem of permanent capture is that a body that follows an orbit initially unbound to a planet must lose or otherwise redistribute some of its kinetic energy to become bound to the planet. For a long time, the standard model for the capture of the irregular satellites has been through the action of gas drag forces on heliocentric planetesimals passing through the bloated gaseous envelopes of the young giant planets. This model, which was developed in parallel with models for the formation of gas giant planets like Jupiter and Saturn, implies that the irregular satellites observed today are those objects that were neither too small (ablated and absorbed in the gaseous envelopes like meteors in the Earth's upper atmosphere) nor too large (passed through the envelopes with negligible deceleration to continue in heliocentric orbits). It also relies upon the sudden collapse of the extended envelopes to leave the satellites behind: continued friction would lead to all trapped bodies spiraling into the planets.

A problem with this gas-drag capture model is that the new surveys show that Uranus and Neptune possess irregular satellite systems of their own. In fact, when corrected for the magnitude-limited nature of the observational surveys to the best of our ability, the new surveys show that the gas giants and the ice giants possess about the same number of irregular satellites, measured down to a given satellite absolute magnitude or size. This is seen by comparing Fig. 40 (the apparent magnitude distributions of the satellites of all four giant planets) with Fig. 41 (same as Fig. 40 but corrected for the varying distances of the planets using the inverse-square law [78]). Within the errors, the irregular satellite absolute brightness (size) distributions are the same. This is a remarkable and unexpected observational result. It is difficult to see how Uranus and Neptune, which are relatively gas-free ice giants, formed by processes quite different from those that produced the gas giants Jupiter and Saturn, could capture the irregular satellites by gas drag. At least, gas-drag capture has never been demonstrated for the ice giants in any publication

Apparent Red Magnitude

Fig. 40. Number of irregular satellites of each planet as a function of apparent magnitude. From [78]

Apparent Red Magnitude

Fig. 40. Number of irregular satellites of each planet as a function of apparent magnitude. From [78]

of which I am aware. Taken as a whole, the uniform abundance of irregular satellites around the gas and ice giants argues against gas-drag capture.

What about other capture processes? A separate mechanism has been proposed in which runaway mass-growth of a planet leads to the permanent trapping of objects initially moving within the Hill sphere. This is called "pulldown capture" [59]. Like gas-drag, pull-down capture works best for the gas giants, which had a runaway growth of mass as they attracted gas from the protoplanetary nebula in a hydrodynamic in-flow (Sect. 2). The ice giants, instead, grew slowly by successive collisions with solid bodies in the disk, and they did not experience a runaway growth in mass. Therefore, it seems unlikely that pull-down capture can explain the irregular satellite systematics revealed in Fig. 41.

This leaves the generic class of "three-body interactions" as possible explanation of the capture of the irregular satellites. Three-body capture is appealing because it separates the capture mechanism from the details of planet formation. All that is needed is a sufficient density of objects for three-body interactions (two small bodies within the Hill-sphere of a large one) to occur with high enough frequency to be relevant. Although suggested long ago [22], three-body captures have rarely been discussed in the context of the irregular satellites precisely because the densities of small bodies in the Solar system are so low that the frequency of interaction is negligible. Our changing perspective, in which the density of small bodies may have been

16 18 20 22 24 26

Red Magnitude Scaled to Jupiter

Fig. 41. Number of irregular satellites of each planet as a function of reduced magnitude (i.e., corrected for their differing heliocentric and geocentric distances using the inverse square law). From [78]

16 18 20 22 24 26

Red Magnitude Scaled to Jupiter

Fig. 41. Number of irregular satellites of each planet as a function of reduced magnitude (i.e., corrected for their differing heliocentric and geocentric distances using the inverse square law). From [78]

hundreds or thousands of times larger than now, makes three-body processes more attractive.

Is there any evidence that the irregular satellites were captured from a local source as opposed to a Kuiper belt source, or vice versa? The color distribution of the irregular satellites is different from the color distribution in the Kuiper belt [54,55] with the main difference being that the ultrared matter is absent on the satellites but common on both KBOs and Centaurs. This could indicate that the Kuiper belt is not the source of the irregular satellites, suggesting that sources local to each planet are more likely. Alternatively, there could be a delivery mechanism from the Kuiper belt that operates selectively to exclude the ultrared objects. At Jupiter, it is possible that the colors of the satellites have been modified by rubble mantle formation or by another process, as is inferred for the Trojans at the same heliocentric distance. The authors of the Nice, France model [115] are careful to note that objects captured by Jupiter as Trojans have mostly spent time at smaller heliocentric distances (by which they mean to say that the color differences between Trojans and KBOs may be explained by past outgassing). The same argument could be made for the irregular satellites of Jupiter. Modification by mantling seems unlikely at Saturn, Uranus, and Neptune, however, because of the lower temperatures at 10, 20, and 30 AU and the expected lack of sublimation driven activity at these distances.

The size distribution of the irregular satellites (q ~ 2; [78]) is flatter than the corresponding distribution of the KBOs (q ~ 4; [151]). This does not rule out an origin by the capture of KBOs, however, because the satellite size distribution could have been strongly modified either by the capture process or by size-dependent evolutionary effects [117].

Measurements of the density (1630 ± 33kgm~3) of Saturn's large irregular satellite Phoebe (Fig. 42) have been claimed as evidence for Kuiper belt origin [81]. The argument is that Phoebe is denser than most other Saturnian satellites and that the higher density more closely resembles the densities of Kuiper belt objects such as Pluto and Triton (p ~ 1900kgm~3). This is a difficult argument to sustain, however, given that the densities of KBOs seem to vary over a wide range and that the Saturnian regular satellite Ence-ladus has a density (1606 ± 12kgm~3) essentially identical to that of Phoebe (but there is no suggestion that Enceladus is captured). I note without further comment that the low density of Jovian Trojan (617) Patroclus (p = 800+100 kgm~3) has been asserted as evidence for its origin by capture from the Kuiper Belt [105]. The bottom line is that there is no simple link between density and formation location, and it seems impossible to me to use one to predict the other.

Measurements of diverse surface composition on Phoebe, including ices of water, trapped CO2, and organics and cyanide compounds, suggest to some that this body was formed at a remote location and then captured [21]. Again, the argument is an indirect one, and, as the authors note, it is possible that

Fig. 42. Saturnian irregular satellite Phoebe, roughly 220 km in diameter and in possession of a magnificent impact crater almost half its size. Courtesy Cassini Imaging Team and NASA/JPL/SSI

the surface ice on Phoebe is in part a coating from the impact of a comet itself from distant regions.

4.8 Trojans

The origin of the Trojans has long been a source of mystery. Objects colliding near the Lagrangian L4 and L5 resonances have a small but finite probability of being captured there, particularly if they were already nearly co-moving with Jupiter [19,104,160]. Icy asteroids near the growing Jupiter could also be pulled into trapped orbits by the mass growth of Jupiter [49,104]. It has also been suggested that the Trojans might have originated at remote locations in the Solar system and were captured through the action of outgassing forces [160] or a chaotic disturbance that would have resulted if Jupiter and Saturn were once in 2:1 mean-motion resonance with each other [115].

In terms of what we know from observations, the Trojans may have no connection at all to the Kuiper belt or they may be genetically closely related. The observational constraints are presently too weak for us to determine the origin of these intriguing bodies at any level above the conjectural. One reason for this sorry state of affairs is that most Trojans are twice as distant and so 24 = 16 times fainter than main-belt asteroids of corresponding size. By comparison, the main-belt asteroids represent "low hanging fruit" to most observers, and so, they have received the lion's share of the attention. This situation has only recently started to change. Indeed, until recently only Jovian Trojans were known. Now we are also aware of Trojans of Mars and of Neptune. Planned all-sky surveys should greatly improve our knowledge of the populations and size distributions of these bodies. In this section, we briefly review the known properties of the Trojans and compare them with the KBOs and other bodies.

Surveys show that the number of Jovian Trojans rivals the number of main-belt asteroids when measured down to a common limiting diameter [70,136]. There are about 1.5 x 105 Trojans larger than 1km in radius. They occupy two banana-shaped clouds in Jupiter's orbit, leading and trailing the planet by ±60°. Objects in the clouds librate around the L4 and L5 Lagrangian points in response to the combined gravitational attractions to the Sun and Jupiter (see [49] for a nice discussion of Trojan dynamics, from which the following is taken). In the idealized planar, restricted three-body (Sun-Jupiter-Trojan) approximation their equation of motion is

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