<<

Publications of the Astronomical Society of the Pacific

Vol. 106 1994 May No. 699

Publications of the Astronomical Society of the Pacific 106: 425-435, 1994 May

Invited Review Paper

Comets Disguised as Jane Luu1 Physics Department, Stanford University, Stanford, California 94305-4060 Electronic mail: [email protected] Received 1993 October 12; accepted 1994 January 24

ABSTRACT. and asteroids were previously thought to be two completely distinct groups of solar- system objects, with marked contrast in both physical and dynamical characteristics. A is operationally defined by the presence of a , while an has no coma. However, recent observations have shown that comets can sometimes take on asteroidal appearances and even asteroidal photometric behavior. Thus the observational distinction between comets and asteroids is not as clear cut as it once seemed. The possible presence of comets hidden among known asteroids forces us to reconsider the criterion by which we distinguish comets from asteroids and possibly our inventory of both comet and asteroid populations.

1. INTRODUCTION ets hidden among asteroids. Finally, the Conclusions sum- marize the main ideas presented in the review. This invited review paper is based on a talk given at the 180th American Astronomical Society meeting held in 1992 2. ASTEROIDS June at Columbus, Ohio. Comets and asteroids form two major groups of solar- 2.1 The Main Belt system objects, previously thought to be completely distinct As viewed from the Earth, even the largest asteroid (1 from each other. We identify an object as a comet by its Ceres, diameter 950 km) barely attains an angular diameter coma, an expanding cloud of dust and gas surrounding the of 1 arcsec, and appears marginally resolved in typical ob- nucleus. The coma is created by the sublimation of volatiles serving conditions. Our first close-up glimpse of an asteroid and ejection of entrained dust particles. On the other hand, came in 1991, when the spacecraft Galileo made a close asteroids are ostensibly inert objects; they possess no coma, approach with asteroid 951 Gaspra en route to . A and except for the very largest ones, appear unresolved as picture of Gaspra obtained during this encounter is shown in seen from the Earth. Until recently, comets and asteroids Fig. 1. Gaspra is a member of the main with a were thought to share no common characteristic besides the semimajor axis of 2.21 AU. The figure shows an irregularly fact that they both orbit around the . But the last decade shaped body (19X12X11 km) with a rocky surface pock- has seen the emergence of new evidence suggesting that the marked by impact craters (Belton et al. 1992). boundary between comets and asteroids may be much more The majority of asteroids are found in a beltlike distribu- tenuous than previously believed. tion (the "main belt") located between and Jupiter and In this review paper, I will focus on how comets can be effectively marking the boundary between the terrestrial "disguised as asteroids," i.e., how they adopt an asteroidal planets and the gas giants. There is very little mass in the asteroids, compared with the masses of the adjacent planets. appearance and photometric behavior. The paper is intended 21 for the general (nonspecialist) audience. The main goal of the All together, the main belt contains ~3X10 kg, or about 2% of the mass of the Moon and 0.05% that of the Earth. A paper is to show that the observational distinction between third of that mass is in 1 Ceres alone. A sense of the location comets and asteroids is no longer clear, and that the classifi- of asteroids with respect to the planets can be gained from cation of an object as a comet or asteroid, once a trivial task, Fig. 2, which shows a histogram of the asteroid semimajor is no longer a simple matter. The paper begins with a brief axes. introduction to asteroids and comets and their origins. This is The typical orbital periods of main belt asteroids are 3-6 followed by a discussion of how comets can develop aster- yr, and the orbits generally have low eccentricities (^0.1). oidal appearances and the methods by which to identify com- Most asteroid orbits are stable and are subject to only weak planetary perturbations, whose general effect is to make as- 1 Hubble Fellow. teroids oscillate about their mean orbits. As can be seen from

425 © 1994. Astronomical Society of the Pacific

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 426 LUU

every revolution of Jupiter. Repeated dynamical interactions with Jupiter have cleared asteroids from these resonances, and the gaps are commonly known as "Kirkwood gaps."

2.2 Non-Main Belt Asteroids Outside the main belt, there are only a few localized re- gions where asteroids are found. Inward of the belt lie the near-Earth asteroids (NEAs). As their name suggests, they travel on orbits which approach or cross that of the Earth. Beyond the main belt, the Trojan asteroids populate the L4 and L5 Lagrangian points of Jupiter at 5 AU. Beyond Jupiter, we presently only know of three objects classified as "aster- oids": 944 Hidalgo, 5145 Pholus, and 1993 HA2. (Another object in this region, , was previously classified as an asteroid but now displays a coma and so is a comet by the operational definition.) These objects travel on chaotic, comet-like orbits. It is the asteroids outside the confines of the main belt which play the most important role in the present discussion, and they will subsequently be discussed Fig. 1—Image of asteroid 951 Gaspra taken by the Galileo spacecraft during in greater detail. its encounter with the asteroid in 1991. The picture was taken from a range of 5300 km, with a resolution of —50 m. Photo courtesy of M. Belton, National Optical Astronomy Observatories (NOAO), for the Jet Propulsion 2.3 Physical Properties of Asteroids Laboratory. Asteroids are collisionally evolved: collisions at high rela- Fig. 2, asteroids are distributed almost throughout the entire tive velocities (~5 kms-1) are the main factor responsible 2-4 AU region, with the exceptions of a few clear gaps, such for the evolution of the asteroid's physical properties. A few as at 2.5 AU (3:1 resonance) and 3.3 AU (2:1 resonance). clusters of asteroids in the main belt ("Hirayama families") Asteroids located at these orbital resonances have a mean have similar orbital parameters and are believed to have motion which is in an exact integer ratio to Jupiter's, e.g., formed from common catastrophic collisions (Hirayama those at the 3:1 resonance complete three revolutions for 1918, 1919). Indeed, much of what we know about asteroid

Fig. 2—Histogram of the semimajor axes of known asteroids. Arrows point to the locations of resonances. Figure reprinted from Binzel (1989), courtesy of the University of Arizona Press.

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System COMETS DISGUISED AS ASTEROIDS 427 collisions come from rock-crashing laboratory experiments. Very crudely, the asteroids follow a inverse power-law size distribution described by q N{r)dr^r dr. (1) where r is the radius, N(r)dr is the number density of ob- jects in the radius range r to r + dr, and ^ is a positive power-law index. The power-law index for known asteroids 1:1 ( lies in the range g—2-3, and may depend on the composi- tional types (Gradie et al. 1989). Asteroids are made mainly of refractory material (e.g., 4:3 olivine, silicates, organics, pyroxene, feldspars), although 3:2 iron and nickel also form a large component in the compo- • * ·. · m -, · · sition of some asteroids. may also be present, but usu- 0o no -o vf.» r · ally in the form of chemically bound water (e.g., Jones et al. o C) o^· · . · · O ^v··.. _. 1990). Thus asteroids are generally inert bodies, although the largest asteroids may be able to sustain seasonal "atmo- spheres" by means of sublimating polar caps, as has been 0 suggested for asteroid 1 Ceres (A'Hearn and Feldman 1992). Ο The main belt is roughly divided into three compositional zones (see Fig. 1 of Bell et al. 1989). These compositional zones correspond to clusters of different taxonomic types: at the inner belt (heliocentric distance —2-2.3 AU) we find mostly "S"-type asteroids, then "C"-types further out (i?—2.3-2.8 AU). At the edge of the belt and beyond (ft >2.7 AU), the "P"- and "D"-types dominate. The S-types have moderate to high and a composition of metal, oliv- 0.2 0.6 ine, and pyroxene. The C-types have low albedos and show signs of aqueous alterations. P- and D-types are dark and seem to contain no hydrated minerals, as inferred from their Fig. 3—The distinction between cornets and asteroids in semimajor axis- lack of the 3 μτη water absorption feature (e.g., Jones et al. eccentricity space. The open circles are asteroids, while the solid circles are 1990). The lack of hydrated minerals may indicate that the P- comets. The sizes of the circles and dots are proportional to the sizes of the and D-types have never been sufficiently heated for interior objects. Figure adapted from Kresak (1979) and Weissman et al. (1989), ice to melt. The P- and D-types are thus considered "primi- courtesy of the University of Arizona Press. tive" asteroids. There are also minor asteroid classes, the number and definition of which depend on the particular most of the asteroids were fragmented upon impact and some classification scheme (e.g., Tholen 1984; Barucci et al. 1987; of the original belt mass was lost by nongravitational forces Tedesco et al. 1989). (e.g., inward spiraling due to gas drag, entrainment during outflow of nebular gas). Besides collisional fragmentation, mass may have also been removed by residual planetesimals 2.4 Origin of Asteroids scattered from the Jupiter region (Safronov 1969; Weiden- schilling 1975; Kaula and Bigeleisen 1975). Thus the net The original asteroids are believed to have formed from effect of Jupiter is to retard the aggregation of planetesimals the accretion of smaller bodies. Given the orderly procession in the main belt by increasing the relative velocities to the of the planets, one cannot help but wonder why an asteroid escape speed. This scenario generally requires the prior for- belt formed between Mars and Jupiter instead of a planet. mation of Jupiter (within —1 Myr), and is widely regarded as Furthermore, why is the belt so depleted in mass, compared one of the strongest constraints on the origin of Jupiter (e.g., with its two adjacent planets? Two ideas have been proposed Wetherill 1989). to answer the question: (1) there was never sufficient material there to start with; 3. COMETS (2) there was sufficient material, but much of it was re- Comets were first postulated by Fred Whipple (1950) to moved from the belt. be conglomerates of ice and dust. This basic model has been Since there is no a priori reason to assume that the solar proven correct many times over by both ground-based and nebula was deficient in material in the region of the belt, the spacecraft observations. Comets are of particular relevance present consensus is that much of the original mass of the to both planetary and stellar astronomers because they are belt was removed by collisional fragmentation and/or gravi- thought to be among the first generation planetesimals tational perturbations. The relative velocities among main formed in the solar nebula. It has also been suggested that belt asteroids are higher than escape velocities for most of comet formation stems from the condensation of icy inter- the original asteroid swarm (Wetherill 1989). As a result, stellar molecules on solid grains. In this sense, cometary

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 428 LUU studies are a multidisciplinary area which combine topics Table 1 relevant to the interstellar medium, star forming regions, and Trans-Neptunian Objects our own . By convention, comets are arbitrarily separated into two Object Semimajor axis [AU] Discovery date Red References dynamical groups: the short-period (SP) comets with orbital 1992 QB1 43.8 1992 Aug 30 22.8 Jewitt and Luu (1993a) periods Ρ <200 yr, and the long-period (LP) with Ρ ^200 yr. 1993 FW 42.4 a 1993 Mar 28 22.8 Luu and Jewitt (1993a) Whereas most asteroids are protected from close encounters 1993 RO 32.3 a 1993 Sep 14 23.2 Jewitt and Luu (1993b) with Jupiter, SP comets travel on eccentric, unstable orbits 1993 RP 35.4 a 1993 Sep 15 24.5 Luu and Jewitt (1993b) 1993 SB 33.2 a 1993 Sep 16 22.7 Williams et al. (1993) and have aphelia near Jupiter's orbit, suggesting that Jupiter a strongly influences their dynamical evolution (Carusi et al, 1993 SC 34.5 1993 Sep 17 21.7 Williams et al. (1993) 1985; Belyaev et al. 1986). The dynamical distinction be- assuming a circular orbit tween the comets and asteroids is illustrated by Fig. 3, which plots their semimajor axes a versus their eccentricities e. The figure shows that most of the known comets and asteroids of the solar system, the comet orbits in the will occupy two very distinct regions, separated by a dashed line have been completely randomized by passing stars and the from upper left to lower right. The line is defined by the cloud is therefore isotropic. Tisserand invariant Τ (Krésak 1979) More recent studies place the semimajor axis of the Oort 4 dj a . cloud at ~4X10 AU (Marsden et al. 1978), slightly smaller Τ= 1-2 Λ/— {\—e) cos /, (2) than the radius originally calculated by Oort. This suggests a V aj the presence of other perturbers to the comet cloud such as where «y is the Jovian semimajor axis, and i is the inclina- tidal effects from the galactic field (Heisler and Tremaine tion. Τ defines the path followed by most cometary orbits 1985), and encounters with giant interstellar molecular and was initially used to identify returning SP comets. The clouds (Hut and Tremaine 1985). The existence of external dashed line refers to Τ=3. Most comets are characterized by perturbers requires a larger comet population in order to sup- Γ<3 while the asteroids generally have Γ>3; the Tisserand ply the observed comet flux, placing the current estimate of invariant thus serves as a rough guideline to distinguish com- the Oort cloud population at ~1012 comets. If comet Halley ets and asteroids by their orbits. However, a few objects is representative of the 1012 comets, then the cloud must clearly defy the Tisserand boundary in Fig. 3: for example, contain more than 100 MEarth, or about 1/3 of the mass of asteroid 944 Hidalgo (α =5.80 AU, ¢=0.66, Γ=2.46) is Jupiter. More likely, comets occupy a range of sizes. Esti- clearly in the cometary region, while ((2=2.21 mates for the cloud mass range from about 14 to 1000 AU, ^=0.85, Γ=3.02) is on an Earth-crossing orbit. The M Earth. with the upper limit being more than twice the total implication here is that objects such as Hidalgo may be in- mass of the planetary system. Unfortunately, it is currently active comets, although they have exhibited no cometary ac- not possible to observe any solar system object at 104 AU. If tivity. It is now also known that comets can develop asteroi- comet Halley were removed to the Oort cloud, for instance, dal appearances, and thus, like the Tisserand invariant, a it would appear at roughly magnitude 61. Thus Oorfs model classification scheme based solely on appearances has lim- describes a cloud which is completely inaccessible and un- ited validity. observable with present technology.

3.1.2 The 3.1 Origin of Comets Until the last two decades or so, it was generally assumed From their different dynamical characteristics, the SP and that, like the LP comets, the SP comets also originated in the LP comets are believed to have different origins. Oort cloud and were brought to the planetary region through capture by the giant planets. Recent years have seen growing 3.1.1 The Oort Cloud evidence that this explanation is not viable. For example, the efficiency of capture by the giant planets is too low to pro- In 1950, Jan Oort presented a model where the LP comets duce the observed number of SP comets (e.g.. Joss 1973; are derived from a cloud of comets located at ~105 AU (or Fernandez and Ip 1983). Furthermore, recent numerical mod- about 0.5 pc) and containing -1011 comets (the "Oort eling revealed that the inclination distribution of the orbits is cloud," Oort 1950). The —1000 comets observed in the plan- conserved during capture (Duncan et al. 1988). The SP com- etary region represent a very small fraction of the total num- ets have low-inclination orbits, implying that they must ber. Oort's cloud extends almost halfway out to the nearest originate in a flattened source. The spherical Oort cloud thus star, so that comets in the cloud are affected by perturbations cannot be the main source of the observed SP comets. In- from random passing stars. In fact, Oort proposed that re- stead, Duncan et al. suggested that the SP comets are cap- peated stellar encounters are responsible for the comet peri- tured from a "comet belt." This belt, the so-called "Kuiper helia slowly diffusing into the planetary region. The per- belt," would be a surviving remnant of the outermost part of turbed comets random-walk inward toward the Sun until the solar nebula (Kuiper 1951; Whipple 1964; Cameron they are ejected, captured into a short-period orbit, collide 1972). The Kuiper belt is postulated to lie beyond , with a planet or the Sun, or simply disintegrate. Over the age with a semimajor axis in the range 50-500 AU. Duncan et al.

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System COMETS DISGUISED AS ASTEROIDS 429

Table 2 Observed Cometary Nuclei Period Radiusb Axis Ratio F c [hrs] [km] act[%] Arend-Rigaux 13.56 1 0.032 5Z 1.9:1 0.1 - 1 ¿ Neujmin 1 12.67 3 0.034 104 1.6:1 0.1-14 Encke 15.08 5 0.04 5 3.5 5 1.8:1 0.2 6 Tempel 2 8.95 7 0.028 5 8 1.9:1 0.1 - 1 7 "Rock" Halley > IS3 0.04 9·10 510 2 10 10 10 M Tune 2060 Chiron 5.92 11 > 0.04 12 < 150 12 1.1 : 1 Schwassman- Wachmann 2 14 5.58 < 3.1 1.6:1 "Rock' a Rotation period b Circular equivalent radius 0 Fractional active area (see §3.2)

1. Jewitt andMeech (1985); 2. Millis, A'Heam, and Campins (1988); 3. Jewitt and Meech (1988); 4. Campins, A'Hearn, and McFadden (1987); 5. Luu and Jewitt (1990a); 6. Jewitt and Meech (1987); 7. Jewitt and Luu (1989); 8. A'Hearn et al. (1989); 9. Jewitt and Danielson (1984); 10. Keller (1990); 11. Luu and Jewitt (1990b); 12. Jewitt and Luu (1992); Time 13. Bus et al. (1989); 14. Luu and Jewitt (1992b). Table adapted from Table 1 of Jewitt (b) (1992). Fig. A—(a) Irradiation mantle. Bombardment by cosmic rays slowly con- verts surface volatiles into refractory organic material, (b) Rubble mantle. estimated the number of comets in the belt to be 108-1010, Sublimation of volatiles eject small grains from the surface, leaving behind large particles too heavy to escape from the nucleus. Figure adapted from yielding a minimum belt mass Mbelt>0.02 MEarth. Jewitt (1992). Unlike the Oort cloud, the Kuiper belt at —40 AU is within reach of our ground-based telescopes. Furthermore, the Duncan et al. model makes specific predictions which are observing task is exacerbated by the often small sizes of the testable by observations. The last five years saw several cam- nuclei and their low albedos (see Table 2). The typical stud- paigns in search of the belt by Luu and Jewitt (1988), Kowal ied nucleus has apparent brightness in the range 19-21 mag. (1989), and Levison and Duncan (1990), among others. Posi- So far data are available for only ~6 nuclei; the small tive results finally came in 1992, when Jewitt and Luu sample size bears testimony to the difficulties involved in (1993a) discovered the first Kuiper belt candidate, 1992 identifying cometary nuclei suitable for study. QBj. Other discoveries then came quickly: the second What we currently know about cometary nuclei is sum- Kuiper Belt candidate, 1993 FW, was found 6 months later marized in Table 2. The measured nuclei are very dark, ~5 (Luu and Jewitt 1993a), followed by four more objects a year km in radius, highly aspherical, and perhaps most relevant to later. At the time of writing (1994 January), a total of six this review, have a very low fractional active area. We define trans-Neptunian objects have been found; they are listed in the fractional active area, Fact, as Table 1. The object 1993 FW was found 180 degrees away ^act A act/A, (3) from QBi, supporting a belt-like distribution. Four of the six objects lie —60 degrees from Neptune, suggesting the possi- where Aact is the active (sublimating) area, and A is the total bility that they are in fact Neptunian Trojans (Marsden surface area. Physically, Fact is the fraction of the surface 1993a). As yet, very little is known about these objects, in- area that is responsible for the observed mass loss rate. For cluding their true orbits and physical natures, and it is not most of the listed nuclei, Fact is less than 1%. Even for a clear how they fit into the current comet-asteroid picture. comet as bright as Halley, Fact is only —10%. Whatever their true nature may be, these objects constitute solid evidence that the outer solar system is not the empty 3.3 How Comets Become Asteroidal place it was believed to be, and the Kuiper belt is most likely The idea that comets might evolve into asteroids was a reality, not just a convenient theory. probably first suggested by Opik (1963). Comets can develop an asteroidal appearance when sublimation is inhibited, ei- 3.2 Physical Properties of Cometary Nuclei ther by low temperatures, or by mantle growth. Models of cometary nuclei predict two types of mantles: (a) "irradia- Observations of comet nuclei only became available in tion mantles," which are developed while a comet lies dor- the last decade or so. Our closest look at a mant in the outer reaches of the solar system, and (b) "rubble was provided by spacecraft encounters with comet Halley in mantles," which are direct consequences of sublimation. 1986. Ground-based observations of nuclei generally must wait until the comets are sufficiently far from the Sun {R >2-3 AU) and thus sufficiently cold that little cometary ac- 3.3.1 Irradiation Mantles tivity remains. These comets are then point sources and in- The main external effect on cometary nuclei while dor- distinguishable from asteroids in appearance. However, the mant in the Oort cloud or the Kuiper belt is irradiation by

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 430 LUU

10u

1(Γ

ΙΟ4 CO ^

co2 x 1(Γ

1(Γ f\ I I I I I I I I I 5 10 15 R [AU]

Fig. 6—Radius of the largest particle that can be lifted from a 5 km radius nucleus ( 0.04, 6 hr) by H2O, CO, and CO2 as a Fig. 5—Image of the nucleus of comet Halley, taken by the Halley Multi- function of heliocentric distance. color Camera on board the European Space Agency's Giotto spacecraft dur- ing its encounter with the comet in 1986. Photo courtesy of H. U. Keller, Max-Planck-Institut für Aeronomie. understood by examining the basic physical processes at the nucleus surface, as shown in Fig. 4(b). Upon heating by sun- light, surface volatiles sublimate, entraining dust particles in galactic cosmic rays. The irradiation level over the age of the the gas flow. The largest dust particles will be too heavy to solar system is sufficient to introduce chemical changes reach escape speed and will accumulate on the surface to which can penetrate a significant depth into the nucleus. The form a coherent dust layer—this is presumably the dust main changes are the loss of water due to chemical alter- mantle seen on comet Halley and other comets. We can make ation, and polymerization, the conversion of volatile carbon- a simple approximation to this complicated scenario by con- bearing molecules into refractory residue (e.g., Moore et al. sidering the equation of motion for a dust grain on the sur- 1983; Strazzulla and Johnson 1991), as is shown schemati- face of the nucleus cally in Fig. 4(a). It is possible that the building blocks of comets have al-

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System COMETS DISGUISED AS ASTEROIDS 431

Table 3 resonances (Wisdom 1987) and at secular resonances (Scholl Some NEAs with Cometary Characteristics et al. 1989). Similarly, comets may evolve into Earth- crossing orbits either by gravitational capture by a terrestrial Cometary characteristic [AU] planet, or by nongravitational forces arising from cometary activity. We know of at least one comet, comet Encke, pres- 2101 Adonis 1.9 0.76 association 1,2-, 3,4,5 ently moving in an Earth-crossing asteroidal orbit (Krésak 2201Oljato 2.2 0.71 Meteor shower association 2,3,4,6,7 1977), and the heavily mantled surfaces of known cometary 2212Hephaistos 2.2 0.83 Meteor shower association 2,3,4,8 nuclei strongly suggest an end fate as asteroid-like bodies. 3200 Phaethon 1.3 0.89 Parent of Geminid meteor stream 6, 9 Furthermore, several NEAs have been found to have 3552 1983 SA 4.2 0.71 Chaotic orbit 4,6 cometary characteristics, as can be seen in Table 3. Some are a Scmimajor axis on comet-like orbits, while others are associated with meteor b streams, long thought to be debris of comets. Out of —200 0 Eccentricily Inclination known NEAs, —10-15 are identified with cometary charac- References for Table 3 teristics. Wetherill (1988) estimated that as much as 40% of 1. Krësak (1977); 2. Drummond (1982); 3. Babadzhanov and Obrubov (1983); 4. the NEAs has a cometary origin, although this number is Olssen-Steel (1988); 5. Marsden (1970); 6. Veeder er a/. (1989); 7. Harris and Young (1983); 8. Krésak (1979); 9. Whipple (1983). Table adapted from Table ΠΙ of Weissman very uncertain. If extinct comets can be shown to exist e/a/. (1989). among the NEAs, we will have resolved two important ques- tions in solar system astronomy, namely, the origin of the NEAs, and the end fate of dead comets. a max calculated from the two representations of gas drag is a function of the grain density and can be large if the density is 4.2 Trojan Asteroids low (see Fig. 5 of Crifo 1991). Rubble mantle development is supported by both theoreti- The Jovian Trojan asteroids also figure prominently in the cal models (e.g., Fanale and Salvail 1984; Rickman et al. study of the comet-asteroid connection. Trojans are domi- 1990) and by laboratory simulations (Grün et al. 1991). nated by P- and D-type asteroids and share surprisingly Mantles as thick as a few centimeters were produced as a many properties in common with cometary nuclei. Both result of sublimation in laboratory experiments, and greater groups have low albedos of a few percent, reddish colors thickness is possible. As cometary grains are known to con- (e.g., Cruikshank 1977), and elongated shapes (Jewitt and tain a significant amount of organics (e.g., Kissel et al. 1986; Meech 1988; Hartmann et al. 1988). The elongated shapes Kissel and Krueger 1987), the rubble mantle is also believed may have resulted from the absence of disruptive collisions, to be organic rich. An organic-rich composition is consistent or from anisotropic mass loss (Hartmann and Tholen 1990). with the low albedos of the known (old) comet nuclei. Be- A spectroscopic survey by Jewitt and Luu (1990) found no yond this, little is known about the surface composition of significant difference between the color distributions of Tro- nuclei. The available broadband colors show a wide range of jan asteroids and known cometary nuclei. The cause of the colors from neutral to red (Luu 1993). No diagnostic spectral striking resemblance between these two groups is presently feature is found in the few existing spectra. not known. Their shared properties may indicate a similar An organic-rich composition may thus be characteristic of origin, or the presence of comets captured into the both the irradiation and the rubble mantle. A more detailed Lagrangian points (Rabe 1972). assessment of the differences/similarities between the rubble mantle and the irradiation mantle, however, must await more 4.3 Trans-Neptunian Objects laboratory experiments and observations. The newly discovered trans-Neptunian objects have so far shown no signs of mass loss, and are not likely to do so 4. COMETARY CANDIDATES given their large heliocentric distances. They therefore do not 4.1 Near-Earth Asteroids fit the canonical definition of a comet but nevertheless are the best candidates for the progenitors of the short-period The ubiquitous presence of mantles on SP comets begs comets. The scant information available on these objects is the question: if comets become heavily mantled, is it pos- given in Table 4, where it is seen that QBj may be almost as sible for the surface to become 100% covered so that comets red as Pholus, while FW possesses a more moderate red essentially turn into asteroids? And if this can happen, where color. From the limited data base, it appears that the irradia- are the extinct comets? The answer to these questions may tion mantle, like the rubble mantle, may also assume a wide lie hidden among the NEAs. Since the orbits of these aster- range of colors, rendering it difficult to identify a mantle by oids cross the orbits of the terrestrial planets, collisions with surface color alone. the planets reduce their mean dynamical lifetimes to 7 8 ~10 -10 yr, short compared to the age of the solar system. 4.4 Centaurs A source is thus needed to maintain the observed flux of NEAs. Perhaps as mysterious as the trans-Neptunian objects are The most plausible source regions are the main asteroid the "Centaurs," objects on elliptical orbits which cross the belt and cometary nuclei. Main belt asteroids can be trans- orbits of one or more gas giants. Since planet-crossing orbits ported into the near-Earth region by chaotic motion at orbital are short lived, we believe that these objects may be in tran-

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 432 LUU

Table 4 Properties of Trans-Neptunian Objects and Centaurs 1992 QBl 1993 FW Pholus Chiron Diameter [km] 250 ^ 2 250 ^ 3 189 ±26 4 < 300 5 V-R 0.6 ±0.1 0.4 ±0.1 0.76 0.34 ± 0.037 R -1 1.0 ± 0.2 - 0.72 ± 0.06 6 0.28 ± 0.03 7 S' [%/103 A] 8 -- -- 46.1 ± 0.3 9 -3.9 ± 0.4 9 Cometary activity? no no no yes Semimajor axis [AU] 44.4 10 43.9 11 20.5 13.7 Eccentricity 0.11 10 0.04 11 0.58 0.38 N.B.; solar color: V - R = 0.32, R - / = 0.4 1 assuming an albedo of 0.04 2 Jewitt and Luu (1993a) 3 Luu and Jewitt (1993a) 4 minimum diameter (Davies et al. 1993b) 5 3σ upper limit (Jewitt and Luu 1992) 6 Mueller eí al (1992) 7 Hartmann et al. (1990) Fig. 7—Surface-brightness profile of near-Earth asteroid 1917 compared 8 Reflectivity gradient with profile of a field star. The two profiles are identical within the noise, 9 Luu (1993) implying that no coma was evident. Figure taken from Luu and Jewitt 10 Marsden (1993b) (1992a). 11 Marsden (1993c) asteroids; Hartmann et al. 1988; Jewitt and Luu 1990); (3) sition from the Kuiper belt to the planetary region, i.e., tran- chaotic orbital motion (e.g., NBAs, trans-Jovian asteroids; sition comets. The known Centaurs include 2060 Chiron, Krésak 1979; Hahn and Rickman 1985); (4) meteor stream 5145 Pholus, and 1993 HA2. Discovered in 1977, Chiron association (NBAs; Drummond 1982). However, according was initially classified as an asteroid but its identity as a to current standards, the only unambiguous evidence for a comet was finally confirmed when cometary behavior was cometary nature is mass loss, and most searches for hidden discovered (Tholen et al. 1988; Meech and Belton 1989). comets aim at detecting mass loss in their target objects. Chiron thus serves as the perfect example of a disguised comet whose true identity was eventually revealed. 5.1 Spectroscopy Versus Direct Imaging The observational history of Pholus is very similar to that of Chiron, with the exception that it still has shown no sign The searches can be spectroscopic or photometric in na- of cometary activity and thus retains the asteroid classifica- ture. Spectroscopic searches look for gaseous emissions (De- tion. However, its extremely red color {V—R=Q.1\ Mueller gewij 1980; Cochran et al. 1986; McFadden et al. 1984), et al. 1992; Fink et al. 1992; Binzel 1992), stands in sharp while photometric searches aim to detect a dust coma. These contrast with the neutral-blue color of Chiron (Luu and Jew- searches are usually focused on the NBAs, as their proximity itt 1990b; Luu 1993). A consistent but nonunique explanation to the Sun maximizes the chance of detecting signs of out- for the color of 5145 Pholus is a surface rich in , gassing. The major disadvantage of the spectroscopic method organic residues formed by irradiation of CH4 and other is that spectra of many comets are dominated by continua, carbon-bearing molecules (Davies and Sykes 1992; Wilson with no signs of emission lines. The absence of emission et al. 1994). Near-IR spectra of Pholus show features that lines in an object's spectra thus is not conclusive proof may indicate the presence of organics (Davies et al. 1993a; against a cometary nature. For that reason, direct imaging Luu et al. 1994). The absence of cometary activity on Pholus may be a more promising method in detecting mass loss and its unusual color suggest the preservation of a primordial (e.g., the appearance of a coma around Chiron). To date, irradiation mantle (Luu 1993). In contrast, the neutral color gaseous emission has been reported in one asteroid: 1 Ceres of Chiron may refer to a rubble mantle created by sublima- (A'Heam and Feldman 1992). A'Heam and Feldman re- tion. We can test the irradiation mantle hypothesis if Pholus ported OH emission off the northern limb of Ceres shortly changes color at the onset of sublimation. after the asteroid passed perihelion (#=2.75 AU), and attrib- A comparison of 1992 QBj, 1993 FW, Pholus, and Chiron uted to it to a dissipating polar cap. is shown in Table 4, and may represent the properties of comets in various stages of evolution. 5.2 High-Resolution Surface-Brightness Profiles One direct imaging method recently used by Luu and Je- 5. SEARCHING FOR COMETS AMONG ASTEROIDS witt (1992a) compared high-resolution surface-brightness The sometimes asteroidal appearance of comets has in- profiles of NBAs with star profiles. An extended NBA profile spired several searches for cometary objects hidden in the (i.e., broader than that of the star) signifies coma. This asteroid population. A variety of circumstantial evidences method requires good seeing to be effective. However, when have been presented to associate some asteroids with a the seeing is good, it has the benefits of being simple, effi- cometary nature, including (1) nonasteroidal photometric be- cient to carry out, very sensitive, and yields quantitative pa- havior (e.g., Chiron before the appearance of coma; Tholen rameters which can be compared with cometary values. An et al. 1988); (2) low albedo, elongated shape (e.g., the Trojan example of the comparison is shown in Fig. 7, where the

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System COMETS DISGUISED AS ASTEROIDS 433

Table 5 In Eqs. (5) and (6), ^ is a proportionality constant, ρ ΝΕΑ Mass Loss Rates and Fractional Active Areas 3 [kg m~ ] is the grain density, rNEA [m] is the radius of the Λ ΝΕΑ, R [AU] is the heliocentric distance, J[arcsec] is the ^ ΝΕΑ M 1 [AU] [AU] [km] [kg sec ] angular radius of the diagram, Δ [AU] is the geocentric distance, μ is the gas-to-dust ratio (assumed to be 1917 1.29 0.44 1.5 <0.07 < 0.6 χ ΙΟ"4 1), and Ζ [kg m-2 s-1] is the mass ñux of water (assumed to 2059 1.27 0.95 2.0 <0.06 < 0.3 χ ΙΟ"4 4 be the dominant volatile). Derived upper limits to M and Fact 2122 2.33 1.46 6.5 <0.30 < 3.0 χ ΙΟ"4 2744 1.55 0.65 1.5 <0.09 < 1.5 χ ΙΟ"5 for the observed NEAs are listed in Table 5. The sensitivity 3200 1.61 1.48 1.5 <0.02 < 3.5 χ ΙΟ"4 of the method is demonstrated by the fact that the M upper 3362 1.24 0.53 0.5 <0.07 < 4.8 χ ΙΟ"5 3753 1.48 0.88 2.0 <0.06 < 4.6 χ ΙΟ"4 limits are at least as good as or better than previous limits 1987 QA 1.70 0.77 1.5 <0.04 < 0.9 χ ΙΟ"5 derived spectroscopically. 1989 JA 1.75 1.07 1.0 <0.01 ^ 6.7 χ ΙΟ"4 1989 OB 1.29 0.29 1.0 <0.05 < 1.0 χ ΙΟ"4 Figure 8 compares the asteroidal fractional active areas 1989 PB 1.07 0.07 0.5 < 0.08 < 3.5 χ ΙΟ" with the cometary values. The most interesting feature of the figure is that the upper limits for the NEAs are clustered near Heliocentric distance b Geocentric distance the cometary values, implying that these NEAs could have c Circular equivalent radius fractional areas comparable to the fractional areas on low- Assuming a = 0.5 χ ΙΟ'6 m. ρ = 1000 kg rr , and d= \ arcsec (sec Eq. (5), §3.2) c Fractional active area (see §3.2) activity comets. The average ΝΕΑ in Table 5 is ~1 km in radius, 25 times smaller in area than an average comet nucleus. The figure thus raises the question on how the size profile of an ΝΕΑ is plotted with a star profile. In this par- of an object influences its classification: could it be that ticular case, there is no evidence for coma. larger objects are classified as comets because they give rise The profile-fitting survey found no coma among the 11 to detectable mass loss rates, while smaller objects (with observed NE As, but upper limits on the presence of coma comparable fractional active areas) are classified as asteroids were obtained by fitting models to the profiles. The relevant because their mass loss rates are below the current detection parameter was 77, defined as the ratio of coma cross section limit? Statistical properties of comet nuclei derived from a to nucleus cross section. For most of the observed NEAs, large sample may help answer the question. 77^0.01, i.e., the allowable coma cross section was less than 1% of the nucleus cross section. Upper limits to the mass loss rates and the fractional active area Fact can also be cal- 6. CONCLUSIONS culated from 77 if one assumes an optically thin coma, a mean particle size and particle ejection speed (1) The physical distinction between comets and asteroids is clear: asteroids have no free near-surface ice, while free α ice is a large fraction of the composition of comets. How- πΡ VrNEA M = K 2 (5) ever, the observational distinction between comets and aster- R dA oids is less distinct: comets are now known to develop aste- roidal appearance when sublimation is inhibited. M (2) The absence of coma no longer guarantees that an (6) Λττ^μΖ object is an asteroid. We may be forced to revise the "bound- ary" between comets and asteroids. Current detection limits and object sizes may influence how these objects are classi- fied. I I ι ι ι ι ι ι ι I ^ I I I I I I I I I I I I I I I I I Halley Χ (3) Searches for comets disguised as asteroids have not - • «- - Comet Halley been able to rule out the existence of extinct comets among o Other Comets asteroids. Observations show that some near-Earth asteroids o Encke • NEAs SW1 - could have fractional active areas comparable to those on o IAA low-activity comets. fe (4) The search for comets among asteroids is a difficult bû o Tempel 2 one, as we still do not possess a thorough characterization of 2 # * Neujmin 1 the physical properties of nuclei. Such characterization is \I/Y I essential if we are to understand the connection between - w Arend-Rigaux comets and asteroids. It may reveal other more effective cri- teria to distinguish comets from asteroids, or it may reveal Ml I I I I I I I I I I I I I I I I links hitherto unsuspected. 2 3 4 R [AU] The author thanks Space Telescope Science Institute for the Hubble Fellowship. Part of this work was supported by NASA through Grant No. HF-1035.02-92A awarded by Fig. 8—Fractional active areas of near-Earth asteroids compared with those Space Telescope Science Institute which is operated by the of low-activity comets. Diamonds denote comets, circles denote near-Earth asteroids. Arrows pointing downward indicate upper limits. Figure taken Association of Universities for Research in Astronomy, Inc., from Luu and Jewitt (1992a). for NASA under Contract No. NAS5-26555.

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 434 LUU

REFERENCES Hartmann, W. K., Tholen, D. J., Goguen, J., Binzel, R. P., and Cruikshank, D. P. 1988, Icarus, 73, 487 A'Heam, M. F., and Feldman, P. D. 1992, Icarus, 98, 54 Hartmann, W. K., Tholen, D. J., Meech, K., and Cruikshank, D. P. A'Heam, M. F., Campins, H., Schleicher, D. G., and Millis, R. L. 1990, Icarus, 83, 1 1989, ApJ, 347, 1155 Heisler, J., and Tremaine, S. 1985, Icarus 65, 13 Babadzhanov, P. B., and Obrubov, Y. V. 1983, in Asteroids, Comets, Hirayama, K. 1918, AJ, 31, 185 Meteors, ed. C.-I. Lagerkvist and H. Rickman (Uppsala, Univer- Hirayama, K. 1919, Proc. Phys.-Math. Soc. Jpn., 3rd Ser., No. 1, 52 sity of Uppsala), pp. 411-417 Hut, P., and Tremaine, S. 1985, AJ, 90, 1548 Barucci, Μ. Α., Capria, M. T., Coradini, Α., and Fulchignoni, M. Jewitt, D. C. 1992, in Proceedings of the 30th Liege International 1987, Icarus, 72, 304 Astrophysical Colloquim, ed. A. Brahic, J.-C. Gerard, and J. Bell, J., Davis, D. R., Hartmann, W. K., and Gaffey, M. J. 1989, in Surdej (Liege, University Liege Press), pp. 85-112 Asteroids II, ed. R. R Binzel, T. Gehrels, and M. S. Matthews Jewitt, D. C., and Danielson, G. E. 1984, Icarus, 60, 435 (Tucson, University of Arizona Press), pp. 921-945 Jewitt, D. C, and Luu, J. X. 1989, AJ, 97, 1766 Belyaev, Ν. Α., Kresak, L. Pittich, Ε. M., and Pushkarev, A. N. Jewitt, D. C., and Luu, J. X. 1990, AJ, 100, 933 1986, Catalog of Short-Period Comets (Bratislava, Astron. Inst. Jewitt, D. C, and Luu, J. X. 1992, AJ, 104, 398 Slovak Acad. Sei) Jewitt, D. C, and Luu, J. X. 1993a, Nature 362, 730 Belton, M. J. S., Veverka, J., Thomas, P., Helfenstein, P., Simonelli, Jewitt, D., and Luu, J. 1993b, IAU Circ., 5865 D., Chapman, C., Davies, M. E., Greeley, R., Greenberg, R., Jewitt, D. C, and Meech, K. 1985, Icarus, 64, 329 Head, J., Murchie, S., Klaasen, K., Johnson, T. V., McEwen, Α., Jewitt, D. C, and Meech, K. 1987, AJ, 93, 1542 Morrison, D., Neukeum, G., Fanale, F., Anger, C, Carr, M., and Jewitt, D. C, and Meech, K. 1988, ApJ, 328, 974 Pilcher, C. 1992, Science 257, 1647 Jones, T. D., Lebofsky, L. Α., Lewis, J. S., and Marley, M. S. 1990, Binzel, R. R 1989, in Asteroids II, ed. R. P. Binzel, T. Gehrels, and Icams, 88, 172 M. S. Matthews (Tucson, University of Arizona Press), pp. 3-18 Joss, P. C. 1973, Astron. Astrophys., 25, 271 Binzel, R. P. 1992, Icarus, 99, 238 Kaula, W. M., and Bigeleisen, P. E. 1975, Icams 25, 18 Bus, S. J., Bowell, E., Harris, A. W., and Hewitt, Α. V. 1989, Icarus, Keller, H. U. 1990, in Physics and Chemistry of Comets, ed. W. F. 77, 223 Huebner (Berlin, Springer), pp. 13-68 Cameron, A. G. W. 1972, Icarus, 1,13 Kissel, J., and Krueger, F. R. 1987, Nature, 326, 755 Campins, H. C, A'Heam, M. F., and McFadden, L. 1987, ApJ, 316, Kissel, J. et al. 1986, Nature, 321, 280 847 Kowal, C. 1989, Icams, 77, 118 Carusi, Α., Kresak, L, Perozzi, E., and Valsecchi, G. B. 1985, Long- Krankowsky, D. 1991, in Comets in the Post-Halley Era, ed. R. L. Term Evolution of Short-Period Comets (Bristol, Adam Hilger) Newbum, Jr., M. Neugebauer, and J. Rahe (Dordrecht, Kluwer Cochran, W. D., Cochran, A. L., and Barker, E. S. 1986, in Aster- Academic), pp. 855-877 oids, Comets, Meteors II, ed. C.-I. Lagerkvist, B. A. Lindblad, Krésak, L. 1977, in Comets, Asteroids, Meteorites: Interrelations, H. Lundstedt, and H. Rickman (Uppsala, Uppsala University Evolution, and Origins, ed. A. H. Delsemme (Toledo, University Press), pp. 181-185 of Toledo Press), pp. 313-321 Crifo, J. F. 1991, in Comets in the Post-Halley Era, ed. R. L. New- Kresak, L. 1979, in Asteroids, ed. T. Gehrels (Tucson, University of bum, Jr., M. Neugebauer, and J. Rahe (Dordrecht, Kluwer Aca- Arizona Press), pp. 289-309 demic), pp. 937-989 Kuiper, G. 1951, in Astrophysics, ed. J. A. Hynek (New York, Cruikshank, D. 1977, Icarus, 30, 224 McGraw-Hill), pp. 357-427 Davies, J. K., and Sykes, M. V. 1992, IAU Cire., 5480 Levison, H., and Duncan, M. 1990, AJ, 102, 787 Davies, J. K., Sykes, M. V., and Cruikshank D. P. 1993a, Icarus, Luu, J. X. 1993, Icams, 104, 138 102, 166 Luu, J. X., and Jewitt, D. C. 1988, AJ, 95, 1256 Davies, J,, Spencer, J., Sykes, M., Tholen, D., and Green, S. 1993b, Luu, J. X., and Jewitt, D. C. 1990a, Icams, 86, 69 IAU Circ., 5698 Luu, J. X., and Jewitt, D. C. 1990b, AJ, 100, 913 Degewij, J. 1980, ApJ, 85, 1403 Luu, J. X., and Jewitt, D. C. 1992a, Icams, 97, 276 Drummond, J. D. 1982, Icarus, 49, 143 Luu, J. X., and Jewitt, D. C. 1992b, AJ, 104, 2243 Duncan, M., Quinn, T, and Tremaine, S. 1988, ApJ, 328, L69 Luu, J. X., and Jewitt, D. C. 1993a, IAU Circ., 5730 Fanale, F., and Salvail, J. R. 1984, Icarus, 60, 476 Luu, J. X., and Jewitt, D. C. 1993b, IAU Circ., 5867 Fernandez, J. Α., and Ip, W.-H. 1983, in Asteroids, Comets, Mete- Luu, J. X., Jewitt, D. C, and Cloutis, E. 1994, Near-infrared spec- ors, ecf. C-I. Lagerkvist and H. Rickman (Uppsala, University of troscopy of primitive solar system objects, Icams, in press Uppsala), pp. 387-390 Marsden, B. G. 1970, AJ, 75, 206 Fink, U., Hoffman, M., Grundy, W., Hicks, M., and Sears, W. 1992, Marsden, B. G. 1993a, IAU Circ., 5865 Icarus, 97, 145 Marsden, B. G. 1993b, Circ. 22594 Gradie, J. C, Chapman, C. R., and Tedesco, E. F. 1989, in Asteroids Marsden, B. G. 1993c, IAU Circ., 5856 II, ed. R. P. Binzel, T. Gehrels, and M. S. Matthews (Tucson, Marsden, B. G., Sekanina, Z., and Everhart, E. 1978, AJ, 83, 64 University of Arizona Press), pp. 316-335 McFadden, L. Α., Gaffey, M. J., and McCord, Τ. B. 1984, Icams, Greenberg, M. 1982, in Comets, ed. L. L. Wilkening (Tucson, Uni- 59, 25 versity of Arizona Press), pp. 131-163 Meech, K., and Belton, M. 1989, IAU Circ., 4770 Grün, E. et al. 1991, in Comets in the Post-Halley Era, ed. R. L. Millis, R. L., A'Heam, M. F., and Campins, H. C. 1988, ApJ, 324, Newbum, Jr., M. Neugebauer, and J. Rahe (Dordrecht, Kluwer 1194 Academic), pp. 277-311 Moore, M. H., Donn, B., Khanna, R., and A'Heam, M. F. 1983, Hahn, G., and Rickman, H. 1985, Icams, 61, 417 Icarus, 54, 388 Harris, A. W., and Young, J. W. 1983, Icarus, 54, 59 Mueller, Β. Ε. Α., Tholen, D. J., Hartmann, W. K., and Cmikshank, Hartmann, W. K., and Tholen, D. J. 1990, Icarus, 86, 448 D. P. 1992, Icarus, 97, 150

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System COMETS DISGUISED AS ASTEROIDS 435

Olsson-Steel, D. 1. 1988, Icarus, 75, 64 Tholen, D. J. 1984, Ph.D. Thesis, University of Arizona Oort, J. H. 1950, Bull. Astron. Inst. Netherlands, 11, 91 Tholen, D. J., Hartmann, W. K., and Cruikshank, D. P. 1988, IAU Öpik, Ε. J. 1963, Adv. Astron. Astrophys., 2, 219 Circ. 4554 Rabe, Ε. 1972, in The Motion, Evolution of Orbits, and Origin of Veeder, G. J., Manner, M. S., Matson, D. L., Tedesco, E. F., Lebo- Comets, IAU Symposium No. 45, ed. G. A. Chebotarev, Ε. I. fsky, L. Α., and Tokunaga, A. 1989, AJ, 97, 1211 Kazimirchak-Polonskaya, and B. G. Marsden (New York, Weidenschilling, S. J. 1975, Icarus, 26, 361 Springer), pp. 55-60 Weissman, P. R., A'Hearn, M. F., McFadden, L. Α., and Rickman, Rickman, H., Fernandez, J. Α., and Gustafson, B. A. S. 1990, AJ, H. 1989, in Asteroids II, ed. R. P. Binzel, Τ Gehrels, and M. S. 237, 524 Matthews (Tucson, University of Arizona Press), pp. 880-920 Safronov, V. S. 1969, Evolution of the Protoplanetary Cloud and Wetherill, G. 1988, Icarus, 76, 1 Formation of the Earth and Planets (Nauka, Moscow), in Rus- Wetherill, G. 1989, in Asteroids II, ed. R. Binzel, T. Gehrels, and M. sian, translated NASA TTF-677, 1972 S. Matthews (Tucson, University of Arizona Press), pp. 661- Scholl, H., Froeschle, Ch., Kinoshita, H., Yoshikawa, M., and Wil- 680 liams, J. G. 1989, in Asteroids II, ed. R. P. Binzel, T. Gehrels, Whipple, F. L. 1950, ApJ, 111, 375 and M. S. Matthews (Tucson, University of Arizona Press), pp. Whipple, F. L. 1964, Proc. Natl. Acad. Sei. USA, 51,711 845-861 Whipple, F. L. 1983, IAU Circ., 3881 Strazzulla, G. 1985, Icarus, 61, 48 Williams, L, Fitzsimmons, Α., and O'Ceallaigh, D. 1993, IAU Strazzulla, G., and Johnson, R. E. 1991, in Comets in the Post- Circ., 5869 Halley Era, ed. R. L. Newburn, Jr., M. Neugebauer, and J. Rahe Wilson, P. D., Sagan, C., and Thompson, W. R. 1994, The organic (Dordrecht, Kluwer Academic), pp. 243-275 surface of 5145 Pholus: Constraints set by scattering theory, Tedesco, E. F., Williams, J. G., Matson, D. L., Veeder G. J., Gradie, Icarus (in press) J. C., and Lebofsky, L. A. 1989, AJ, 97, 580 Wisdom, J. 1987, Icarus, 72, 241

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System