| 2 | The Structure of Comet Nuclei from Observations and Experiments \It has been stated that within the head of a comet there is usually a bright point termed the nucleus. This is the only part of its structure which excites any suspicion of a solid substance." Robert Grant, History of Physical Astronomy, 1852. 2.1 Size and Composition Only the nuclei of Comets 1P/Halley, 19P/Borrelly, and 81P/Wild 2 have been measured with some accuracy from the Giotto, Vega 1 and 2, Deep Space 1 (DS1), and Stardust spacecraft investigations. Dimensions of Comet 1P/Halley are about 15.5 km 8.5 km 8 km (Keller et al., 1986; Keller, × × 1990). Dimensions of Comet 19P/Borrelly are about 8 km 4 km 4 km, × × while those of Comet 81P/Wild 2 are about 5.5 km 4.0 km 3.3 km. From × × ground-based observations of nuclei of several other comets, the aspect ratio of Comet 1P/Halley's dimensions of about 2 : 1 : 1 appears to be typical. Determining the size of a comet nucleus from ground-based observations is difficult. When the comet is close to the Earth, its gas and dust coma conceal the nucleus. At large heliocentric and therefore large geocentric distances, it is difficult to spatially resolve the nucleus. Measurements that are made are a product of the cross section of the nucleus and the albedo of its surface. To separately determine these two quantities, measurements must also be made in the infrared. This has been done for several comets, including Comet 46P/Wirtanen. This nucleus diameter appears to be only about 800 m. It is one of the smaller comet nuclei. Comet Hale-Bopp (C/1995 O1) on the other hand appears to have a very large nucleus. Es- timates are that its diameter is about 40 km. 2060 Chiron may be one of the biggest nuclei with a diameter of about 150 to 200 km. At the other extreme are the Kreutz group of comets. These comets appear to be frag- ments of a large comet that broke up during a close encounter with the Sun. Comet Ikeya-Seki (C/1965 S1) is one of the larger fragments of this group. It passed through the Sun's corona in October 1965 and survived. Many of the smaller fragments, which have almost the same orbital parameters, do 9 10 2. The Structure of Comet Nuclei Table 2.1: Relative atomic element abundances of the gas and dust released by Comet 1P/Halley. The results of a study by Geiss (1988) renormalized to Mg with the solar Mg/Si-ratio and the abundances in the primordial Solar System and in CI-chondrites are listed (Anders and Ebihara, 1982) for comparison. Geiss (1988) Grun¨ & Jessberger (1990) Solar System CI H/Mg 39. 31. 25200. 4.9 C/Mg 12. 11.3 11.3 0.71 N/Mg 0.4 - 0.8 0.7 2.3 0.06 O/Mg 22.3 15. 18.5 7.1 N/C 0.03 - 0.06 0.06 0.2 0.08 O/C 1.8 1.3 1.6 10.0 not survive their passage through the corona. We know that many of these fragments have small nuclei because they remain undetected until shortly before they enter the Sun's corona. Data from Comet 1P/Halley has been analyzed by Geiss (1988) and by Grun¨ and Jessberger (1990). Grun¨ and Jessberger suggested that since the ratio of C to Mg in the dust is almost, but not quite, as high as the solar ratio, the missing carbon must be in the ice. Making this assumption, the results of the analyses are given in Table 2.1. Combining the known gas composition (Krankowsky and Eberhardt, 1990) with that of the dust, the bulk composition of 1P/Halley can be derived. This composition can be compared to the composition of the Sun and CI chondrites. Compared to solar composition, nitrogen is underabundant by a factor of about 3 and hydrogen is deficient by more than a factor of 700. However, the ratios of the other elements are very similar to the solar values, but differ significantly from CI values. This finding corroborates the contention that comets are only slightly altered relics from the solar nebula. The dust to gas mass ratio, resulting from the above argument, is 1 :1 with an uncertainty of a factor of two. This value is well within the much wider range of values derived from direct measurements in the coma. One can approximate the abundances of molecular species in comets by making the following assumptions: (1) Only molecules that are condens- able at about 25 to 30 K exist in comet nuclei, (2) the elemental number abundances of C, O, Mg, Si, S, and Fe are solar, (3) N is depleted by a factor of about 3, and (4) the abundance of H is determined by its abil- ity to chemically bind with other available species. We assume that the silicate abundances are adjusted such that all Si is consumed in silicates, all iron is in Fe2SiO4 and all magnesium is in Mg2SiO4. Then the amount 2.1. Size and Composition 11 Table 2.2: Molecular distribution of elements in condensable molecules as- suming solar abundances (except for H) with N depleted by a factor of 3. Elmt. Solar Comet Silic. Rem H2O HCO Rem HCNS number number 1 Comp 2 Comp abund. abund. C 305 305 0 305 0 72 233 232 N 84 28 0 28 0 0 28 28 O 608 608 122 486 401 84 0 0 Mg 24 24 24 0 0 0 0 0 Si 31 31 31 0 0 0 0 0 S 16 16 0 16 0 0 16 16 Fe 37 37 37 0 0 0 0 0 H 802 80 464 of oxygen contained in silicates can be determined from 18.5[Fe2SiO4] + 12.1[Mg2SiO4], which exhausts the available Si, Mg, and Fe. We further assume that the remainder of the oxygen (labeled Rem 1 in Table 2.2) is in H2O, with 5% (relative to H2O) in CO, 3% in CO2 (including a small amount of CH3OH), and 10% in H2CO (the most likely distributed source for CO in the coma). The fractions of CO, CO2, and H2CO relative to H2O are based on Comet 1P/Halley measurements. The result is a mixture of H-, C-, and O-bearing molecules that is equivalent to the hypothetical compound H20C18O21 (labeled HCO Comp in Table 2.2). This results in the abundance ratio of 118% of H20C18O21 with respect to H2O (100%) and exhausts the remainder of the available oxygen (Huebner, 2002). We can assume that the remainder (labeled Rem 2 in Table 2.2) of the carbon, nitrogen, and sulphur is in CH2-type polycondensates (i.e. an organic dust component without oxygen). The result is a mixture of H-, C-, N-, and S-bearing molecules equivalent to a molecule of the hypothetical compound C58H116N7S4 (labeled HCNS Comp in Table 2.2). The resulting mass frac- tions are summarized in Table 2.2. The last line in Table 2.2 determines the relative number of H atoms in a comet: 1346 relative to 31 atoms of Si. The total number of H atoms relative to the number bound in water is 1.68, and the total number of O atoms relative to the number bound in water is 1.52. This means that only about 3/5 of all hydrogen and 2/3 of all oxygen in a comet are in H2O. Table 2.3 summarizes the results in terms of mass fractions. We have separated the HCO compounds into the refractory organic forms (simply labeled H2CO) and the icy form (approximately 5 CO and 3 CO2, labeled as C8O11). Further, we assume that half of the HCNS compound is icy and half is refractory organic. We note that H2O is about 38% and silicates 12 2. The Structure of Comet Nuclei Table 2.3: Mass fractions of the components discussed in Table 2.2 Molecule Total Ice Dust % Ice % Dust H2O 7218 7218 0 38.3 0.0 H2CO 1203 0 1203 0.0 6.4 C8O11 1091 1091 0 5.8 0.0 C58H116N7S4 3896 1948 1948 10.3 10.3 Silicates 5454 0 5454 0.0 28.9 Totals 18862 10257 8605 54.4 45.6 about 29% by mass of the comet nucleus. Greenberg (1998) obtains similar values (31% and 26%, respectively). Greenberg's values are based in part on laboratory results of organic fractions, while the fractions used here are based on analyses of measurements from Comet 1P/Halley made by space- craft. It is also apparent from Table 2.3 that the mass ratio of dust to ice is about 1 : 1, very similar to Greenberg's result. This ratio does not depend strongly on how the organics are distributed between the ice and the dust phases. The analysis again points out that the abundances in the coma may change significantly from dust rich to dust poor, but this may be the result of outgassing and mantle development, not necessarily an innate property. The observed chemical composition in the coma is characterized by chemical disequilibrium including high abundance ratios of isomeric pairs such as HNC/HCN and of deuterated-to-normal abundances for many sim- ple molecules. The deuterium enrichment is reminiscent of the analogous isotopic anomaly found in certain organic fractions of carbonaceous chon- drites, and has led to the suggestion that some interstellar material has sur- vived the accretion shock in molecular form to be incorporated into primitive objects such as carbonaceous meteorites and comets.