a semi-major axis of the binary system. b eccentricity. c inclination.
d Dynamical type: 3:2, 2:1 = resonant, Clas = Classical, Sca = Scattered. e Angular separation. f Orbital period.
and a larger fraction of the KBOs must have multiple satellites. The largest satellite of the first-known (but mis-labeled) KBO Pluto has been known for decades, but it still surprising to see how many KBOs observed at high angular resolution are double. What can we learn from the binaries?
First, binaries are present in the classical, scattered, and resonant KBO populations. Systematic observations of 81 KBOs spread across these classes reveal 9 binaries at the resolution (and magnitude difference) accessible to the Hubble Space Telescope and its NICMOS camera, giving an average binary fraction of 11+2% . Given that binaries of very small separation and those having a large magnitude difference between the components cannot be detected, this must be taken as a strong lower limit to the binary fraction.
Second, low inclination (i < 5°) Classical KBOs have a binary fraction 22+5°% , which is different from the average value at the ~2a level. The mean value for all KBOs other than the i < 5° Classicals is 5.5+2%, which is different enough from 22+5°% to be interesting. The difference, if real, could be a hint that the diverse dynamical histories of the bodies have had an effect on the survival of binaries. For example, perhaps whatever excited, the orbital inclinations and eccentricities of KBOs also acted to split a fraction of the binaries.
Third, the binaries appear to be of different types. Pluto (and probably 2003 UB313 and others) have short orbital periods and orbital eccentricities e ~ 0. Together these strongly suggest the effects of tidal damping. Close binaries like these might be produced by glancing impacts between large precursors . The number density of large KBOs is presently far too low to account for such collisions. If this is the correct explanation, the collisionally produced binaries must be relics from an earlier time at which the number density in the belt was much (probably two to three orders of magnitude) higher than now [15,71].
Where measured, most KBOs have periods from months to years and the eccentricities of the orbits are in the range 0.2 < e < 0.8 (see Table 5). These wider, more eccentric binaries are unlike the binaries expected to be produced by glancing, massive impacts, and other explanations must be sought. Several have already been proposed, including binary formation through dynamical friction , three-body interactions [52, 156], and exchange reactions . These models are all good in the sense that they make observationally testable predictions. The exchange model predicts binary eccentricities larger than observed and can probably be ruled out, at least in its simplest form. Three-body interactions should produce mainly weakly bound binaries. It is not yet clear if the distribution of semimajor axes of the known binaries is incompatible with three-body captures, but this seems likely (Table 5). Capture by dynamical friction (exerted on large, growing bodies by the "sea" of smaller bodies surrounding them and now dissipated) is expected to produce a large binary fraction (as observed) with a high abundance of tight binaries (maybe consistent with the data). Continued action of dynamical friction should lead the binary components to spiral together, making contact binaries (one, 2001 QG298, is already suspected), but it is not clear that observed eccentricities 0.2 < e < 0.8 can be explained. At this early stage, I do not know if the proposed models fail because they are completely wrong, or because they tell only part of the story. Binaries could form by dynamical friction, for example, and then be excited by external agents after the source of dynamical friction had dissipated. Long-term (4 Gy) survival of the KBO binaries appears to be possible, but the existing pairs may constitute only a fraction of those initially present, with the softest binaries having all been disrupted .
4.5 Kuiper Belt Physical Properties: Densities
Densities have been discussed here and there throughout this chapter. For convenience, I have summarized them graphically in Fig. 38, where they are plotted as a function of the object diameters. The densities of cometary nuclei plotted in the figure have been estimated from various techniques as discussed in Sect. 3. Densities of KBOs are estimated from binary motions and size estimates (Pluto, Charon, and 1999 TC36, ), from lightcurves interpreted as rotational deformation of the shape ((20000) Varuna  and 2003 EL61 ) and from a contact binary model (2001 QG298, ). The densities of the planetary satellites are obtained nearly directly from gravitational perturbations on the motions of spacecraft, except that the densities of small Saturnian satellites including Pandora and Prometheus are estimated from a more complicated model of these satellites' interaction with nearby rings.
What does Fig. 38 show? The most obvious feature is a general trend toward higher densities at larger diameters, adequately described by the power law relation p = 340 D0 2 (with p in kgm~3 and D in km). This trend is
Fig. 38. Densities of KBOs, cometary nuclei, planetary satellites, and Jovian Trojan Patroclus. Abbreviations in the plot are Comets Bo = 19P/Borrelly , C-G = 67P/Churyumov-Gerasimenko , SL9 = D/Shoemaker-Levy 9 , SW2 = 31P/ Schwassmann-Wachmann 2, Wild 2 = 81P/Wild 2 , 133P = 133P/Elst-Pizarro  Kuiper Belt Objects EL61 = 2003 EL61 , Pl = Pluto, TC36 = 1999 TC36 , QG298 = 2001 QG298 [134,141] Planetary Satellites Enc = Enceladus, Ti = Titan, Eu = Europa. These densities are culled from the NASA-JPL site at http://ssd.jpl.nasa.gov/, mostly based on data from the Voyager, Galileo, and Cassini missions. The single Trojan is (617) Patroclus . Plotted error bars are 1a uncertainties. Single-sided errors below or above the points indicate either upper limits or lower limits to the density, respectively
Fig. 38. Densities of KBOs, cometary nuclei, planetary satellites, and Jovian Trojan Patroclus. Abbreviations in the plot are Comets Bo = 19P/Borrelly , C-G = 67P/Churyumov-Gerasimenko , SL9 = D/Shoemaker-Levy 9 , SW2 = 31P/ Schwassmann-Wachmann 2, Wild 2 = 81P/Wild 2 , 133P = 133P/Elst-Pizarro  Kuiper Belt Objects EL61 = 2003 EL61 , Pl = Pluto, TC36 = 1999 TC36 , QG298 = 2001 QG298 [134,141] Planetary Satellites Enc = Enceladus, Ti = Titan, Eu = Europa. These densities are culled from the NASA-JPL site at http://ssd.jpl.nasa.gov/, mostly based on data from the Voyager, Galileo, and Cassini missions. The single Trojan is (617) Patroclus . Plotted error bars are 1a uncertainties. Single-sided errors below or above the points indicate either upper limits or lower limits to the density, respectively apparent within the various populations (i.e., the planetary satellites and the KBOs independently show this trend) and, although there is considerable scatter in the densities of bodies at any particular diameter, the trend appears to be real.
The mean density of a composite body consisting of rock and ice is where p; and pr are the densities of ice and rock and f and fr are the fractional volumes occupied by ice and rock, respectively. The latter are related by in which fv is the fractional void space, also known as "porosity." In the context of Fig. 38, much of the trend in the bulk density is likely to be related to size-dependent variations in fv. This is because self-compression of ice and rock is not very important across most of the plotted diameter range [the central hydrostatic pressure in a body of radius r and average density p is Pc — Gp2r2. With p = 1000 kg m-3 and r = 500 km, Pc — 20MPa (Mpa = 106 Nm-2)], or roughly 200 bars, but densification through collapse of void space is likely. Laboratory experiments with ice at 77 K show brittle failure at comparable pressures  and suggest that part of the density-radius correlation may result from self-compression, particularly by the closing of void-space in porous bodies [71,107].
Any object less dense than pure water ice (p — 1000 kg m-3) must be porous. This includes most of the comets in Fig. 38 (but not 133P, the one MBC for which we possess a density constraint) and several of the co-orbital satellites of Saturn (Pandora and Prometheus both have p — 500 kg m-3). More surprisingly, Jupiter's innermost satellite Amalthea (—160 km in diameter) has p = 800 ± 200 kg m-3  and so is likely porous and ice-rich. This is a big surprise, given that before the density determination, Amalthea was always described as one of the most refractory, high-temperature products of Jupiter's long-gone accretion disk. The evidence for porosity is strong and independent infrared spectral observations  show a deep hydration feature that supports a watery constitution.
Porosity can be due to large, empty spaces ("macroporosity") or to open structure on a small scale "microporosity" and everything in between. Micro-porosity in stony meteorites averages 10% and can reach 30% in some samples . Macroporosity can be produced by past impacts that have cracked and even dissociated bodies leading to their re-assembly as a collection of irregularly shaped blocks with considerable internal void space. Evidence for this is seen even in the main-asteroid belt (e.g., rocky asteroid (253) Mathilde has p = 1300 ± 200 kg m-3 [11,159]). Porosity caused by collisional shattering and reassembly should become less important at larger diameters both because sufficiently energetic impacts are rare and because of closure of pore space at the higher hydrostatic pressures in large objects. I suspect that most of the
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