Au

Inner boundary of Oort cloud

(Cross-section)

Figure 3.13 The inner part of the Oort cloud of comets, and the E-K belt of comets.

The outer reaches of the Oort cloud are at a significant fraction of the distances between neighbouring stars in the solar neighbourhood - currently the nearest star (Proxima Centauri) is 2.7 x 105 AU away. The stars are in motion with respect to each other, so it is to be expected that from time to time a passing star will perturb the cloud. As a result, some members are drawn out of the Solar System, whilst others have their perihelion distances greatly reduced, so that near perihelion a coma and tails are developed, and a new LPC is observed. Giant molecular clouds in the interstellar medium can have similar effects to stars, as can the Galactic tide (Section 2.2.6). These perturbations on the outer Oort cloud explain the highly eccentric, large, randomly oriented orbits of the LPCs, and the frequency with which these comets are observed. Bodies reaching us from beyond the Solar System might constitute a small proportion of the LPCs.

The HFCs are thought to be LPCs, mainly from the inner Oort cloud, that have had their orbits reduced through interactions with the giant planets.

In Section 2.2.6 you saw that the E-K belt is thought to be a mixture of icy-rocky planetesimals composed of a population left over in the giant planet region that was then scattered further out by the giants, and a population formed directly from the solar nebula.

□ How does the giant planet migration model explain why the space within about 40 AU of the Sun is largely devoid of EKOs? This was cleared by the 3:2 mmr with Neptune during its outward migration.

Regardless of how it was emplaced, the E-K belt is now thought to be the source of the SPCs. It used to be thought that the SPCs were LPCs that had had their orbits perturbed by the giant planets. However, detailed simulations failed to produce an essential feature of the orbits of the SPCs - namely, orbital inclinations predominantly less than 35°. By contrast, it is easy to produce this feature from a source population already in low-inclination orbits. Because the SPCs have active lifetimes of a few thousand years before devolatilisation, the population of active SPCs needs to be resupplied. A reservoir of millions of bodies is needed to meet the required rate, and the resupply would occur in two stages. First, an orbit is modified by gravitational perturbations, partly by the outer planets, but particularly by the larger members of the belt itself, of order 103km across. Orbital changes can also result from collisions between EKOs. These result in fragmentation. Second, if the new orbit is such that the object can approach a giant planet, a possible outcome is that the orbit is further modified into one typical of a SPC.

The E-K belt satisfies the requirement for a source population in fairly low-inclination orbits. Its existence was first proposed in 1943, long before EKOs began to be discovered. The idea came from the Anglo-Irish astronomer Kenneth Essex Edgeworth (1880-1972), and eight years later from the Dutch-American astronomer Gerard Peter Kuiper (1905-1973) (which is why it is sometimes called the Kuiper belt). The first EKO was discovered in 1992, and has the name 1992 QBj (QBj identifies when it was discovered in 1992). It is about 200 km across and occupies an orbit with a semimajor axis of 43.8 AU, an eccentricity of 0.088, and an inclination of 2.2°.

Over 1000 EKOs are presently known, and their numbers are steadily rising. Very many more await discovery as surveys are extended. Those in the inner E-K belt can presently be detected down to the order of 10 km across, depending on albedo. For a fixed albedo, the brightness decreases as r-4, where r is the distance from the Sun to the EKO - this is a factor r-2 for the decrease in solar radiation, and another factor of r-2 for the (approximate) distance of the EKO from our telescopes. Therefore, as r increases the population is increasingly undersampled. The estimates of the total population differ widely. One estimate is of at least 105 objects greater than 100 km across out to about 50 AU. Thus, given that 50 AU is not the outer boundary, the total population will exceed 105, probably by a huge factor for such sizes, and vastly more for sizes greater than 1 km across. The total mass could approach an Earth mass, though other estimates are about a tenth of this, or even less. Figure 3.13 shows the E-K belt blending into the Oort cloud. This is conjectural.

The population of EKOs is divided into three subpopulations: the classical EKOs, the resonant EKOs, and the scattered disc EKOs.

Classical EKOs

These are defined to have perihelion distances q>35 AU, semimajor axes a in the approximate range 40-50 AU, and low eccentricities e, around 0.1. They also have low inclinations i, though this might be an observational selection effect, most searches concentrating near the ecliptic plane. Over 600 are known, accounting for nearly two-thirds of the presently known EKOs. There seems to be a sharp outer edge, which they might have inherited from their birth, or because more distant ones were trimmed off in a close encounter with a star early in Solar System history.

Resonant EKOs

These are the EKOs that have been found in mmrs with Neptune, mostly in the 3:2 resonance, but also a few in the 4:3, 5:3, and 2:1 resonances. The resonances have generally produced larger e and i values than in the classical population. □ What are the semimajor axes of these four resonances?

From equation (1.3), ares = aN(Pres/PN)2/3 where aN = 30.1 AU. Thus, with Pres/PN = 1.33, 1.50, 1.67, and 2.00 for the 4:3, 3:2, 5:3, and 2:1 resonances, we get 36.4 AU, 39.4 AU, 42.3 AU, and 47.8 AU respectively. You should recognise 39.4 AU as close to Pluto's current semimajor axis (it varies slightly) of 39.8 AU. The EKOs in this resonance are thus called Plutinos, and over 100 are known, though it is estimated that roughly 1500 larger than 100 km across await discovery.

Recall that the Plutinos are thought to have been pushed there as Neptune migrated outwards. Some Plutinos, and Pluto, have perihelion distances less than 30 AU and so cross Neptune's orbit. Like Pluto, the position of each Plutino in its orbit is such as to avoid a close encounter -a configuration maintained by the 3:2 resonance. If this were not so, the Plutino would not be there!

Scattered disc EKOs

The scattered disc EKOs (SDOs) are characterised by eccentricities greater than those of the classical EKOs, the dividing line being somewhat arbitrary, but 0.25 is in the midst of the various proposals. Values up to 0.9 have been observed, corresponding to aphelia of several hundred AU. Such extremes might be due to a stellar encounter. SDOs also have a greater range of inclinations than the classical objects, extending above 20°. Their semimajor axes are predominantly greater than 35 AU, extending to at least 120 AU. A few hundred SDOs are known, though our searches are very incomplete, and so a far greater number surely await discovery.

The SDOs with perihelia less than about 35 AU could well have been classical EKOs that have been perturbed by Neptune. Those with greater perihelia could be increasingly primordial as the perihelion distance increases, i.e. they could be icy-rocky planetesimals scattered by the giant planets in their migration phase, with the outward migration of Uranus and Neptune making the largest contribution. One theoretical estimate is that about 30 000 planetesimals greater than 100 km across were scattered outwards. This, and other estimates, foretell a cornucopia of discoveries.

The origin of the SDOs and the classical EKOs seems not to be very different. Both could be mixtures of a primordial population and a scattered population. It is not fully understood why their orbital characteristics are somewhat different.

Physical properties of EKOs

Albedos have been obtained for a few EKOs. Among the larger EKOs Pluto has a geometric albedo p varying from 0.5 to 0.7 across its surface, and its satellite Charon 0.38. Varuna, about 40% of Pluto's radius, is dark, with p ~ 0.07, but Eris (which HST images show has a 20% greater radius than Pluto) is bright, with p ~ 0.9. The albedos of other EKOs mostly lie within the range 0.04-0.4. It is likely that the higher the albedo, the more recently the object has been collisionally resurfaced with fresh icy materials. The colours of the EKOs show significant diversity, from neutral grey through various degrees of redness, uncorrelated with brightness or orbit. Spectra have been obtained for only very few. Some show water-ice features, others do not. Surface temperatures are 50-60 K in the inner E-K belt, depending on the distance from the Sun and the proportion of solar radiation absorbed (see equation (9.8)). Internal temperatures in the larger EKOs could be considerably greater, as you will see in Section 5.2.2.

The mass of Eris will soon be determined from the orbit of its satellite Dysnomia, discovered in 2005 by the Keck telescopes. We will then be able to calculate its density and hence its composition will be constrained.

As well as supplying the SPCs, an EKO could also account, as you have seen, for Neptune's large satellite Triton, which has a peculiar orbit (Section 2.3.1) and resembles Pluto. It could have been captured from the belt, as could some of the small icy-rocky satellites.

Question 3.9

Discuss which feature(s) of the orbits of HFCs indicate an inner Oort cloud origin for most of them, rather than an origin in the E-K belt.

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