Comet nuclei and Trojan asteroids: A new link and a possible mechanism for comet splittings

ICARUS 86, 448--454 (1990)

Comet Nuclei and Trojan Asteroids: A New Link and a Possible Mechanism for Comet Splittings WILLIAM K. HARTMANN Planetary Science Institute, 2421 East 6th Street, Tucson, Arizona 85719 AND

DAVID J. THOLEN Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, Hawaii 96822

Received October 25, 1989;revised February 1, 1990 New evidence indicates that comet nuclei and Trojan asteroids both have an incidence of high amplitude lightcnrves larger than that of main belt asteroids of similar sizes, apparently indicating relatively elongated shapes. Elongated shapes may have evolved among comet nuclei and Trojans due to volatile loss; this hypothesis may explain observed comet splitting. © 1990AcademicPress,Inc.

During recent years, a growing number of similarities have been found between outer solar system asteroids and comet nuclei. As predicted by Gradie and Veverka (1980), colorimetric similarities have been found between Trojan asteroids and comets in the visual to near-infrared spectral regions (Hartmann et al. 1982, 1987a, Campins et al. 1987). Comet colors range from neutral, like the dark, C-class asteroids of the outer belt, to redder, like Trojans. A reddening trend with solar distance may be due to progressive chemical or temperature effects among hydrocarbons (Vilas and Smith 1985). A second similarity is albedo. Contrary to early expectations (reviewed by Belton 1985 and A'Hearn 1988), comet nuclei typically have extremely low albedos. On the basis of colorimetric matches with Trojans, Cruikshank et al. (1985) proposed an albedo of 0.04 for P/Halley, instead of the pre-Giotto best estimate 0.26 (Belton 1985); this albedo was confirmed by Giotto (Mohlmann et al. 1986). Later groundbased measurements of other comet nuclei confirm values around 0.03 (e.g., Campins 448 0019-1035/90 $3.00 Copyright © 1990by Academic Press, Inc. All rights of reproduction in any form reserved.

et al. 1987, Millis et al. 1988). Clark (1980) explained these by showing that even highly icy surface regoliths with a small admixture of black carbonaceous compounds can have very low albedos. Similarities of Trojans and comets raise the possibility that Trojans (and perhaps Cclass outer belt asteroids) and comet nuclei come from related planetesimal pools, and encourage a search for other similarities or differences. Shoemaker et al. (1989) conclude that Trojans are planetesimals from the broad Jupiter zone, 5 to 9 AU, while most comet nuclei are planetesimals formed beyond the present location of the Trojans. The comets may simply have more ice and/or different dynamical histories. More recently a new, striking connection has come to light, involving shape. French (1987) and Hartmann et al. (1987b, 1988) concluded that Trojan (and possibly Hilda) asteroids have an incidence of high-amplitude lightcurves greater than that of belt asteroids of the same size. Among the maximum amplitudes at random epochs, the average among Trojans is about 0.33 to 0.4 mag, while among belt asteroids of similar

COMET NUCLEI AND TROJAN ASTEROIDS size it is around 0.2 mag. Recently we updated amplitude data for Trojans and Hildas observed by us, and including several objects observed by French, by Zappal;i et al., and by others, giving data on 35 objects (Fig. 1). Among high values are 1.2 mag. for Trojan 624 Hektor, 0.6 mag. for Trojan 1172 Aneas, and 1.34 mag. for Hilda 2483 Guinevere. The Trojan average may be high due to a tail of very high amplitudes on the amplitude distribution, rather than a

shift in the mean of a distribution curve, but this is not clear (Hartmann 1988). Now, as shown in Fig. 1, a sample of seven comet nuclei with reliable amplitudes indicates amplitudes similarly high, or even higher than those of Trojan. For example, Jewitt and Meech (1985) and Millis et al. (1988) reported 0.7 mag. for the nucleus of P/Arend-Rigaux. Wisniewski et al. (1986) reported 0.5 mag. for the nuclei of P/Neujmin 1 and P/Arend-Rigaux. From Giotto

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MAX. OBS'D AMPLITUDE (MAG) FxG. 1. F r e q u e n c y distributions of largest o b s e r v e d amplitudes for: (a) 50 C-class asteroids in the main belt; (b) a m i x e d sample of 50 C ' s and 50 S ' s more representative o f the whole main belt; (c) 35 Trojan and Hilda asteroids; (d) s e v e n c o m e t nuclei and comet-like asteroid 3551; and (e) 17 small belt asteroids in the s a m e size range as the c o m e t nuclei. H i s t o g r a m s (a)-(c) refer to a fixed diameter range at larger sizes; (d) and (e) refer to a fixed diameter range a m o n g objects. Full c o m e t n a m e s are given in text. (For more details see H a r t m a n n et al. 1987, 1988, H a r t m a n n 1988, and Jewitt and M e e c h 1988.)

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images of P/Halley's nucleus, Mohlmann et al. (1986) and others found dimensions corresponding to a lightcurve amplitude of 0.51 to 0.75 mag. if seen in the equatorial plane, or less (depending on a : b : c axial ratios) if seen from random directions. Jewitt and Meech (1987) found an amplitude of 0.8 mag. for P/Encke near aphelion. Wisniewski (IAU Circ. 4603) found 0.51 mag. for P/Tempel 2 on 20-22 May, 1988. A high amplitude was confirmed some nights later by A'Hearn, Campins, and Schleicher (IAU Circ. 4614). Fay and Wisniewski (1978) found an amplitude of 0.15 + 0.02 mag. for Comet d'Arrest though this is perhaps a minimum value because coma was visible visually. Radar observations of Comet Iras-Araki-Alcock showed an elongated nucleus with axial ratio near 2:1 (Goldstein et al. 1984). These comet data are not all new; Jewitt and Meech (1988) used some of them to point out that the comet nuclei were unusually elongated relative to main belt asteroids. However, they did not have access to our updated Trojan data and gave little attention to the Trojan link; our contribution is to provide the new Trojan and belt plots in Fig. 1, to point out the possible sequence from the main belt to the Trojans and on to comet nuclei, and to consider the possible common denominator of volatiles in further detail. Binzel and Mulholland (1983) studied amplitudes of small belt asteroids, allowing Jewitt and Meech, and us, to compare our comet samples with a belt sample of similar-sized objects. The bottom box of Figure 1, shows their sample of 17 asteroids with exactly the same size range as reported for the comet nuclei. As can be seen, these resemble the distributions for belt asteroids, confirming a proportion of high amplitudes lower than that among comets. Statistics of Earth-approaching asteroids down to diameters around a kilometer show amplitudes higher than those of larger belt objects, but some of them may be extinct comet nuclei or at least outer solar system objects, rather than a sample of perturbed

belt asteroids. This might be part of the cause of the higher amplitudes, rather than some purely size-dependent trend. In support of this, Earth-approacher 3552 1983 SA was classified by us as one of the four best candidates to be a dormant or extinct comet nucleus (Hartmann et al. 1987b); like many comets, its spectrum fits that of spectral class D. It has since been found to have an unusually high lightcurve amplitude, in agreement with the correlation discussed here (Weidenschilling et al. 1989; see Fig. ld.) 1 Thus, elongated shapes have turned up even among objects that were initially classified as asteroids, but were later dynamically identified as comet nuclei candidates. For this reason, we include 3552 in the box labeled " c o m e t nuclei" in Fig. 1. We now consider different processes that might affect shape, producing the observed results. 1. Fragmentation. Laboratory rock fragments yield amplitudes averaging around 0.2 when seen from random directions, consistent with belt asteroids, but too small for Trojans and comets (see summary by Hartmann et al. 1988). The only way to bring Trojans and comets into consistency with fragment data is to assume that the Trojans and comets are seen systematically in their equatorial planes. But this is known not to be the case for at least a few Trojans (Dunlap and Gehrels 1969, and our observations) and seems excluded for the sample of comets. Thus, we argue that Trojan and comets are more elongated than can be explained by simple fragmentation. 2. Primordial low-velocity coalescence processes. Hartmann et al. (1987a, 1988), French (1987), and Zappal~i et al. (1989)

~ A n o t h e r o f o u r four c o m e t candidates, 2060 Chiron, s u b s e q u e n t l y turned into a c o m e t in 1987-88. At s o m e 180-km diameter, it is bigger and further from the Sun t h a n m o s t objects d i s c u s s e d here. Later in this note we will argue that volatile loss m a y be a factor in developing elongated s h a p e s ; C h i r o n ' s lightcurve amplitude is only 0.07 mag, but it m a y be so pristine that it has n e v e r u n d e r g o n e e n o u g h volatile loss to evolve an elongated shape.

COMET NUCLEI AND TROJAN ASTEROIDS suggested from the Trojan evidence that Trojans may have retained relatively primordial elongated shapes, possibly due to lower velocities and frequencies of collision. H a r t m a n n and Cruikshank (1978) and Hartmann et al. (1988) suggested that the initial elongated shapes may have arisen by partial coalescence of planetesimals of similar size into " c o m p o u n d asteroids" during relatively low-velocity primordial collisions; the 1988 work suggested that belt asteroids, especially weak C-classes, may have been subsequently rounded by collisional erosion. These ideas need further study. 3. Evolution by volatile loss. This general idea is favored if active comets are generally more elongated than Trojans. Loss of volatiles may produce three effects, all of which would drive shapes toward greater elongation. First, Jewitt and Meech considered anisotropic volatile loss, which they likened to changing a spherical apple's shape by eating down to the core. Second, Colwell and Jakosky (1987, Colwell et al. in preparation) assert that if topography, such as a valley, is created on an icy surface undergoing sublimation by sunlight, the topography in typical cases tends to grow more exaggerated. During rotation, insolation is maximized in troughs due to reflection, causing troughs to deepen. This effect is somewhat controversial and is still being analyzed. A third effect is simply the geometric effect of more isotropic volatile loss. Consider a smooth ellipsoid, neglecting the Colwell-Jakosky mechanism. As a first-order approximation, if ice sublimes at a relatively uniform rate over the whole object, on average, the shape will grow more elongated as the object gets smaller. Even though discrete jets are present on Giotto photos of Halley's comet, these jets may change configuration with season and with comet evolution, so that isotropic mass loss may be approximated over the long term. Thus, initially aspherical comet nuclei may be expected to grow more elongated due to their c o m e t a r y activity, as shown in Fig. 2a. Jewitt and M e e c h ' s anisotropic loss is

451

C. FIG. 2. Idealized evolution of shape of (a) a roughly cylindrical body, (b) a compound planetesimal, and (c) a planetesimal fractured by a large crater, from an initial profile (solid) to a later profile (dashed) by mass loss through uniform sublimation from the entire surface. The first body becomes increasingly elongated; the compound body could evolve to a body with a narrow neck, and the fractured body could evolve until the fracture penetrates the entire diameter of the body. Each case could lead to splitting of a rotating body.

not required to make irregular comets grow more elongated, as long as they lose an appreciable part of their volume during sublimation. Thus we conclude that planetesimals may have evolved toward more elongated shapes if a substantial volume fractions o f their substances acted as volatiles during some stage of their history. Trojans may have undergone this process to a modest degree during the clearing of the solar nebula if they formed with a c o m p o n e n t of lowsublimation-temperature ices (such as

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if they were exposed to a period of higher solar luminosity after they formed, or if they went through the orbital scattering history envisioned by Shoemaker et al. (1989). Most observed comets have undergone a more extreme version of this process, explaining their tendency toward even more elongated shapes. The discovery that comets and Trojan asteroids have elongated shapes, possibly as a result of volatile loss, offers a new clue to explain comet splitting. Classical discussions of comet splitting focused on forces that would overcome a substantial tensile strength in the comet, such as tidal forces or impact shocks (Whipple and Stefanik 1966, Sekanina 1968). Formulae in these discussions usually involved spherical nuclei, with disclaimers added to the effect that "irregularity in the shape of the nucleus should materially aid in these splitting processes" (Whipple and Stefanik 1966, p. 50). Even Sekanina's (1982, p. 283) discussion of comet splitting mechanisms begins with the lines: " T h e r e are two requisites needed for the understanding of comet splitting: (a) the knowledge of the tensile strength . . . and (b) the recognition of a mechanism . . . that can build in the nucleus stresses sufficiently powerful to disrupt it." In considering rotational splitting, he requires rotational forces to overcome the tensile strength of the nucleus, and among 21 split comets, he mentions only one candidate for this process. Whipple (1963) did briefly consider the possibility that " an irregularly shaped cometary nucleus sublimates away and splits under a relatively slow rate of rotation . . . . " We suggest that rotational splitting may occur specifically as a result of evolution toward elongated shape, when a comet nucleus (1) sublimes through a narrow connecting waist (Fig. 2b); (2) sublimes to a narrow enough dimension that preexisting fracture planes connect one side to the other (Fig. 2c); or (3) sublimes to a point where rotational stresses, assisted by gas pressure, overcome the tensile strength in C02) , or

the weakest region. In processes (1) and (2), tensile strength of the material is almost irrelevant, since the comet sublimes to a point where there is essentially zero tensile strength holding it together, contrary to the classical approach of Sekanina and others noted above. In support of these ideas, separation velocities of rotationally splitting elongated nuclei would be in the range of a few m/sec, which is exactly the observed range. For example, consider a cylindrical comet nucleus with an element becoming detached at one end. If the element were moving at escape velocity, the separation velocity at large distance (resolvable from Earth) would be zero except for nongravitational accelerations, such as gas pressure. If the element were moving at, say, 1.5 x escape velocity, the separation velocity at large distance would be independent of the axis ratio of the cylinder (length over thickness), and would be given by Useparation = ~v/5rrGb2p/4, where b = minor axis and p = density. For comets of minor axis 0.5 to 5 km, and density 1000 to 1500 kg/m 3, the observed separation velocities would range 0.3 to 3 m/ sec, respectively. Radial and normal velocity components listed by Sckanina (1982) among 20 determinations range from 0.1 to 4.9 m/sec, in good agreement with these considerations. Consider the rotation period, P, needed to eject a body that has broken loose, through sublimation, from the end of a cylindrical nucleus. Escape velocity is exceeded when p2 <

~E2/Gp,

where E equals the "elongation," or axis ratio a/b. The lightcurve data show elongations reaching values of 2.5 to 3. In this range, the densities of 1000 to 1500 kg/m 3, critical rotation periods range from 3.9 to 5.7 hr. If sublimation produced detachment at shorter periods, nuclei fragments would

COMET NUCLEI AND TROJAN ASTEROIDS

separate. Among 47 period determinations, Whipple (1982) lists four in this range. He also asserts that "spinup by sublimation is fairly probable," so that comets may evolve to a condition of instability and separation. Thus, weak fast rotators, elongated by sublimation, plausibly could throw off subnuclei at velocities of a few m/sec or less, as observed. In further support of this model, it would predict breakups near, but not always at, closest solar approach, contrary to the tidal or impact models. Consistent with this, Sekanina's (1982) listing of 33 breakup events among 21 comets shows eight events within 0.5 AU, the median at about 1.5 AU solar distance, but with some events as far as 9 AU from the Sun. In terms of time, eight events were within l0 days of perihelion passage, the median was at 141 days, and a few events occurred more than 3 years after perihelion passage. In summary, new data on comets' and Trojan asteroids' shapes support the idea of similarity among these objects, and suggest an explanation of comet splitting as a result of shape evolution. The ideas presented here also appear to be consistent with the occurrence of occasional double craters on moons and planets, since bodies on the verge o f spontaneous splitting could separate by a few diameters due to tidal or atmospheric drag forces during planetary approach. Note added in Proof. On March 31-April 3, 1990, we obtained new lightcurve data on seven Trojans and one Hilda. No unusually high amplitudes were found among any of the eight. For five of the objects, our data file already contained amplitudes that had been observed earlier by ourselves and/or others; our new data refined the periods and added new amplitudes in some of these cases. However, the earlier-observed amplitudes were higher than, or comparable to, the new results so that none of the five was displaced to a higher-amplitude bin in Fig. lc. According to preliminary data reduction for the three remaining objects, Trojans 3793 Leonteus and 4060 Deipylos had amplitudes in the 0.20 to 0.249 magnitude bin, just above the center of the bell curve found for C-class belt asteroids, and Trojan 3063 Makhaon had a low amplitude,

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probably in the 0.05 to 0.099 magnitude bin. These new results fill in a bit of the dotted bell curve in Fig. lc, but still leave the Trojan/Hilda histogram with fewer low amplitudes, and with an anomalous tail of high amplitudes, relative to the belt samples in Figs. la and lb. We hope to publish completely reduced lightcurves and further analysis soon. A new paper by Jewitt and Luu (1990, submitted for publication) supports the spectroscopic similarity of Trojans and comet nuclei at wavelength 4000-7400A.

ACKNOWLEDGMENTS We thank W. Wisniewski for stimulating discussions and for providing recent lightcurve observations of Comet Tempel 2 and asteroids, respectively. We also thank Linda French and our colleagues at PSI for useful critiques and suggestions; Michael A'Hearn for discussions of comet nuclei; and Dale Cruikshank and Gene Shoemaker for discussions of Trojans and associated problems. This work is supported by NASA contracts NASW-4266 and NASW-4296.

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