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Fig. 11. Flow diagram for the Solar system. This chart shows, at the top, the Kuiper belt and Oort cloud reservoirs. Arrows indicate dynamical flow-down into other populations, including the Jupiter family comets (JFCs), Halley family comets (HFCs), and other long-period comets (LPCs). Escaped Trojans would resemble JFCs. Although no specific cases are known, I have indicated the Trojans as a possible source by an arrow marked "?". The reservoir from which the HFCs are derived is not well understood, but most researchers believe that a source in the inner Oort cloud is likely. This is indicated by another arrow with a "?". On the left is shown the newly identified MBC class, co-located with their source region in the asteroid belt. At the bottom are four processes that represent the demise of the comets semimajor axes are clustered at large values. The key observation made by Oort was that the orbital energies of many long-period comets (which Oort expressed by the inverse semimajor axes of their orbits) are smaller than the characteristic value of the energy change resulting from gravitational perturbations exerted by Jupiter in a single passage [119]. He concluded that comets were falling into the planetary region from large (but finite) distances, and that many of the long-period comets had not been through the planetary region before, for otherwise they would already have been scattered out of the narrow (bound) energy peak in which they sit. This basic conclusion remains unchanged, to the undying credit of Mr. Oort. Likewise, available data, much improved in quantity and quality since Oort's time, continue to show that the cloud is closely spherical in shape, albeit with a characteristic diameter (~100,000AU) that is about half the value he calculated (see [158] and [51] for refreshingly written overviews of the observational constraints on the Oort cloud).

Other features of Oort's model are more puzzling. He found very few examples of comets that have been scattered out of the Oort peak (to more tightly bound, smaller orbits), relative to the number of comets in the peak. Three possibilities exist to explain this mismatch between the dynamical model and the data: (1) the model could be wrong, or incomplete, (2) incoming comets could become intrinsically fainter (and therefore harder to detect) once they have passed through the inner Solar system, or (3) a large fraction of the incoming comets could vanish after their first few journeys through the Solar system. There seems to be no great enthusiasm amongst dynamicists for concluding that Oort's dynamical model is wrong or incomplete. Indeed, no dynamical explanation could be found (by Oort in 1950 nor by Wiegert and Tremaine [158] in a careful analysis some 50years later). Like Oort [119], all researchers have assumed that the disagreement between the data and the model is best explained by fading or disintegration of the incoming comets. However, the nature and reality of the fading remain unidentified. The low rate of detection of weakly active or completely inactive long-period comets has been interpreted as evidence that objects from the Oort cloud do not merely run out of gas but physically disintegrate [94]. This conclusion rests on a poorly known relation between the brightness of active long-period comets and the sizes of their underlying nuclei. For example, if the nuclei are much smaller than assumed in [94], then they might escape detection without disintegrating.

The population and mass of the Oort cloud are also uncertain. The population is derived from measurements of the rate of arrival of new comets from the Oort cloud coupled with models of the rate of erosion of the cloud by external perturbers. Oort considered passing stars to be the main external perturbers. The asymmetric tide of the Milky Way is now thought to be a larger perturber [58]. In addition, the rate of arrival of new comets is subject to observational biases that are difficult to quantify. Until recently, published population estimates relied on the work of visual observers [43,64], most of whose survey techniques and other details went unpublished. A recent attempt to use data from the LINEAR survey (whose parameters are better, but still not completely, known) gives ^5 x 1011 comets with absolute magnitude H < 11 [51], about 10 times smaller than estimated previously.

Lastly, the relation of the Halley family comets to the Oort Cloud is unclear. These objects have distinctly non-random distributions of inclinations (with some retrograde members but many more prograde ones) and orbital periods, by definition, <200 year. The most likely source is the inner Oort cloud, but the location and population of this region remain poorly constrained.

Kuiper Belt Source

The Kuiper belt became real with the discovery of 1992 QB1 [73]. Before that time, its only observed member was Pluto, misleadingly given planetary status for a host of mostly socio-scientific reasons. In fact, if Pluto had been accurately interpreted in 1930, our study of the structure of the Solar system could have advanced by many decades over the actual case (e.g., many bright KBOs have been "precovered" in photographic plates taken in the 1950s. They were not discovered using plates because astronomers did not think to look for them until after the discovery of 1992 QB1). Indeed, at least one astronomer correctly recognized in 1930 that Pluto must be just one of many trans-Neptunian objects [92] based on the dubiousness of the proposition that Tombaugh had been lucky enough to find the only one so soon after starting his survey. This reasoned position was drowned out by the assertion that Pluto must be the long-sought "Planet X," predicted by Percival Lowell on the basis of a model of (what turned out to be unreal) deviations in the motion of Uranus. Still, everything is obvious in hindsight, and it is too easy to see what should have been done knowing what we know, and too difficult to reconstruct the full state of confusion that reigned only a few decades ago. For example, Edgeworth in 1943 [40] speculated about "clusters" in the trans-Plutonian region (clusters were his idea for the structure of comets) while Kuiper (for whom the belt is somewhat ironically named) in 1951 [85] considered that this region should be empty, having been cleared of objects by strong perturbations from "massive" Pluto. Later, Fernandez in 1980 [45] reasoned that a flat disk source was needed to explain the inclination distribution of the short-period comets. Before this time, most researchers had been happy with the contention that short-period comets were somehow dynamically evolved versions of long-period comets. Later still, in 1988, Duncan and collaborators [38] showed, using numerical methods, the correctness of Fernandez' argument.

The dynamics of the Kuiper Belt are extensively and masterfully discussed in the Saas Fee lectures by Alessandro Morbidelli [112].

Main Belt Source

Main belt comets (MBCs) have orbits in the main asteroid belt between Mars and Jupiter. At the time of writing, three MBCs have been identified ( [63]; see Fig. 12). The best known is asteroid 7968 also known as 133P/Elst-Pizarro, first observed to be accompanied by a dust trail in 1996. Initially interpreted as an impact-produced dust cloud [150], the reappearance of the trail near perihelion in 2003 showed that another explanation is required [62]. The newest examples are comet P/2005 U1 (Read) and (118401) 1999 RE70, both of which show persistent dust emission over timescales of months. These three objects have similar semimajor axes located beyond 3 AU, in the outer regions of the main belt. Their orbital inclinations are also all small, but the similar a and i are at least in part results of observational bias, because our surveys have targeted exactly these types of object. The MBC orbits are decoupled from both Mars and Jupiter and appear to be dynamically stable on billion year timescales, like those of the main-belt asteroids that occupy exactly the same region of orbital element space (Fig. 13).

Could the MBCs be comets captured from other regions, for example from the Jupiter family comet (JFC) or long-period comet (LPC) populations? As

Fig. 12. Three main-belt comets (MBCs) in deep CCD images from Mauna Kea. These objects emit dust like comets but have orbits that are like those of outer main-belt asteroids. Background stars and galaxies appear trailed owing to the non-sidereal motions of the MBCs. From [63]

observers, we are open to this possibility, but dynamical simulations of the motions of comets suggest that this is very unlikely. In fact, pure dynamical calculations completely fail to inject comets into MBC-like orbits even when the perturbations of the Terrestrial planets are included [47, 95]. Some work has been done on the effects of non-gravitational accelerations (caused by asymmetric mass loss from cometary nuclei), but again, MBC-like objects are not produced. Failing some dramatic revision of the dynamics, we are forced to the conclusion that the MBCs are what they appear to be: asteroids that outgas like comets.

Several lines of argument indicate that the mass loss from MBCs is driven by sublimation, probably of near-surface water ice. First, mass loss from 133P has been observed at consecutive perihelia but not in between. This is exactly as expected for sublimation-driven activity. The sunward "nose" of the coma of P/2005 U1 (Read) is well resolved, with an apex scale of several arcseconds. This implies that the particles are ejected from the nucleus at considerable speed (>100ms_1), as expected for water ice sublimating at —3AU. Other explanations for mass loss seem less viable. The nucleus of 133P is rapidly rotating, and it is possible that centripetal effects assist the launching of dust

Fig. 13. Semimajor axis vs. orbital eccentricity for asteroids (small black dots), Jupiter family comets (blue circles) and the known MBCs (red circles). Vertical dashed lines mark the semimajor axes of the orbits of Mars and Jupiter and the 2:1 mean-motion resonance with Jupiter, which practically defines the outer edge of the main belt. Curved dashed lines show the locus of orbits which are just Mars and Jupiter crossing. Objects below these two curves cross neither Mars nor Jupiter, like essentially all of the main-belt asteroids. The MBCs fall within the domain occupied by stable main-belt asteroids and far from the periodic comets. From [63]

Fig. 13. Semimajor axis vs. orbital eccentricity for asteroids (small black dots), Jupiter family comets (blue circles) and the known MBCs (red circles). Vertical dashed lines mark the semimajor axes of the orbits of Mars and Jupiter and the 2:1 mean-motion resonance with Jupiter, which practically defines the outer edge of the main belt. Curved dashed lines show the locus of orbits which are just Mars and Jupiter crossing. Objects below these two curves cross neither Mars nor Jupiter, like essentially all of the main-belt asteroids. The MBCs fall within the domain occupied by stable main-belt asteroids and far from the periodic comets. From [63]

particles from its surface. However, centripetal effects alone cannot explain the observation that activity is confined to perihelion. Neither do we find evidence for rapid rotation in P/2005 U1 (Read) or 1999 RE70: these objects spin so slowly that rotation can play no role in the mass loss. Electrostatic levitation of dust grains has been observed in the terminator regions of the moon, where the derived velocities of the dust grains are ~1ms_1. Such low speeds are incompatible with the extended coma of P/2005 U1 (Read) and, furthermore, it is hard to see how electrostatic ejection of grains could be episodic (as on 133P), or why it would be confined to only three of several hundred asteroids examined in detail by our ongoing survey.

For these reasons, it appears that the MBCs are really comets in a special population where the source reservoir and the current locations are one and the same. Unlike the long- and short-period comets, the MBCs are not activated by being brought from cold storage locations into the hot inner Solar system. Instead, we suspect that they are activated collisionally. For example, the mass loss from P/2005 U1 (Read) corresponds to sublimation from an exposed patch of dirty water ice having a diameter of only ^20 m. Such a patch could be exposed by the impact of a meter-scale boulder into the nucleus surface. The mass loss rate at 3 AU is about 10~5 kgs-1 m~2 (Fig. 10) and, with density p ~ 1000kgm~3, the surface recession rate is di/dt ^10~8 ms_1. An ice patch 20 m in diameter would sublimate to a depth equal to its diameter on timescale t ~ 2 x 109 s (50 years), thereafter declining into inactivity from self-shadowing. Triggering collisions involving the impact of 1-m scale boulders should not be overly rare: we expect to find many MBCs in planned all-sky surveys such as Pan STARRS.

Is ice in the asteroid belt surprising? It should not be. Some meteorites show textural and geochemical evidence that they have been aqueously altered, probably by being bathed in liquid water at temperatures not far above the triple point [84]. This evidence includes the presence of clay minerals and serpentines that most naturally form with water, as well as carbonates and mineral deposits in veins that cross-cut other structures in the meteorites (showing that the vein materials were emplaced after formation). Spectrally, about half of the outer belt asteroids show absorption features attributed to water of hydration in minerals (not free ice, but water bound chemically within other materials such as clays [16]). At both smaller and larger distances, the prevalence of these hydration features decreases. One interpretation that fits the available data is that, at smaller distances, the asteroids were too hot for liquid water to have survived while at larger distances the ice was so cold as to never be melted, foreclosing the possibility of hydration reactions that could produce water of hydration bands [82].

The greatest excitement behind the MBCs lies in the potential relation between these objects and the oceans (and, through water, life). Earth probably formed too hot to trap much water, and so, it is widely believed that a separate source is required. Possible sources include the comets (but the measured deuterium/hydrogen (D/H) ratios in the three that have been measured seems higher than in the oceans [109]) or watery asteroids like the MBCs [113]. MBCs are so close to Earth that we should soon be able to visit them with a mass spectrometer, to measure their D/H (and other isotope ratios, including 16O/17O/18O) abundances, and so to make a direct comparison with the oceans.

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