Margot J.-L., Pravec P., Taylor P., Carry B., and Jacobson S. (2015) Asteroid systems: Binaries, triples, and pairs. In Asteroids IV (P. Michel et al., eds.), pp. 355–374. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch019.

Asteroid Systems: Binaries, Triples, and Pairs

Jean-Luc Margot University of California, Los Angeles

Petr Pravec Astronomical Institute of the Czech Republic Academy of Sciences

Patrick Taylor Arecibo Observatory

Benoît Carry Institut de Mécanique Céleste et de Calcul des Éphémérides

Seth Jacobson Côte d’Azur Observatory

In the past decade, the number of known binary near-Earth asteroids has more than qua- drupled and the number of known large main-belt asteroids with satellites has doubled. Half a dozen triple asteroids have been discovered, and the previously unrecognized populations of asteroid pairs and small main-belt binaries have been identified. The current observational evidence confirms that small <( 20 km) binaries form by rotational fission and establishes that the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect powers the spin-up process. A unifying paradigm based on rotational fission and post-fission dynamics can explain the forma- tion of small binaries, triples, and pairs. Large (>20 km) binaries with small satellites are most likely created during large collisions.

1. INTRODUCTION (Merline et al., 2002c; Noll et al., 2008). As such, they pro- vide an invaluable window on accretional, collisional, tidal, 1.1. Motivation and radiative processes that are critical in planet formation. The distribution and configurations of the multiple-asteroid Multiple-asteroid systems are important because they systems also provide a rich array of constraints on their en- represent a sizable fraction of the asteroid population and vironment, their formation, and their evolutionary pathways. because they enable investigations of a number of properties Observations rely primarily on groundbased telescopes and processes that are often difficult to probe by other means. and the Hubble Space Telescope (HST). For an up-to-date The binaries, triples, and pairs inform us about a great variety list of binaries and triples in the solar system, see Johnston of asteroid attributes, including physical, mechanical, and (2014). We describe observational techniques only briefly thermal properties, composition, interior structure, formation because this material is available elsewhere (e.g., Merline et processes, and evolutionary processes. al., 2002c). A few emerging techniques will be described in Observations of binaries and triples provide the most more detail. Likewise, we refer the reader to other texts for powerful way of deriving reliable masses and densities for an extensive history of the field (e.g., Merline et al., 2002c) a large number of objects. The density measurements help and highlight only a few of the developments here. us understand the composition and internal structure of mi- nor planets. Binary systems offer opportunities to measure 1.2. History thermal and mechanical properties, which are generally poorly known. Early search programs for asteroid satellites were unsuc- The binary and triple systems within near-Earth asteroids cessful, returning negative or dubious results, such that the (NEAs), main-belt asteroids (MBAs), and transneptunian authors of the Asteroids II review chapter chose the prudent objects (TNOs) exhibit a variety of formation mechanisms title “Do asteroids have satellites?” (Weidenschilling et al.,

355 356 Asteroids IV

1989). The chapter provides an excellent discussion of the objects are substantially affected by the Yarkovsky-O’Keefe- physics of several formation mechanisms that were postu- Radzievskii-Paddack (YORP) effect during their lifetime. lated at the time. The perspective changed with the flyby of For typical NEAs and MBAs, this dividing line corresponds (243) Ida by the Galileo spacecraft in 1993 and the discovery to a diameter of about 20 km (Jacobson et al., 2014a). of its small satellite Dactyl (Chapman et al., 1995; Belton We define very small asteroids as those with diameters of et al., 1995). Groundbased efforts intensified and resulted in <200 m. This is the approximate size below which many the discovery of a satellite around (45) Eugenia by Merline asteroids are observed to spin faster than the disruption rate et al. (1999). Several other discoveries followed in rapid of a body with no shear or tensile strength wd = 43πρG , succession. The relatively small sizes of the MBA satellites where r is the density and G is the gravitational constant. suggested formation in subcatastrophic or catastrophic colli- We use two additional acronyms. The YORP effect is a ra- sions (Durda, 1996; Doressoundiram et al., 1997). diation-powered rotational acceleration mechanism for small The discovery of MBA satellites, coupled with analysis asteroids (Rubincam, 2000). The binary YORP (BYORP) ef- of terrestrial doublet craters (Bottke and Melosh, 1996a,b) fect is a radiation-powered acceleration mechanism that may and anomalous lightcurve observations (Pravec and Hahn, expand or contract the orbits of some synchronous asteroids 1997), suggested the existence of binary asteroids in the near- (Ćuk and Burns, 2005). Earth population as well. The unambiguous detection of five NEA binaries by radar cemented this finding and indicated 2. OBSERVATIONS that NEA satellites form by a spin-up and rotational fission process (Margot et al., 2002). Lightcurve observers reached Several observational techniques are available for discover- the same conclusion independently (Pravec and Harris, ing, detecting, and studying binaries, triples, and pairs, each 2007). Both radar and lightcurve observations revealed that, with its strengths and weaknesses. This section describes far from being rare, binary asteroids are relatively common recent results and illustrates the complementarity of the ob- (Pravec et al., 1999, 2006; Margot et al., 2002). By the time servational techniques that characterize individual asteroid the Asteroids III review chapter was written, a more decisive systems and entire populations. title (“Asteroids do have satellites”) had become appropriate (Merline et al., 2002c). This review focuses on the develop- 2.1. Radar Observations of Near-Earth ments that followed the publication of Asteroids III. Asteroid Systems

1.3. Terminology Radar has proven to be a powerful method of detect- ing secondaries to NEAs, enabling the discovery (as of Two- and three-component asteroids that are gravitation- September 2014) of the satellites in 71% of the 49 known ally bound will be referred to as binary asteroids (or bina- multiple-component NEA systems, including 33 of 47 ries) and triple asteroids (or triples), respectively. (Triple is binaries and both undisputed triple systems. Of the 14 favored over the more directly analogous terms trinary and binary NEAs discovered via optical lightcurve techniques, ternary because of long-established usage in astronomy.) 6 have been confirmed with follow-up radar observations Asteroid pairs denote asteroid components that are geneti- during later apparitions. Overall, radar detections suggest cally related but not gravitationally bound. Paired binaries that about one in six NEAs larger than 200 m in diameter or paired triples are asteroid pairs where the larger asteroid are multiple-asteroid systems (Margot et al., 2002; Taylor is itself a binary or triple asteroid. The larger component et al., 2012a), although 200 m is not a sharp cutoff. Three in binaries, triples, and pairs is referred to as the primary binary NEA systems identified by radar have primary component or primary. The smaller component in binaries components with suggested diameters of 120 m to 180 m: is referred to as the secondary component or secondary. 2003 SS84 (Nolan et al., 2003), (363599) 2004 FG11 (Tay- There has been some confusion in the literature about lor et al., 2012c), and 1994 CJ1 (Taylor et al., 2014). For the meaning of the word “asynchronous.” Here, we adopt comparison, the largest primaries of binary NEAs imaged the terminology proposed by Margot (2010) and later with radar — (5143) Heracles (Taylor et al., 2012b), the implemented by Jacobson and Scheeres (2011b) and Fang possible triple (276049) 2002 CE26 (Shepard et al., 2006), and Margot (2012c). Binaries with an absence of spin-orbit and (285263) 1998 QE2 (Springmann et al., 2014) — are synchronism are called asynchronous binaries. Binaries with more than an order of magnitude larger at >3 km in diam- a secondary spin period synchronized to the mutual orbit eter. It is likely that ~8-km-diameter (1866) Sisyphus has a period are called synchronous binaries. Binaries with both secondary based on analysis of frequency-only observations primary and secondary spin periods synchronized to the obtained on four separate dates in 1985 (S. Ostro, personal mutual orbit period are called doubly synchronous binaries. communication, 2001). If generalization to systems with more than one satellite is Radar observations can be used to detect asteroid satel- needed, we affix the terms synchronous and asynchronous lites because of the ability to resolve the components of the to the satellites being considered. system both spatially (along the observer’s line of sight) It is useful to present results for small and large asteroids. and in terms of frequency (due to Doppler shifts from the We place an approximate dividing line at the size at which rotational and orbital line-of-sight velocities), resulting in Margot et al.: Asteroid Systems: Binaries, Triples, and Pairs 357

a measurable separation between the components in two dimensions. Direct detection of a satellite in frequency- (a) only spectra or radar images typically occurs within one observing session and often within minutes of observation. The bandwidth of the echo of a component scales directly with the diameter and rotation rate. Thus, in a frequency- only experiment, the signal of the smaller, relatively slowly rotating satellite is condensed to a smaller bandwidth that is superimposed upon the broadband signal of the larger, often rapidly rotating, primary (Fig. 1a). Not all radar-observed

binaries present this characteristic spectrum (e.g., where the secondary spins faster than the synchronous rate), but all are readily detected in radar images when the components are also resolved spatially (Fig. 1b). Because the spatial resolution achieved with radar instruments corresponds to an effective angular resolution of better than ~1 milliarcsecond –10 –5 0 5 10 (mas), there is no bias against the detection of satellites Doppler Frequency (Hz) orbiting very close to the primary component. Multiple measurements of the range and frequency separations of the components over days of sky motion provide the geometric (b) leverage required to determine the orbit of the secondary around the primary. This can be done for any orbital ori- entation and yields the total system mass, a property that is difficult to estimate otherwise. Other techniques involve analyzing spacecraft flyby and orbit trajectories (e.g., Yeo- mans et al., 1999), measuring the Yarkovsky orbital drift in conjunction with thermal properties (e.g., Chesley et al., 2014), or observing the gravitational perturbations resulting from asteroid encounters (e.g., Hilton, 2002). Most binary NEA systems observed to date have a rapidly rotating primary and a smaller secondary on the order of a few tenths the size of the primary (a secondary-to-primary mass ratio of roughly 0.001 to 0.1), whose rotation is synchronized to the mutual orbit period. The majority of primaries rotate in less than 2.8 h, although they range from 2.2593 h for (65803) Didymos (Pravec et al., 2006) to 4.749 h for 1998 QE2 (P. Pravec, personal communication, 2013). The known outlier is the nearly equal-mass binary (69230) Hermes, whose components both appear to have 13.894-h periods synchronized to their mutual orbit period (Margot et al., 2006). This doubly synchronous configura- Fig. 1. Binary near-Earth asteroid (285263) 1998 QE2 as tion is most likely due to rapid tidal evolution (Taylor and detected using the Arecibo planetary radar system. (a) In Margot, 2011). While the rotations of satellites in NEA this frequency-only spectrum showing echo power as a binaries tend to be tidally locked to their orbital mean mo- function of Doppler frequency, the narrowband echo of the tions with periods typically within a factor of 2 of 24 h tidally locked secondary stands out against the broadband (often resulting in the characteristic appearance shown in echo of the larger, faster-rotating primary. (b) In this radar Fig. 1), about one in four radar-observed multiple-asteroid image, the components are spatially resolved (7.5 m/pixel). systems have an asynchronous satellite (Brozović et al., The vertical axis represents distance from the observer in- 2011), all of which rotate faster than their orbital rate. creasing downward. The horizontal axis is Doppler frequency Well-studied examples include (35107) 1991 VH (Naidu due to the orbital and rotational motion of the components. et al., 2012), (153958) 2002 AM (Taylor et al., 2013), Note that if one summed the pixel values in each column of 31 the image, the intensity as a function of Doppler frequency (311066) 2004 DC (Taylor et al., 2008), and the outer satel- would approximate the spectrum above. The secondary is lites of both undisputed triple systems (153591) 2001 SN263 roughly one-fourth the size of the primary (measured in the (Nolan et al., 2008; Fang et al., 2011; Becker et al., 2015) vertical dimension), although the Doppler breadth of the and (136617) 1994 CC (Brozović et al., 2011; Fang et al., primary gives the illusion of a greater size disparity. The 2011). Of the known asynchronous satellites, all have wide shape of the secondary (inset on (b)) is distinctly nonspheri- component separations (>7 primary radii), translating to cal when viewed with finer frequency resolution. 358 Asteroids IV longer-than-typical orbital periods, and/or eccentric orbits (AU) of Earth. Satellites in the main asteroid belt simply (>0.05) that are either remnants of their formation mecha- tend to be too small and too far away to detect with pres- nism or products of subsequent dynamical evolution (Fang ent radar capabilities and require application of different and Margot, 2012c). observational techniques. The shortest orbital periods detected with radar so far are +00. 3 those of Didymos and 2006 GY2 with Porb = 11.90−00. 2 h 2.2. Lightcurve Observations of Near-Earth-Asteroid and 11.7 ± 0.2 h, respectively (Benner et al., 2010; Brooks, and Small-Main-Belt-Asteroid Systems +00. 4 2006). For Didymos, the semimajor axis is a = 1.18−00. 2 km, just outside the classical fluid Roche limit of ~1 km for A photometric lightcurve is a time series of measurements equal-density components. Other systems with satellites of the total brightness of an asteroid. Detections of binary orbiting near the Roche limit include 2002 CE26 and asteroids by photometric lightcurve observations utilize the 2001 SN263. The significance of this is unclear, as ~100-m fact that the components can obscure or cast a shadow on secondaries with a cohesion comparable to comet regolith one another, producing occultations or eclipses, respectively. or sand can likely survive on orbits interior to the Roche The attenuations can be used to both reveal and characterize limit (Taylor and Margot, 2010, and references therein). binaries (Fig. 2). The observational, analysis, and modeling Inversion of a series of radar images can provide a three- techniques were described in Pravec et al. (2006), Scheirich dimensional shape model and complete spin-state description and Pravec (2009), and Scheirich et al. (2015). given sufficient signal, resolution, and orientational coverage Early reports (Tedesco, 1979; Cellino et al., 1985) of (Hudson, 1993; Magri et al., 2007). Shape reconstruction asteroids suspected to be binaries on the basis of anomalous of the larger component of (66391) 1999 KW4 (Ostro et lightcurves [including (15) Eunomia, (39) Laetitia, (43) Ari- al., 2006) demonstrated that the canonical shape of an NEA adne, (44) Nysa, (49) Pales, (61) Danae, (63) Ausonia, primary has a characteristic circular equatorial bulge, uni- (82) Alkmene, (171) Ophelia, and (192) Nausikaa] have formly sloped sides, and polar flattening akin to a spinning remained largely unconfirmed despite extensive follow-up top. Such a shape is shared by the primaries of 2004 DC, searches. The first serious candidate for detection with this 1994 CC, 2001 SN263, and (185851) 2000 DP107 (Naidu et technique was NEA (385186) 1994 AW1 (Pravec and Hahn, al., 2015), although some primaries have less pronounced 1997), whose binary nature was confirmed by photometric equatorial belts, e.g., 2002 CE26 and 1998 QE2. Some single observations in 2008 (Birlan et al., 2010). Since 1997, nearly asteroids have a similar shape, e.g., (101955) Bennu (Nolan 100 binaries among NEAs and small MBAs have been et al., 2013) and (341843) 2008 EV5 (Busch et al., 2011), detected with the photometric method. The binary asteroid but do not have satellites, possibly because one has not yet database constructed by Pravec and Harris (2007) (http:// formed or has been lost in the past. Shape model renditions www.asu.cas.cz/~asteroid/binastdata.htm) includes data are shown in the chapter by Benner et al. in this volume. for 86 MBA and NEA binaries that were securely detected Often the resolution of radar images of the smaller satellites by photometry and for which basic parameters have been is insufficient for shape inversion, but radar images suggest derived, such as the primary spin period, the orbital period, that the satellites are typically elongated, e.g., 2000 DP107, and the primary-to-secondary mean diameter ratio. A few 1999 KW4, 2001 SN263, 1991 VH, and 1998 QE2. tens of additional MBAs and NEAs are suspected to be Shapes and volumes obtained from inversion of radar binaries and await confirmation with more detailed observa- images, combined with the system mass derived from the tions in the future. orbital motion observed in radar images, provide the density Among the main findings obtained from photometric ob- of the system (or of the individual components if the mass servations is that binary asteroids are ubiquitous. They have ratio is measurable from reflex motion). Low densities on the been found among NEAs and Mars-crossers (MCs), as well order of 1 g cm–3 (Shepard et al., 2006; Becker et al., 2015) as throughout the main belt, both among asteroids that have to 2 g cm–3 (Ostro et al., 2006; Brozović et al., 2011) sug- been identified as family members and among asteroids that gest significant internal macroporosity on the order of 50%, have not. Pravec et al. (2006) derived the fraction of binaries implying a rubble-pile internal structure for the components. among NEAs larger than 300 m to be 15 ± 4%. A binary At such low densities, the rapid rotation of the primary fraction among MBAs has not been derived precisely due places particles along the equatorial belt in a near-weightless to less-well-characterized observational selection effects, but environment. The combination of rapid rotation, shape, and their photometric discovery rate is similar to the discovery implied porosity and rubble-pile structure has implications rate of binaries among NEAs. Thus, binaries are suspected for the formation mechanism of small multiple-asteroid to be as frequent among MBAs as they are among NEAs. systems (section 4). There appears to be an upper limit on the primary diameter While radar allows for direct, unambiguous detection of for photometrically detected binaries of about 13 km; the asteroid satellites, its range is limited. Because radar requires largest detected binary is (939) Isberga with Dp = 13.4 ± the transmission and reception of a signal, the strength of 1.3 km (Carry et al., 2015). A lower size limit on the primary the received signal falls as the fourth power of the distance diameter Dp is less clear. The smallest detected binary is to the target and, thus, is best suited for detecting multiple- 2000 UG11 with Dp = 0.26 ± 0.03 km (Pravec et al., 2006), component systems passing within ~0.2 astronomical units but smaller binaries are known to exist (section 2.1). Their Margot et al.: Asteroid Systems: Binaries, Triples, and Pairs 359

12.4

12.5

12.6

12.7 Relative 12.8 (a) 12.9 (1338) Duponta 12.4 12.5 12.6

12.7 (b) 12.8 0 0.2 0.4 0.6 0.8 1 12.4 Phase (Epoch 2454184.28, Porb = 17.57 h) 12.5 2007-03-06.9 to 22.9 (Modra) 2007-03-18.2 to 25.3 (GMARS) 12.6 2007-03-22.2 to 24.2 (Badlands) 12.7 2007-03-23.5 (Hunters Hill) (c) 2007-03-23.6 (Leura) 12.8 2007-03-24.1 and 26.1 (Carbuncle Hill) 0 0.2 0.4 0.6 0.8 1

Fig. 2. Lightcurve data of (1338) Duponta, which has a secondary-to-primary diameter ratio of about 0.24. (a) The original data showing both lightcurve components, folded with the orbit period. (b) The orbital lightcurve component, derived after subtraction of the primary lightcurve component, showing the mutual events between components of the binary system. (c) The primary lightcurve component. Figure from Pravec et al. (2012).

absence in lightcurve datasets may be due in part to a bias of the components due to the effect on mutual event timing. against detecting small binaries in the initial surveys. An extensive set of photometric observations of the synchro- Another key finding is that small binary asteroids have, nous binary (175706) 1996 FG3 obtained during 1996–2013 with only two or three exceptions, a near-critical angular places an upper limit on the drift of its semimajor axis that momentum content (Fig. 3). As shown by Pravec and is 1 order of magnitude less than estimated on the basis of Harris (2007), their angular momentum is consistent with the BYORP theory (Scheirich et al., 2015). This system may formation by fission of critically spinning parent bodies of be in an equilibrium between BYORP and tidal torques, as a cohesionless, rubble pile structure. The exceptions are the proposed for synchronous binary asteroids by Jacobson and semi-wide systems (32039) 2000 JO23 and (4951) Iwamoto, Scheeres (2011a). and possibly also (1717) Arlon, with orbital periods of 117 h Some datasets strongly suggest the presence of triple aster‑ to 360 h and supercritical total angular momentum content. oids. In these cases, an additional rotational component The orbital poles of main-belt binaries were found to that does not belong to the primary or the close eclipsing have a highly anisotropic distribution, concentrating within secondary is present in the lightcurve. This additional rota- 30° of the poles of the ecliptic (Pravec et al., 2012). The tional component does not disappear during mutual events preferential orientations of the orbital poles suggest that where the eclipsing close secondary is obscured by or in their parent bodies or the primaries were tilted by the YORP the shadow of the primary. Pravec et al. (2012) identified effect toward the asymptotic spin states near obliquities 0° three such cases: (1830) Pogson, (2006) Polonskaya, and and 180°, consistent with observations of single asteroids (2577) Litva. The latter has been confirmed by direct imaging (Hanuš et al., 2011). observations of the third body (second satellite) on a wide Another significant finding is that there appears to be orbit (Merline et al., 2013). a lower limit on the separation between components of Other datasets reveal the existence of paired binaries/ binary systems of about a/Dp = 1.5, corresponding to an triples. Two such cases have been published: the pair orbital period of 11–12 h for typical densities. Lightcurve composed of (3749) Balam and 2009 BR60 (Vokrouhlický, observations indicate that the orbital period of Didymos is 2009, and references therein) and the pair composed of Porb = 11.91 ± 0.02 h (Pravec et al., 2006), consistent with (8306) Shoko and 2011 SR158 (Pravec et al., 2013). Balam the radar estimate. This suggests an orbit close to the Roche is a confirmed triple, with a distant satellite detected by direct limit for strengthless satellites (but see prior remark about imaging (Merline et al., 2002a) and a close satellite detected orbits interior to the Roche limit). by lightcurve observations (Marchis et al., 2008d). Shoko is Photometric observations of a binary system over multiple a suspected triple as well: Using lightcurve observations, apparitions can be used to detect a change in the separation Pravec et al. (2013) detected an eclipsing, synchronous close 360 Asteroids IV

0.1 1 10 100 100 0.1 1 10 100 1000 3.5 3.5

Ds/Dp ≤ 0.5 Ds/Dp ≤ 0.5

Ds/Dp > 0.5 D /D > 0.5 1 s p 1 3 3 L (32039) 2000 J023 Spin barrier A L

2.5 2.5 10 10 (4951) Iwamoto (h) p B (617) P 3 3 Double, Patroclus synchronous (1717) Arlon B 100 100 1.5 1.5

(90) Antiope

1 1 0.1 1 10 100 1000

Dp (km) A 0.5 0.5 Normalized Total Angular Momentum Content α Total Normalized L Fig. 4. Primary rotation period vs. primary diameter. Groups A, B, and L are defined in the caption of Fig. 3. Three doubly synchronous asteroids with nearly equal-sized components lie 0 0 isolated in the plot: (69230) Hermes on the left, and (90) An- 0.1 1 10 100 100 tiope and (617) Patroclus on the right of group B. Note that members of group A cluster near the disruption spin limit for Dp (km) strengthless bodies. Figure from Pravec and Harris (2007). Fig. 3. Estimated values of the normalized total angular momentum content of binaries vs. primary diameter. The quantity aL is the sum of orbital and spin angular momenta corrected to zero phase angle). This suggests that their pri- normalized by the angular momentum of an equivalent sphere maries may have shapes similar to the top-like shapes that spinning at the critical disruption spin rate wd = 4Gπρ 3 where r is the density and G is the gravitational constant. In have been observed for 1999 KW4 (Ostro et al., 2006) and several other binaries by radar. the Darwin notation, aL = 1 corresponds to J/J′ = 0.4. Group A contains small NEA, MC, and MBA binaries. Group B consists All the properties revealed by photometric observations of doubly synchronous small MBAs with nearly equal-sized indicate that binary systems among NEAs and small MBAs components. Group L represents large MBAs with small were formed from critically spinning cohesionless parent bod- satellites (section 2.5). Two exceptional cases are the dou- ies, with YORP as the predominant spin-up mechanism. This bly synchronous asteroids (90) Antiope and (617) Patroclus finding is consistent with the fact that the observed 0.2–13-km (section 2.5). Figure updated from Pravec and Harris (2007). size range of binaries corresponds to the size range where the spin barrier against asteroid rotations faster than about 2.2 h has been observed (e.g., Pravec et al., 2007). Although lightcurve observations provide powerful con- satellite with Porb = 36.2 h and a third rotational component straints on binaries, there are limitations. Detection of mutual attributed to an outer satellite. events requires an edge-on geometry and observations at the While the population of binary NEAs and small MBAs is time of the events, such that some binaries remain undetected composed primarily of synchronous systems, and secondari- [e.g., (69230) Hermes during its 2003 apparition]. Small ly of asynchronous systems with low secondary-to-primary satellites also escape detection because their effect on the size ratios (Ds /Dp < 0.5), doubly synchronous binaries with lightcurve is not measurable (e.g., satellites with Ds /Dp < nearly equal-sized components also exist (Fig. 4). Nine such 0.17 remain undetected if the minimum detectable relative systems with Ds /Dp > 0.7 and orbital periods between 15 h brightness attenuation is ~0.03 mag). The probability of and 118 h have been reliably identified in the main belt mutual event detection is larger at smaller semimajor axes (e.g., Behrend et al., 2006; Kryszczyńska et al., 2009) (see (expressed in units of primary radius) and at larger size ratios, also the Pravec and Harris binary database described above). resulting in observational biases (e.g., Pravec et al., 2012). Another important observation is that, with the excep- Finally, lightcurve observations yield relative, not absolute, tion of doubly synchronous systems, all binaries have un- measurements of orbital separations. Detection of small or elongated, near-spheroidal primary shapes, as evidenced by distant secondaries and direct measurement of orbital sepa- their low primary amplitudes not exceeding 0.3 mag (when ration must instead rely on other observational techniques. Margot et al.: Asteroid Systems: Binaries, Triples, and Pairs 361

2.3. Lightcurve Observations of Asteroid Pairs 0 1 2 3 4 5 1 1 Vokrouhlický and Nesvorný (2008) reported evidence for pairs of MBAs with bodies in each pair having nearly identical heliocentric orbits. Because chance associations can be ruled out, the asteroids in each pair must be genetically related. Quantifying the difference in orbital parameters is accomplished with a metric d that corresponds roughly to the relative velocity between the bodies at close encounter. 10 10 Vokrouhlický and Nesvorný identified 44 asteroid pairs (ex- cluding family members) with a distance between the orbits of their components amounting to d < 10 m s–1. They showed that, when integrated backward in time, the orbits converge at a certain moment in the past with a physical distance much less than the radius of the Hill sphere and with a low relative Spin Period of Primary Component (h) U = 3 velocity on the order of 1 m s–1. p U = 2 Pravec and Vokrouhlický (2009) developed a method 100 p 100 to identify probable asteroid pairs by selecting candidate 0 1 2 3 4 5 pairs with a similar distance criterion, then computing the ∆ H probability that each candidate pair emerged as a result of 1 0.1 0.01 0.001 a coincidence between two unrelated asteroids. They identi- Mass Ratio (q) fied 72 probable asteroid pairs, reproducing most of the 44 previously known pairs. Most of the new candidates were 1 0.1 later confirmed to be real pairs using backward integrations Size Ratio of their heliocentric orbits. Vokrouhlický and Nesvorný (2008) proposed a few pos- Fig. 5. Primary rotation periods vs. mass ratios of asteroid pairs. The mass ratio values were estimated from the differ- sible formation mechanisms for the asteroid pairs: colli- ences between the absolute magnitudes of the pair compo- sional disruption, rotational fission, and splitting of unstable nents, DH. Circles are data points with quality code rating asteroid binaries. Pravec et al. (2010) conducted a survey of Up = 3, meaning a precise period determination. Diamonds the rotational properties of asteroid pairs, and they found a are data points with Up = 2, which are somewhat less certain strong correlation between the primary rotational periods and estimates. Error bars are one standard deviation. The data the secondary-to-primary mass ratio (Fig. 5). They showed match the predictions (curves) of a model of rotational fis- that this correlation fits precisely with the predictions of sion with a few adjustable parameters. In the model, Aini a model by Scheeres (2007) in which a parent body with is the binary system’s initial orbit semimajor axis, aL is the zero tensile strength undergoes rotational fission. The model normalized total angular momentum of the system (Fig. 3), predicts that primaries of low-mass-ratio pairs (q < 0.05) and ap, bp, cp are the long, intermediate, and short axis of the have not had their spin substantially slowed down in the dynamically equivalent equal mass ellipsoid of the primary. All models shown assume b /c = 1.2. The dashed curve separation process and should rotate rapidly with frequen- p p shows the best-fit model with aL = 1.0, ap /bp = 1.4 and Aini / cies close to the fission spin rate. The observed periods are b = 3. Solid curves represent upper and lower limiting cases between 2.4 and 5 h. Primaries of medium mass ratio pairs p with aL = 0.7−1.2. Figure updated from Pravec et al. (2010). (q = 0.05 to ~0.2) have had their spin slowed down accord- ing to the model because a substantial amount of angular momentum was taken away by the escaped secondary. This trend is observed in the data (Fig. 5). Finally, high-mass-ratio tions 2.1 and 2.2), the primaries of asteroid pairs do not pairs with q > 0.2 should not exist, as the free energy in the tend to be nearly spheroidal. protobinary system formed by rotational fission would be negative and the components would be unable to separate. 2.4. Spectral Observations of Asteroid Pairs Observations mostly corroborate this prediction: All 32 pairs in the sample of Pravec et al. (2010) were found to Colorimetric and spectral observations of about 20 asteroid have a mass ratio <0.2. However, an expanded photometric pairs indicate that members of an asteroid pair generally have survey with 64 asteroid pairs observed between 2012 and similar spectra (Duddy et al., 2012, 2013; Moskovitz, 2012; the date of this writing reveals 3 pairs with high mass ratio Polishook et al., 2014a; Wolters et al., 2014). In some pairs, (q > 0.5). Their formation requires an additional supply of the authors observed subtle spectral differences between the angular momentum. Another important finding by Pravec components and attributed them to a larger amount of weath- et al. (2010) is that the primaries of asteroid pairs have ered material on the surface of the primary. In two pairs, they lightcurve amplitudes that imply shapes with a broad range observed somewhat more significant spectral differences. For of elongations; i.e., unlike the primaries of binaries (sec- the pair (17198)–(229056), both Duddy et al. (2013) and 362 Asteroids IV

Wolters et al. (2014) found that the primary is redder, i.e., it conditions. With a sequence of disk-resolved images that has a somewhat higher spectral slope than the secondary in provide sufficient orientational coverage, it is possible to the observed spectral range 0.5–0.9 μm. It is unclear why estimate the three-dimensional shape of the primary. This their spectra differ despite a strong dynamical link between enables volume and density determinations. the two asteroids. For the pair (19289)–(278067), Wolters et Instruments capable of meeting the contrast and resolution al. (2014) observed a spectral difference similar to that seen requirements include HST and large (10-m-class) ground- in (17198)–(229056), but Duddy et al. (2013) observed very based telescopes equipped with AO. Spacecraft encounters similar spectra. Cross-validation of the methods or additional provide an opportunity to detect small satellites at small observations, perhaps rotationally resolved, are needed to separations because of proximity to the target and the absence resolve the discrepancy. of the point-spread-function halo that affects groundbased AO instruments. 2.5. Direct Imaging of Main-Belt-Asteroid At the time Asteroids III was published, MBA satellite and Trojan Systems discoveries included one by spacecraft [(243) Ida], one by HST [(107) Camilla], and six by groundbased AO instru- Direct imaging of asteroids can reveal the presence of ments. Since then, groundbased AO instruments have been satellites and, following the long tradition of orbit determina- responsible for almost all large MBA satellite discoveries: tion of binary stars and planetary satellites, lead to estimates (121) Hermione (Merline et al., 2002b), (379) Huenna of orbital parameters (Fig. 6). This observing mode remains (Margot, 2003), (130) Elektra (Merline et al., 2003c), a challenging because the satellites are generally much smaller second satellite to (87) Sylvia (Marchis et al., 2005b) and and fainter than their respective primaries and because most to (45) Eugenia (Marchis et al., 2007), (702) Alauda (Rojo satellites known to date orbit at angular separations below and Margot, 2007), (41) Daphne (Conrad et al., 2008), 1 arcsec. Satellite discoveries have therefore followed the two satellites to (216) Kleopatra (Marchis et al., 2008b) development of adaptive optics (AO), and recent advances and (93) Minerva (Marchis et al., 2009), and (317) Roxane have enabled the detection of asteroid satellites that had (Merline et al., 2009). The wide binaries (1509) Esclangona remained undetected in prior searches. (Merline et al., 2003a) and (4674) Pauling (Merline et al., Instruments must have sufficient contrast and resolving 2004), which are small asteroids in our classification, have power to detect asteroid satellites with direct imaging. For also been identified using AO-fed cameras. HST enabled de- a 50–100-km-diameter asteroid in the main belt orbited by a tections of two additional wide binaries: (22899) 1999 TO14 satellite a few kilometers across, the typical angular separa- (Merline et al., 2003b) and (17246) 2000 GL74 (Tamblyn et tion is generally less than an arcsecond with a contrast of al., 2004), both of which are small MBAs. No satellites have 5–10 mag [computed as 2.5 log(Fp/Fs), where F is the flux been discovered around any of the seven asteroids recently and p and s indicate primary and secondary, respectively]. visited by spacecraft: (4) Vesta, (21) Lutetia, (2867) Šteins, In some situations, direct images can actually resolve the (4179) Toutatis, (5535) Annefrank, (25143) Itokawa, and primary. A 50–100-km-diameter asteroid at 2 AU subtends (132524) APL. The number of known large MBAs with 34–68 mas while the diffraction limit of a 10-m telescope satellites is now 16, which includes the only known large at a typical imaging wavelength of 1.2 μm is about 30 mas. doubly synchronous system, (90) Antiope (Merline et al., Although the diffraction limit is not reached, it can be ap- 2000; Michałowski et al., 2004; Descamps et al., 2007, proached with high-performance AO instruments in excellent 2009). The fraction of large MBAs with satellites is difficult

Fig. 6. Satellite detection by direct imaging with adaptive optics (AO). (a) Image of asteroid (41) Daphne (Vmag = 10) obtained with a groundbased AO-fed camera (NACO at ESO VLT, 5 s exposure). (b) Same image after subtraction of the flux from the primary, enabling more accurate measurements of the flux and position of the secondary. (c) Orbit determination. The relative positions of the satellite from VLT/ NACO and Keck/NIRC2 images are indicated. Figure adapted from Carry (2009). Margot et al.: Asteroid Systems: Binaries, Triples, and Pairs 363 to estimate because of a complex dependence of satellite to Hektor’s equator (Marchis et al., 2014). (617) Patroclus detectability on primary-to-secondary angular separation and is unusual because it has two components of similar size in primary-to-secondary flux ratio. However, because several a relatively tight (~680 km) orbit, with a normalized total independent programs have surveyed more than 300 large angular momentum exceeding that available from fission of MBAs, it is likely that the abundance of binaries in large a single parent body (Marchis et al., 2006a). MBAs is substantially smaller than the ~16% abundance in In the transneptunian region, 14 and 64 binary systems NEAs and small MBAs. have been discovered with AO and HST, respectively (John- Properties of large MBA binaries and triples are sum- ston, 2014). The apparent larger abundance of binary TNOs marized in Figs. 7 and 8. With the exception of the nearly in the cold classical belt may be due to a different dynamical equal-mass binary (90) Antiope, the known satellites have environment and formation mechanism (section 5). secondary-to-primary mass ratios between 10−6 and 10−2. All Objects in the Trojan and TNO populations are generally have orbital periods between 1 and 5.5 d, except (379) Huen- too faint for AO observations in natural guide star (NGS) na, whose orbit has a period of ~88 d and an eccentricity mode, in which the science target is also used to measure of ~0.2 (Marchis et al., 2008c). Many orbits have near-zero the properties of the wavefront and command the deformable eccentricity (e.g., Marchis et al., 2008a), likely the result of mirror. These objects can be observed in appulse when their tidal damping, but the inner satellites of triples generally sky position happens to be within <1 arcmin of a bright star. have nonzero eccentricities. These eccentricities may have The advent of laser guide star (LGS) adaptive optics has originated when orbits crossed mean-motion resonances been an important development that has freed the observer while tidally expanding (e.g., Fang et al., 2012). from finding such chance alignments and has opened up a At first glance, large MBA densities appear to cluster in larger fraction of the sky for observation of faint objects. two groups, between 1 and 2 g cm–3 and above 3 g cm–3. Even with LGS, however, the availability of a tip-tilt star However, interpretations are limited by the possibility of (Rmag < 18) within <1 arcmin of the target is still required. systematic errors, including overestimates of volumes and High-resolution and high-contrast imaging capabilities are underestimates of densities (Pravec and Harris, 2007). aggressively sought by instrument builders, in part to enable Because volume uncertainties almost always dominate the direct imaging of exoplanets. Cameras equipped with high- error budget for binary asteroid densities (e.g., Merline et al., performance AO are currently being installed or commis- 2002c; Carry, 2012), it is important to assess the realism of sioned on large groundbased telescopes: the High-Contrast uncertainties associated with volume determinations. Some Coronographic Imager for Adaptive Optics (HiCIAO) on published density values should be regarded with caution Subaru, Gemini Planet Imager (GPI) on Gemini, and Spectro- because overconfidence in the fractional uncertainty of Polarimetric High-contrast Exoplanet REsearch (SPHERE) volume estimates has led to underestimates of bulk density at the European Southern Observatory’s (ESO) Very Large uncertainties. The platinum standard of an orbiting space- Telescope (VLT). These instruments will improve the ability craft yields densities with ~1% accuracy. The gold standard to detect faint satellites orbiting close to their respective pri- of radar observations where tens of images with hundreds maries. However, in most cases, asteroids fall in the faint-end or thousands of pixels per image are used to reconstruct a range of these instrument capabilities. The next generation of detailed three-dimensional shape model yields volumes (and large telescopes (~30 m diameter) such as the Thirty Meter densities) with ~10% accuracy. In contrast, AO images con- Telescope (TMT) and European Extremely Large Telescope tain at most a few independent resolution cells of the target (E-ELT) will provide an improvement in sensitivity by a asteroid. Shape reconstructions based on AO images and/or factor of ~10 and in angular resolution by a factor of ~3 lightcurve data may not routinely yield volume accuracies compared to current 10-m telescopes. With the anticipated at the 10% level, although one analysis reached that level development of AO capabilities at shorter wavelengths, (Carry et al., 2012). In the absence of precise volume infor- the second generation of instruments at these facilities is mation, one might be tempted to infer bulk densities from expected to provide improvements in angular resolution by the theory of fluid equilibrium shapes, but this approach is a factor of ~5. Such instruments may allow detection of the problematic (Holsapple, 2007; Harris et al., 2009). small MBA binaries that are currently beyond the reach of In the Jupiter Trojan population, one satellite to (624) Hek- direct imaging instruments. In many of these systems, the tor has been reported (Marchis et al., 2006b) since the dis- components are separated by only a few milliarcseconds and covery of the first Trojan satellite to (617) Patroclus (Merline the size ratios are larger than in large MBA binaries, resulting et al., 2001). These are the only Trojans confirmed to have in flux ratios closer to unity. satellites in spite of several active search programs. The apparent low abundance of binary Trojans is intriguing and, 2.6. Spectral Observations of Main-Belt-Asteroid if confirmed, may provide additional support for the idea and Trojan Systems that Jupiter Trojans originated in the transneptunian region (Morbidelli et al., 2005; Levison et al., 2009) where they It is generally difficult to separate the light emitted or re- experienced a different collisional environment than in the flected from the secondary from that of the brighter primary. main belt of asteroids. (624) Hektor has a satellite in a ~3-d Nevertheless, such observations can be attempted when the orbit that is eccentric (~0.3) and inclined (~50°) with respect secondary happens to be at a large angular separation from 364 Asteroids IV

1020 10–2

1019 10–3

1018 10–4 Mass Ratio 1017 10–5 System Mass (kg)

1016 10–6

300 5.5 5.0 250 4.5 200 4.0 3.5 150 3.0 100 2.5

Diameter (km) 2.0 50 Orbital Period (d) 1.5 0 1.0

4.0 1400 3.5 1200 )

–3 3.0 1000 2.5 2.0 800 1.5 600 1.0 Density (g cm 400

0.5 Semimajor Axis (km) 0.0 200

8.5 0.18 8.0 0.16 7.5 0.14 7.0 0.12 6.5 0.10 6.0 0.08

5.5 Eccentricity 0.06 Spin Period (h) 5.0 0.04 4.5 0.02 4.0 0.00 (243) Ida (87) Sylvia (283) Emma (41) Daphne (93) Minerva (22) Kalliope (702) Alauda (130) Elektra (45) Eugenia (107) Camilla (87) Sylvia (I) (317) Roxane (379) Huenna (762) Pulcova (87) Sylvia (II) (283) Emma (I) (41) Daphne (I) (216) Kleopatra (93) Minerva (I) (121) Hermione (22) Kalliope (I) (702) Alauda (I) (130) Elektra (I) (45) Eugenia (I) (93) Minerva (II) (107) Camilla (I) (45) Eugenia (II) (762) Pulcova (I) (216) Kleopatra (I) (121) Hermione (I) (216) Kleopatra (II)

Fig. 7. Properties of large MBA binaries and triples, exclud- Fig. 8. Properties of satellites of large MBAs, excluding ing the doubly synchronous (90) Antiope. Error bars or upper outliers (90) Antiope and (379) Huenna (see text). Satellites limits, when available, are shown. Based on data compiled of (243) Ida and (317) Roxane, whose orbits are not well by Johnston (2014) from references therein. known, are not shown. Based on data compiled by Johnston (2014) from references therein. Margot et al.: Asteroid Systems: Binaries, Triples, and Pairs 365 the primary, when the system is undergoing mutual events, 270 N or with the help of an integral field spectrograph. Spectra of (22) Kalliope and its satellite Linus in the 1–2.4- 260 μm region appear to be similar (Laver et al., 2009), which the authors attribute to satellite formation after a major impact on the precursor body. Observations of both components of 250

(90) Antiope in the same spectral region also shows surface E

reflectances that are similar Marchis( et al., 2011). The spec- (km) Y 240 trum of (379) Huenna is characteristic of C-type asteroids and the secondary does not exhibit a significantly different taxonomic type (DeMeo et al., 2011). Both components 230 of (809) Lundia are consistent with a V-type classification (Birlan et al., 2014). 220 In the mid-infrared, Spitzer observations of the Trojan –150 –160 –170 –180 –190 –200 –210 (617) Patroclus, including during mutual events, provided X (km) size estimates for its components and a thermal inertia of 20 ± 15 J s−1/2 K−1 m−2 (Mueller et al., 2010). Spitzer ob- servations combined with photometric results in the visible Fig. 9. The apparent shape of Linus, a satellite of (22) Kal- yielded size and albedo estimates for (624) Hektor (Emery et liope (Margot and Brown, 2003), detected by stellar oc- al., 2006). Spitzer observations did not resolve the binaries cultations. In this analysis, the profile of the satellite (solid and results typically cannot be compared to observations that curve) fitted to the observed chords (straight lines) yields an equivalent diameter of 30 ± 6 km. Dashed curves show the place many resolution elements on individual components. corresponding uncertainty of the fitted profile, and dashed One exception is 2000 DP107, where analysis of Spitzer lines show negative detections. Figure adapted from Des- –3 data yields a system density of 0.9 ± 0.3 g cm (Marchis camps et al. (2008). et al., 2012) and the radar results indicate 1.4 ± 0.2 g cm–3 (Naidu et al., 2015). satellite around the Trojan (911) Agamemnon has been sug- 2.7. Stellar Occultations of Main-Belt-Asteroid gested (Timerson et al., 2013) but not yet confirmed. The oc- and Trojan Systems cultation technique has also been used to detect rings around the Centaur (10199) Chariklo (Braga-Ribas et al., 2014). Stellar occultations provide a way of detecting compo- One strength of the stellar occultation technique lies in nents of a multiple-asteroid system, of placing bounds on the fact that the observability of the event depends mainly component sizes, and of obtaining the relative positions of on the brightness of the star and not of the asteroid or sat- components on the plane of the sky. A recording of star ellite. Stellar occultations can thus be used to detect small light as a function of time shows a deep extinction when a (kilometer-sized) satellites, even those that are close to the target body crosses the line of sight between the observer primary and that would remain undetected in direct imaging. and the star. This can be interpreted in terms of a chord on Another strength of the technique is the potential for the apparent disk of the target body projected on the plane high-precision measurements. Stellar occultations are based of the sky. If several observers are placed across the occul- on time-series photometry. Given a sufficiently high cadence tation path on the surface of Earth, multiple chords can be (e.g., 10–30 images per second), it is possible to obtain a obtained, and the size and shape of the target projected on precision of a few milliarseconds on the relative position the sky can be reconstructed (Fig. 9). When two or more of binary components, which is 5–10 times better than with components are present, it is also possible to measure their direct imaging with current instrumentation. relative position. While the reliability of this technique was Finally, well-sampled stellar occultations allow for re- disputed a decade ago due to the lack of digital recordings, covery of the size and apparent shape of asteroids and their the availability of low-cost cameras and global positioning satellites, whereas optical lightcurves and direct imaging systems has enabled a dramatic improvement in the preci- observations primarily provide the diameter ratio of the sion of timing reports. Stellar occultations have become an components and more limited shape information. So far, four important observational tool for the study of binary asteroids. successful observations of satellite size and shape have been Early reports (e.g., Binzel and van Flandern, 1979) of reported: Linus, satellite of (22) Kalliope (Descamps et al., asteroids suspected to be binaries on the basis of occultation 2008); Romulus, the outer satellite of (87) Sylvia (Berthier et data [including (3) Juno, (6) Hebe, (9) Metis, (12) Victoria, al., 2014); and both components of the equal-sized binaries (18) Melpomene, (146) Lucina, and (532) Herculina] have (90) Antiope (Bartczak et al., 2014) and (617) Patroclus remained largely unconfirmed despite extensive follow-up (Buie et al., 2014). searches. However, it is likely that the outer satellite of Despite all these strengths, there remains a relatively low (216) Kleopatra was detected during a 1980 occultation number of well-covered stellar occultation events. This is (Dunham, 1981; Descamps et al., 2011). The detection of a due, in part, to the requirement of successful observations at 366 Asteroids IV many stations. Owing to uncertainties on both the star and (Harris et al., 2009; Fahnestock and Scheeres, 2009); the asteroid positions, the occultation path can shift by several possibility of significant radiative evolution (Ćuk and Burns, tens or even hundreds of kilometers on Earth compared to the 2005; Ćuk, 2007; Ćuk and Nesvorný, 2010; McMahon and prediction. Observers must therefore spread geographically Scheeres, 2010a,b); and the possibility of a stable equilib- to cover an event, but the detection of a satellite by several rium between tidal and radiative evolution (Jacobson and stations requires a fine grid of observers. Scheeres, 2011a). The situation is, however, expected to improve dramati- Several radar datasets provide exquisite constraints cally with the availability of the Gaia stellar catalog and bet- for dynamical studies. Reflex motion has been measured ter asteroid orbits (Tanga and Delbo, 2007). Predictions of for 2000 DP107 (Margot et al., 2002; Naidu et al., 2015), the occultation paths (for the center of mass) will be accurate 1999 KW4 (Ostro et al., 2006), and 1991 VH (Naidu et to a few kilometers, and the main source of uncertainty will al., 2012), allowing masses of individual components to be become the prediction of the relative position of the satellite determined. Because detailed component shapes are also around the primary. available, one can fully model the system dynamics and study spin-orbit coupling in detail (Scheeres et al., 2006; 2.8. Other Observations Fahnestock and Scheeres, 2008; Naidu and Margot, 2015). One finding from this work is that even moderately elongated There have been several attempts to use groundbased secondaries on mildly eccentric orbits are likely to experience interferometers to measure the angular separation of binary chaotic rotation that substantially affects binary evolution systems (Delbo et al., 2009; Carry et al., 2015). However, timescales (Fig. 10). asteroid satellites are too faint for current interferometers operating in the visible and near-infrared and at the edge of 4. SMALL ASTEROIDS: SYNTHESIS detection in the mid-infrared. Future instrumentation may allow such observations. There are also prospects for obser- 4.1. Rotational Fission Hypothesis vations with the Atacama Large Millimeter Array (ALMA) submillimeter array (Busch, 2009). With the exception of the doubly synchronous binary asteroid systems, the primary asteroids of all small binary 3. DYNAMICS systems are rapidly rotating (within a factor of only a few of the critical disruption spin limit for bodies with no shear In parallel with advances in instrumentation and observ- or tensile strength wd = 43πρG ). Furthermore, almost all ing capabilities, the field has seen tremendous developments in understanding the dynamical processes that affect asteroid systems. This has been enabled in large part by the avail- 3.0 ability of detailed shape models and orbital parameters, by the need to model the dynamics of newly discovered triple 2.5 systems, and by the desire to understand formation and 2.0 evolution processes. A non-exhaustive list of some dynamical problems that 1.5 /n have been explored since Asteroids III includes the stability p . θ of asteroid satellite orbits (Scheeres, 2002; Frouard and Com- 1.0 père, 2012); the dynamics around triaxial bodies (Scheeres, 0.5 2009a); the fate of asteroid ejecta (Scheeres, 2007); the for- mation of contact binaries via dynamical evolution (Scheeres, 0.0 2009a; Taylor and Margot, 2011, 2014); the genesis of eccen- –0.5 tric and mutually inclined orbits (Fang et al., 2011; Fang and 0 90 180

Margot, 2012c); the orbital determination of triple systems θp (°) using point-mass approximations (Marchis et al., 2010) and full N-body calculations (Fang et al., 2012); the influence Fig. 10. Surface of section plot showing the possible rotation- of Kozai cycles on binaries (Perets and Naoz, 2009; Fang al regimes of the ~200 m secondary of 1991 VH (secondary and Margot, 2012b); the effects of close planetary encounters elongation a/b = 1.5 and mutual orbit eccentricity e = 0.05). on mutual orbits (Fang and Margot, 2012a) and spin states The plot shows the angle between the long axis and the line (Takahashi et al., 2013); the complex spin-orbit interactions .of apsides of the mutual orbit, qp, against its time derivative, q with irregular component shapes (Scheeres et al., 2006), p, normalized by the mean motion, n, at each pericenter passage. Five trajectories are illustrated (from top to bot- including the libration and irregular rotation of secondaries tom: nonresonant quasiperiodic, periodic, chaotic, periodic, (Naidu and Margot, 2015); the influence of internal structure periodic). While trapped in the sea of chaos, the secondary (Goldreich and Sari, 2009), material properties (Taylor and experiences torques on its permanent deformation that result Margot, 2011), and nonspherical shapes (Taylor and Margot, in a highly variable spin rate, preventing BYORP-type evolu- 2014) on tidal evolution; the possibility of tidal saltation tion. Figure from Naidu and Margot (2015). Margot et al.: Asteroid Systems: Binaries, Triples, and Pairs 367 known small binary asteroids have high angular momentum as a function of the secondary-to-primary mass ratio q is contents (Pravec and Harris, 2007). These characteristics (Scheeres, 2007) are not consistent with formation following a subcatastrophic impact, capture through a three-body interaction in the near- 1 + q wwqd= 3 (1) Earth or main belt, or capture after a catastrophic impact. 1 + q13/ Instead, they are indicative of formation from a rotational ( ) fission event (e.g., Margot et al., 2002; Pravec and Harris, 2007). The rotational fission hypothesis posits that a parent This is the exact solution for two spheres resting on each other asteroid can be torqued to a rotation rate so great that the with a mass ratio of q and rotating about the axis of maximum centrifugal accelerations overpower the gravitational accelera- moment of inertia. tions holding a strengthless asteroid together (Weidenschilling, The spherical component model described above demon- 1980). It is possible that some small asteroids have cohesive strates the important reality that the larger the mass ratio q or molecular strength in addition to self-gravity (e.g., Rozitis of the two future binary members, the slower the required et al., 2014). In these cases, the centrifugal accelerations must rotation rate necessary to create the binary system. This overcome these additional forces in order for the asteroid to slower required rotation rate translates into a small initial fission (Pravec and Harris, 2000; Sánchez and Scheeres, free energy for the ensuing binary system. The free energy 2014). At rapid rotation rates, loose surface material can flow Ef is the energy that is accessible to the different energy from high-latitude regions to the equator along potential gra- reservoirs in the system, including the rotation states of dients (Ostro et al., 2006). It has been shown that rotational each member and the orbit. It does not include the internal acceleration could trigger local slope failures and landslides, binding energy of each object. The free energy is an impor- which can form the canonical top shape and equatorial bulge tant quantity because it determines the boundedness of the seen on primary components in small multiple-asteroid sys- system. Bound systems have negative free energy, while tems (Walsh et al., 2008; Harris et al., 2009). unbound systems have positive free energy. An unbound Bottke et al. (2002) proposed a YORP-induced rotational binary system implies that the system is capable of disrup- fission hypothesis. It has since been shown that the YORP tion but does not imply that the system will disrupt. For effect controls the rotational acceleration of small asteroids the idealized case of two spheres, the free energy can be (Bottke et al., 2006; Marzari et al., 2011) and naturally ex- expressed as (Scheeres, 2007) plains the period distribution among small asteroids (Pravec 25 et al., 2008; Rossi et al., 2009; Polishook and Brosch, 2009). 2πrwdpR Ef = fq() (2) Furthermore, including the YORP-induced rotational fission 15 hypothesis in size-frequency distribution models improves the agreement with observations (Jacobson et al., 2014a). where Rp is the radius of the primary and f(q) is an algebraic, The observed characteristics of the systems described in monotonically decreasing function for 0 < q ≤ 1. For the sections 2.1–2.3 as well as thermal inertia observations equation above corresponding to two spheres, the function (Delbo et al., 2011) are consistent with a binary formation crosses zero when q ≈ 0.204. Similar equations can be writ- mechanism that involves spin-up and mass shedding. The ten for any two component shapes, but q ~ 0.2 remains near YORP-induced rotational fission hypothesis is the leading the binding energy transition point, so the model uses this candidate for explaining the formation of binaries, triples, point as a simple approximation. This crossing point divides and pairs among small asteroids. bound systems with negative energy and mass ratios q > 0.2 and unbound systems with positive energy and mass ratios 4.2. Asteroid Pairs q < 0.2. Because of this fundamental difference, high-mass- ratio q > 0.2 and low-mass-ratio q < 0.2 binary systems The YORP effect can increase the spin rate of asteroids evolve differently (Scheeres, 2009a; Jacobson and Scheeres, beyond the critical disruption spin limit, thereby triggering 2011b). Primarily, positive-energy low-mass-ratio systems rotational fission. In actuality, there is some uncertainty will chaotically explore orbital phase space until the major- regarding the spin rate at which disruption occurs — there ity find a disruption trajectory creating an asteroid pair; this may be failure and deformation before fission Walsh( et evolutionary route is unavailable to high-mass-ratio systems. al., 2008; Sánchez and Scheeres, 2011; Cotto-Figueroa et The asteroid pair population provides a natural labora- al., 2013). The critical disruption spin limit also depends tory to test this relationship (Scheeres, 2007; Vokrouhlický on the detailed shapes, masses, and interlocking nature of and Nesvorný, 2008). Pravec et al. (2010) examined many the interior components and any cohesive forces (Scheeres, asteroid pair systems and measured the rotation rate of the 2007, 2009b; Sánchez and Scheeres, 2014). Despite ignor- primary and the absolute magnitude difference between the ing these details, simple calculations provide a rotational pair members. These two quantities should follow a simple fission model that can be compared directly and successfully relationship related to wq, although many of the ignored with observations. details mentioned at the beginning of this section can move If a spherical approximation of each component is made, asteroids away from this relationship. Indeed, Pravec et then the rotational breakup spin rate wq necessary for fission al. (2010) discovered that asteroid pairs do follow this 368 Asteroids IV relationship (Fig. 5). Furthermore, they found that the large an important role in distinguishing the two evolutionary members of asteroid pairs have a broader range of elonga- pathways. Along the high-mass-ratio pathway, both binary tions than the primaries of binary systems, consistent with members tidally synchronize and then evolve according to the findings of Jacobson and Scheeres (2011b) that prolate the BYORP effect. primaries are less likely to remain in a bound binary system Along the low-mass-ratio pathway, the binary system is after rotational fission. Thus, there is strong evidence to unbound. Since these systems are chaotic, many are dis- support the hypothesis that asteroid pairs are the products rupted and become asteroid pairs. During this chaotic binary of rotational fission. state, the secondary can often go through rotational fission Asteroid pairs continue to be a fertile observational land‑ itself, although this rotational fission is torqued by spin-orbit scape. Since dynamical integrations can derive the “birth- coupling (Fig. 10) rather than the YORP effect. Loss of ma- date” of such systems, observers can test ideas regarding terial from the secondary stabilizes the remaining orbiting space-weathering timescales and YORP evolution after fis- components. The lost mass may reaccrete onto the primary, sion (Polishook et al., 2014a; Polishook, 2014). Along with perhaps contributing to the observed equatorial ridges, or may binary systems, the surfaces of asteroid pairs may provide escape from the system. In these cases, the system undergoes clues in the future regarding the violence of the rotational another chaotic binary episode with three possible outcomes: fission process (Polishook et al., 2014b). a reshaped asteroid, an asteroid pair, or a stable binary. These binaries still possess positive free energy such that they may 4.3. Binary and Triple Systems disrupt if disturbed. In other cases, the system retains three components after secondary fission. While the numerical Jacobson and Scheeres (2011b) showed that after ro- simulations of Jacobson and Scheeres (2011b) did not yield tational fission there are a number of possible outcomes. this latter outcome, it is possible that this pathway explains Their numerical studies produced the evolutionary flow chart the existence of stable triple systems. shown in Fig. 11; many of these outcomes were also found After stabilization of the low-mass-ratio binary system, by Fang and Margot (2012c). The high- and low-mass-ratio the secondary synchronizes due to tides (e.g., Goldreich and distinction for rotational fission emphasized above plays Sari, 2009), although some satellites may be trapped in a

YORP Process Tidal Process 5 6 Contact Binary ~ 10 –10 yr ~ 104–106 yr BYORP Process 5 6 q ~> 0.2 ~ 10 –10 yr Chaotic Binary Doubly Synchronous Binary Asteroid Pair Tidal Process ~ 106–107 yr

Chaotic Triple Stable Triple Asteroid Dynamic Processes ~< 1 yr

YORP Process Tidal Process Reshaped Asteroid < 5 6 ~ 104–106 yr q ~ 0.2 ~ 10 –10 yr BYORP Process ~ 105–106 yr Chaotic Binary Stable Binary

Asteroid Pair Dynamic Processes ~< 1 yr

Reshaped Asteroid Asteroid Pair

Fig. 11. Flowchart showing the possible evolutionary paths for an asteroid after it undergoes rotational fission. Each arrow is labeled with the dominant process and an estimated timescale for this process. Underlined states are nominally stable for a YORP effect timescale. Figure from Jacobson and Scheeres (2011b). Margot et al.: Asteroid Systems: Binaries, Triples, and Pairs 369 chaotic rotation state for durations that exceed the classic spin synchronization timescales (Naidu and Margot, 2015). Then the system evolves according to the BYORP effect and tides. These binary evolutionary processes and their outcomes are discussed in the chapter by Walsh and Jacob- son in this volume. As shown in Fig. 11, these evolutionary paths include each of the binary morphologies identified in this chapter and by other teams (Pravec and Harris, 2007; Fang and Margot, 2012c). In particular, the formation of wide asynchronous binaries such as (1509) Esclangona, (4674) Pauling, (17246) 2000 GL74, and (22899) 1999 TO14 is best explained by a rotational fission mechanism Pol( - ishook et al., 2011) followed by BYORP orbital expansion (Jacobson et al., 2014b). An alternative formation mechanism for triples such as Fig. 12. Numerical simulations show that binaries can form (153591) 2001 SN263 and (136617) 1994 CC is that after creating a stable binary system, the primary undergoes rota- as a result of large impacts between asteroids. In some tional fission a second time. As long as the third component scenarios, impact debris can remain gravitationally bound to the target body, forming a satellite (SMATs). This process is on a distant enough orbit, then this process may result in likely explains the formation of large MBA binaries. In other a stable triple system (Fang et al., 2011; Fang and Margot, scenarios, two fragments from the escaping ejecta have suf- 2012c; Jacobson et al., 2014b). ficiently similar trajectories, such that they become bound to one another (EEBs). Figure from Durda et al. (2004). 5. LARGE ASTEROIDS: SYNTHESIS

The primaries of most known binary and triple asteroids greater than 20 km have spin periods in the range of 4 h to 6. CONCLUSIONS 7 h (Fig. 7). While these spin rates are not near the disruption spin limit, they are typically faster than the mean spin rates Studies of binaries, triples, and pairs remain a fertile for asteroids of similar sizes. The total angular momentum ground for observing processes that are important in planet content, however, is well below that required for rotational formation and for measuring quantities that are difficult to fission. The secondary-to-primary mass ratios in these sys- obtain by other means. These include masses and densities as tems range from 10−6 to 10−2. These properties are consistent well as thermal, mechanical, and interior properties. Binaries with satellite formation during large collisions (Fig. 12). or triples have been found in ~50 NEAs, ~50 small MBAs, Durda et al. (2004) have shown in numerical simulations ~20 large MBAs, and 2 Trojans. A unifying paradigm based that impacts of 10- to 30-km-diameter projectiles striking on rotational fission and post-fission dynamics explains the at impact velocities between 3 km s−1 and 7 km s−1 can formation of small binaries, triples, and pairs. Because the produce satellites that match observed properties. Multiple Sun-powered rotational fission process is unrelenting, and asteroid systems, e.g., (45) Eugenia (Merline et al., 1999; because the production of pairs is a frequent outcome of this Marchis et al., 2007) and (87) Sylvia (Margot and Brown, process, a substantial fraction of small bodies likely originated 2001; Marchis et al., 2005a), can also plausibly form through in a rotational disruption event. This origin affects the size collisions. distribution of asteroids and may explain the presence of There is more uncertainty related to the formation of single NEAs with equatorial bulges observed with radar. Small (90) Antiope and (617) Patroclus, which are both too large satellites of large MBAs are likely formed during large colli- to be substantially affected by YORP. Hypotheses for the sions. Advances in instrumentation, observational programs, formation of (90) Antiope include primordial fission due to and analysis techniques hold the promise of exciting findings excessive angular momentum (Pravec and Harris, 2007), in the next decade. an improbable low-velocity collision of a large impactor (Weidenschilling et al., 2001), or shrinking of an initially REFERENCES wide binary formed by gravitational collapse (Nesvorný et Bartczak P., Michałowski T., Santana-Ros T., and Dudziński G. (2014) al., 2010). Gravitational collapse in a gas-rich protoplanetary A new non-convex model of the binary asteroid 90 Antiope obtained disk has been invoked to explain the formation of numer- with the SAGE modelling technique. Mon. Not. R. Astron. Soc., 443, ous binaries in the transneptunian region. (617) Patroclus 1802–1809. Becker T. M., Howell E. S., Nolan M. C., Magri C., Pravec P., Taylor may be a primordial TNO that avoided disruption during P. A., Oey J., Higgins D., Világi J., Kornoš L., Galád A., Gajdoš emplacement in the Trojan region (Nesvorný et al., 2010). Š., Gaftonyuk N. M., Krugly Y. N., Molotov I. E., Hicks M. D., Wide TNO binaries would not be expected to survive this Carbognani A., Warner B. D., Vachier F., Marchis F., and Pollock J. T. (2015) Physical modeling of triple near-Earth asteroid (153591) process, but encounter calculations (e.g., Fang and Margot, 2001 SN263 from radar and optical light curve observations. Icarus, 2012a) show that tight binaries would. 248, 499–515. 370 Asteroids IV

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