MNRAS 000,1–26 (2020) Preprint 23 March 2021 Compiled using MNRAS LATEX style file v3.0

Astrocladistics of the Jovian Trojan Swarms

Timothy R. Holt,1,2★ Jonathan Horner,1 David Nesvorný,2 Rachel King,1 Marcel Popescu,3 Brad D. Carter,1 and Christopher C. E. Tylor,1 1Centre for Astrophysics, University of Southern Queensland, Toowoomba, QLD, Australia 2Department of Space Studies, Southwest Research Institute, Boulder, CO. USA. 3Astronomical Institute of the Romanian Academy, Bucharest, Romania.

Accepted XXX. Received YYY; in original form ZZZ

ABSTRACT The Jovian Trojans are two swarms of small objects that share Jupiter’s orbit, clustered around the leading and trailing Lagrange points, L4 and L5. In this work, we investigate the Jovian Trojan population using the technique of astrocladistics, an adaptation of the ‘tree of life’ approach used in biology. We combine colour data from WISE, SDSS, Gaia DR2 and MOVIS surveys with knowledge of the physical and orbital characteristics of the Trojans, to generate a classification tree composed of clans with distinctive characteristics. We identify 48 clans, indicating groups of objects that possibly share a common origin. Amongst these are several that contain members of the known collisional families, though our work identifies subtleties in that classification that bear future investigation. Our clans are often broken into subclans, and most can be grouped into 10 superclans, reflecting the hierarchical nature of the population. Outcomes from this project include the identification of several high priority objects for additional observations and as well as providing context for the objects to be visited by the forthcoming Lucy mission. Our results demonstrate the ability of astrocladistics to classify multiple large and heterogeneous composite survey datasets into groupings useful for studies of the origins and evolution of our Solar system. Key words: minor planets , asteroids: general – methods: data analysis – surveys – astronomical databases: miscellaneous

1 INTRODUCTION skies. As a result, more than 8700 Jovian Trojans have been discov- ered to date1. We show the current distribution of objects around At the Jovian Lagrange points, 60◦ ahead (L ) and behind (L ) 4 5 the Jovian Lagrange points in Fig.1. Whilst objects can still be the giant planet in its orbit, there are two swarms of small Solar temporarily captured to orbits within the Trojan clouds, without the system objects, collectively termed the Jovian Trojans. Members destabilisation of the clouds caused by planetary migration, such of the leading swarm, which librate around Jupiter’s L Lagrange 4 captures are very short-lived (e.g. 2019 LD Hsieh et al. 2021; point, are named after the Greek heroes in the Iliad (Nicholson 2 Steckloff et al. 2020; Bolin et al. 2021). At any time, it is likely that 1961), with members of the trailing swarm being named for the there are a number of such ‘temporary Trojans’, whose residence in Trojan heroes. The first Jovian Trojans, 588 Achilles (1906 TG), the swarms can be measured in years, decades, or centuries at most 617 Patroclus (1906 VY), 624 Hektor (1907 XM) and 659 Nestor (e.g. Horner & Wyn Evans 2006). (1908 CS) were discovered in the early 20th century (Wolf 1907; arXiv:2103.10967v1 [astro-ph.EP] 19 Mar 2021 It is now well established that the Jovian Trojans did not form in Heinrich 1907; Strömgren 1908; Ebell 1909). In the decades that their current orbits (see Emery et al. 2015, for review). Instead, they followed, the number of known Trojans grew slowly, as a result of are thought to have been captured as a byproduct of the migration of ongoing work at the Heidelberg observatory (e.g. Nicholson 1961; Jupiter. Such capture would require some mechanism by which the Slyusarev & Belskaya 2014). With the advent of CCD imaging, in Trojans could become trapped in such dynamically stable orbits. the later part of the 20th Century, the rate at which Trojans were One leading theory to explain the capture of the Jovian Tro- discovered increased markedly, such that, by the end of the century, jans is the proposed period of instability in the early Solar system a total of 257 had been confirmed (Jewitt et al. 2000). Nesvorný et al.(2013) that has come to be known as the ‘Nice’ Over the last twenty years, the rate at which Jovian Trojans model (Tsiganis et al. 2005b; Morbidelli 2010; Levison et al. 2011; have been discovered has increased still further, as a result of new instrumentation and automated surveys coming online to scour the 1 Taken from the NASA-JPL HORIZONS Solar system Dynamics Database https://ssd.jpl.nasa.gov/ (Giorgini et al. 1996) taken 13th October, ★ E-mail: [email protected] (TRH) 2020 October 13

© 2020 The Authors 2 T. R. Holt et al.

models, by invoking mixing in the Jovian feeding region. There- fore, the observed inclinations are considered to be primordial in these simulations, and are preserved during transportation as Jupiter migrates. In contrast to the idea that the captured Trojans formed on inclined orbits, earlier studies of smooth, non-chaotic migration (e.g. Lykawka & Horner 2010) showed that Jupiter could capture a significant population of Trojans. The common feature of all of the proposed capture models, however, is that the capture of the Jo- vian Trojans occurred during the Solar system’s youth (Emery et al. 2015). These two competing theories for the origins of the Trojans highlight the importance of the population in our understanding of the early Solar system.

1.1 Taxonomy and wide Field Surveys The methods by which the Solar system’s small bodies are classified, can be broken down into two broad categories. First, the objects are grouped based on their orbital parameters, in combination with any evidence of cometary activity, into broad dynamical clusters (Near- Earth Asteroid; Main Belt Asteroid; Centaur etc. see Horner et al. 2020, for review). Those objects can then be further classified based on their visual and infrared spectra. This classification is useful as Figure 1. Distribution of the Jovian Trojans after Horner et al.(2020). The the resulting taxonomy can indicate that certain objects share a upper panels show the positions of the Trojans relative to the planets on 2000 common origin. January 1, 00:00 in XY (left) and XZ (right) planes. The lower panels show Building on an original taxonomy by Tholen(1984, 1989), the the Trojans in semi-major axis vs inclination space (left) and semi-major modern iteration of this observationally-motivated categorisation is axis vs eccentricity space (right). All data from NASA HORIZONS (Giorgini based on the works of Bus(2002) and DeMeo et al.(2009, 2015), et al. 1996), access on 2020 October 13. Black points are initially stable and is collectively termed the Bus-DeMeo taxonomy (see DeMeo objects, from the AstDyS (Knežević & Milani 2017) dataset. Grey points et al. 2015, for summary). In this taxonomy, spectra are used to are potentially transient objects. Blue points identify those objects used in place objects into categories known as ’types’. Each type reflects a this work. major compositional category, for example, the C-types are the most numerous and correspond to Carbonaceous chondrite meteorites. Since the Bus-DeMeo taxonomy requires spectral information in Nesvorný & Morbidelli 2012; Nesvorný 2018). The Nice model order to classify asteroids, its use is naturally limited to those objects invokes a period of instability triggered by the slow migration of bright enough for such data to have been obtained – either through Jupiter and Saturn, in response to their interactions with the debris wide-field surveys, or targeted observations. As a result, to date left behind from planet formation. Eventually, that migration drove less than 1 per cent of the Trojan population have been officially the two planets into an unstable architecture, leading to a period classified under this scheme. In the initial Tholen(1984, 1989) of chaotic evolution for objects throughout the Solar system. Dur- data-set, 22 Trojans were classified, with a further 12 in the Small ing that period of instability, the Jovian Trojan clouds would also Solar system Object Spectral Survey (S3OS3)(Lazzaro et al. 2004). have been destabilised. As a result, some of the debris being flung In these initial surveys, D-types (85.29 per cent) were found to around the system by the migrating giant planets would have expe- dominate the population. This is consistent with the dynamical rienced temporary capture to the Jovian Trojan clouds. As Jupiter modeling, as the D-types are thought to have formed in the outer and Saturn migrated away from the location of the instability, the solar system (Morbidelli et al. 2005; Levison et al. 2009) and those Jovian Trojan clouds would have become stable once again, freezing found in the Main belt are interlopers (DeMeo et al. 2014). in place those temporarily captured Trojans, making their capture Two large members of the Trojan population, 617 Patroclus permanent (Roig & Nesvorný 2015). More recently, it has been (1906 VY) and 588 Achilles (1906 TG), were initially classified suggested that the required instability in the outer Solar system may as P-type objects, though in recent years, that category (P-type) has have been triggered by the ejection of a fifth giant planet (Nesvorný been degenerated into the X-types Bus(2002); DeMeo et al.(2009). & Morbidelli 2012; Deienno et al. 2017) from the Solar system. For this work, we substitute any members of the ‘P-type’ from their This scenario has become known as the Jumping-Jupiter model, original works into the X-types, including the hybrid ‘DP-type’ and has been invoked to explain a number of peculiarities in the (now DX-type) and ‘PD-type’ (now XD-type). Amongst the small distribution of Solar system small bodies, including the origin of number of Trojans classified in those initial studies, the population the Jovian Trojans. was found to include another X-type, 3451 Mentor (1984 HA1), and A recent alternative to the scenarios painted above proposes an Xc-type, 659 Nestor (1908 CS), as well as two C-types, namely instead that the Trojans were captured from the same region of the 4060 Deipylos (1987 YT1) and 1208 Troilus (1931 YA). Solar system’s protoplanetary disc as Jupiter, and were both cap- Following these initial spectral surveys, Bendjoya et al.(2004) tured and transported during the planet’s proposed inward migration investigated 34 Trojans spectrally between 0.5 and 0.9 휇푚, finding (Pirani et al. 2019a). A recent update to this in-situ transport model again that the majority were D-type (70.6 per cent), with several (Pirani et al. 2019b) explains the observed excitation in the orbital X-types (11.7 per cent) and C-types (5.8 per cent). There were inclinations of the Jovian Trojans, which is a natural byproduct two objects, 7641 (1986 TT6) and 5283 Pyrrhus (1989 BW), that of the chaotic evolution proposed in the Nice and Jumping-Jupiter showed a negative slope and were not classified, although 7641

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 3

(1986 TT6) was later classified as as D-type by Hasselmann et al. (2012), based on new observations. In a larger set of visual spectral 1.0 MOVIS surveys, Fornasier et al.(2004, 2007) examined a further 80 Jovian 0.8 GAIA

Trojans, and added their classifications. Though these classifications e s n comprise a total of just 2.14 per cent of the Trojan population, they o p 0.6 g s can still provide indications of the compositional distribution of the e R

r e population as a whole. t 0.4 l i F In recent years, a number of studies have begun to gather data Y J H K WISE 1 WISE 2 on the colour and physical properties of the Trojans. Wide-band sur- 0.2 s veys can give indications of taxonomic classification, circumventing ug r i z 0.0 SDSS the need for full spectra to be obtained of object. Several studies 1 2 3 4 5 have investigated the colours of the Jovian Trojans (e.g. Emery & Wavelength [um] Brown 2003; Dotto et al. 2006). Once again, the initial observations Figure 2. Wavelengths of the filters surveys used in this study. were limited in number, yielding data for less than 100 objects in the Jovian swarm in the infrared (Emery & Brown 2003; Emery et al. 2006, 2011), visual (Fornasier et al. 2004; Dotto et al. 2006; (2017), with the mission visiting two C-types, two D-types and two Fornasier et al. 2007) and broadband UBVRI (Karlsson et al. 2009). X-types. The mission will also visit 3548 Eurybates (1973 SO), As in the prior studies, these initial surveys found that the majority a C-type and the parent body of a collisional family. In combina- of objects studied were best classified as D-types. tion with the Lucy mission, in the coming decades, several relevant With the current generation of large ground-based facilities observational surveys coming online including the Vera Rubin Ob- and space telescopes, recent years have seen a significant increase servatory, with the Legacy Survey of Space and Time (Rubin Obs. in the numbers of Trojans being observed and given preliminary LSST LSST Science Collaboration et al. 2009), the James Web classifications. Grav et al.(2012) observed 557 Trojans at infrared Space telescope (JWST Rivkin et al. 2016), Twinkle (Savini et al. wavelengths, using two Wide-field Infrared Survey Explorer (WISE) 2018) and Nancy Grace Roman Space Telescope ((RST, formally filters. In doing so, they confirmed the prevalence of D-types in the WFIRST) Milam et al. 2016). We explore these in further depth, Trojan population, with such objects dominating both the L4 and with a specific focus on how they relate to the Jovian Trojans and L5 swarms, independent of the size of the Trojans studied (Grav our work, in section6. et al. 2011). Grav et al.(2011, 2012) noted that the population in the WISE dataset was quite heterogeneous, with a mean albedo of 0.07 ± 0.03. In the visual five-band Sloan Digital Sky Survey 1.2 Clustering Methods (SDSS) catalogue (Carvano et al. 2010; Hasselmann et al. 2012), a Contemporary studies of the Jovian Trojans have attempted to iden- total of 461 Trojans have been classified. Unlike previous surveys, tify groups of objects within the population that share common the catalogue includes a measure of the confidence in the assigned dynamical properties. The most effective of these models to date taxonomy. Of the 461 objects in the SDSS dataset, only 106 have has been the Hierarchical Clustering Method (HCM; Zappala et al. significantly high confidence value, greater than 50, to be considered 1990). Several collisional families have already been identified in valid classifications. In using this dataset to make inferences about the Trojan population using this method, despite the number of asteroid taxonomy as across the Solar system, DeMeo & Carry known Trojans being some two orders of magnitude smaller than (2013, 2014) noted that again, the Jovian Trojans are heterogeneous the known population of the main belt (e.g. Milani 1993; Beauge in comparison to other populations. & Roig 2001; Nesvorný et al. 2015). Another family identification In summary, taking data from each of these data-sets (Tholen method, uses the size dependent drift pattern due to the Yarkovsky 1989; Bendjoya et al. 2004; Fornasier et al. 2004, 2007; Lazzaro effect (Bottke et al. 2006) to identify ancestral dynamic families et al. 2004), including those Trojans classified in the SDSS catalogue in main-belt Asteroids (Walsh et al. 2013; Bolin et al. 2017, 2018; with a confidence score of greater than 50 (Hasselmann et al. 2012), Deienno et al. 2020). The technique, while useful in the Main belt, there is a canonical set of 214 Trojans that are classified under the has reduced usefulness in the Trojans. This is due to the depen- 2 Bus-DeMeo taxonomy . As other authors have noted (Grav et al. dence of the Yarkovsky effect on the Solar flux. At the 5.2au mean 2012; Hasselmann et al. 2012; Emery et al. 2015; DeMeo & Carry semi-major axis of the Jovian Trojans, the mean Yarkovsky effect 2013), 72.2 per cent are classified as D-type, which is a much higher is minimal, particularly for Trojans over 1km in diameter (Wang & fraction than is seen in the Main Belt (DeMeo et al. 2015; DeMeo & Hou 2017; Hellmich et al. 2019). Carry 2013; DeMeo et al. 2014) and in the Hilda (Wong & Brown The HCM is a technique that uses Gauss’ equations to find 2017) populations. The remainder of the Trojans classified to date groups in proper element (semi-major axis, eccentricity and incli- in the canonical set are split between the C-types (10.8 per cent) nation) parameter space (Zappala et al. 1990). The rationale behind and X-types (16.5 per cent). these calculations is that the dispersal velocities of the clusters cre- The current generation of surveys are laying the groundwork ated by the collisional disruption of an object would be similar to for our future exploration of the Trojan population. A NASA dis- the escape velocities of the parent body. The unique dynamical sit- covery class mission, Lucy, is set to visit six Jovian Trojans between uation of the Jovian Trojans makes the identification of dynamical 2025 and 2033. One of the justifications for this mission is the di- families using the traditional HCM difficult. Despite this, several versity of taxonomic classes found in the population Levison et al. collisional families are thought to be present amongst the Trojan population (e.g. Nesvorný et al. 2015). More modern dynamical analysis of the Jovian Trojans has identified a total of six canonical 2 The taxonomy is included in the online datasets, available from the families (Brož & Rozehnal 2011; Emery et al. 2015; Vinogradova Github repository for this study https://github.com/TimHoltastro/ 2015; Nesvorný et al. 2015; Rozehnal et al. 2016; Vinogradova holt-etal-2021-Jovian-Trojan-astrocladistics.git 2015). The individual members and numbers in each work are in-

MNRAS 000,1–26 (2020) 4 T. R. Holt et al. consistent, and for this work we follow the canonical six families with similar characteristics are related to one another. As cladistics found in Nesvorný et al.(2015), with their associated members. was originally developed to incorporate incomplete fossil records There are two other modern sets that could be considered, Rozehnal (Hennig 1965), not all characteristics need to be known in order for et al.(2016) or Vinogradova & Chernetenko(2015). Vinogradova a cladistical analysis to be carried out. This allows for the use of & Chernetenko(2015) found families in the L 4swarm using HCM a larger number of characteristics and organisms, without needing with independently derived proper elements, though questioned the to truncate the dataset due to missing values. Whilst cladistics can existence of any families in the L5swarm. Rozehnal et al.(2016) is account for these unknown characteristics, the more that is known incorporated into the canonical set Nesvorný et al.(2015), with sev- about an object/organism, the more confidence that can be placed eral exceptions in the population. In our discussion, we note where in the analysis. Minimising missing data in the analysis would also these differ from the canonical set (Nesvorný et al. 2015). Initial decrease the number of equality parsimonious trees, trees that min- imaging surveys suggested that there is some spectral conformity imises the number of changes, produced during the analysis. The within these dynamical families in the Jovian Trojans (Fornasier result of a biological cladistical analysis is a hierarchical dendritic et al. 2007). More recent observational data has brought this into tree, the ‘Tree of Life’ (Darwin 1859; Hennig 1965; Hug et al. 2016, question (Roig et al. 2008), with a heterogeneity being seen in the e.g.), in which those organisms that are most closely related to one colours of the identified family members. another other are joined by the shortest branch lengths. The advan- The disadvantage of the HCM system is that it only identifies tage of cladistics over other analytical techniques is that it allows the recent family breakups, with the vast majority of objects considered use of multiple characteristics from disjointed datasets, including ‘background’. Another issue with HCM is the issue of ‘chaining’, those that are unknown in some objects. where families are identified with interlopers included due to near The application of cladistics in an astronomical context is anal- proximity in phase space. In an attempt to overcome some of these ogous to the biological framework, in that it facilitates the identi- issues Rozehnal et al.(2016) offer an expansion to the HCM de- fication of groups of objects that likely share a common origin. veloped by Zappala et al.(1990). This new ‘randombox’ method For example, the members of collisional families are expected to uses Monte Carlo simulations to gain statistics on the probability cluster together, due to similarities in their orbital and physical el- that the identified clusters are random in parameter space. Carruba ements. The previously identified collisional families can thus be & Michtchenko(2007) also tried using elements in the proper fre- used to comment on the cladistical methodology. The technique quency domain instead of orbital element space to overcome some has already been used in a growing body of work called ‘astro- of the issues of the HCM. The inclusion of ‘background objects’ can cladistics’ (Fraix-Burnet et al. 2006). Astrocladistics has been used be further mitigated by the inclusion of colours (Parker et al. 2008), to study a wide range of astronomical objects, including galaxies albedo (Carruba et al. 2013), and taxonomy into the family identi- (e.g., Fraix-Burnet et al. 2006), gamma-ray bursts (e.g., Cardone fication pipeline (Milani et al. 2014; Radović et al. 2017), though & Fraix-Burnet 2013) and stellar phylogeny Jofré et al.(2017). these methodologies have focused on the Main-belt families. Within the planetary sciences, Holt et al.(2018) used the technique Though these methods do improve some of the faults identified to investigate the satellite systems of Jupiter and Saturn. in HCM, they still suffer from the issues inherent to the method. In order to use the HCM, a complete parameter space is required. This restricts the dataset in one of two ways, due to the limited information available for most small Solar system bodies. For the 1.3 This work majority of family identification work, (for review, see Nesvorný et al. 2015), only the dynamical elements are used. In order to ex- This is the first time that astrocladistics has been applied to large So- pand the technique to include photometric information, albedo and lar system survey datasets. The extension of the technique presented colours, the number of objects needs to be restricted. For exam- in Holt et al.(2018) to these large datasets could greatly improve our ple, Carruba et al.(2013) used a subset of only 11,609 main belt understanding of the relationships between Solar system objects. By asteroids, out of the approximately 60,000 available in the Sloan increasing the number of Solar system objects that can be studied Digital Sky survey (SDSS) (Ivezić et al. 2002), 100,000 from WISE using astrocladistics, this project will help to establish the method (Masiero et al. 2011), and over 400,000 for which proper elements as a valid analytical tool for the planetary science community. To were available at the time. In the main-belt, Milani et al.(2014) sim- do this, we combine proper orbital elements (Knežević & Milani ilarly attempted to combine together the AstDys database consisting 2017), WISE albedos (Grav et al. 2012), SDSS colours (Hassel- of ∼340,000 asteroids, the WISE (Masiero et al. 2011) database con- mann et al. 2012), G-band colour from the Gaia DR2 (Spoto et al. sisting of ∼95,000 asteroids and the SDSS database (Ivezić et al. 2018) datasets and the Moving Objects from VISTA Survey (MOVIS) 2002) consisting of ∼60,000 asteroids into family classifications. near-infrared colours (Popescu et al. 2018), into a single cladistical In order to overcome some of the issues inherent in the HCM, analysis. As a result, this paper will provide a methodological basis as well as incorporating disparate colour surveys, in this work, we for future astrocladistical studies in the planetary sciences. apply a technique called ‘cladistics’ to the Jovian Trojan swarms. In section2 we present an overview of the methodology of Cladistics is traditionally used to examine the relationships between our work, and describe how astrocladistics is applied in the context biological organisms, and has played an important role in the study of the Jovian Trojan population. Section3 shows the results of of our own history as a species. The namesake of the Lucy mission, a the Jovian Trojan L4 and L5 swarm taxonomic analysis, including near complete Australopithecus afarensis, was used in some of the the dendritic trees and a discussion of the previously identified first hominid cladistical investigations (Johanson & White 1979; collisional families. As part of our analysis, we identify multiple Chamberlain & Wood 1987), and continues to be an important objects of interest, presented in section4. The implications for the resource for studies into human origins today (Parins-Fukuchi et al. targets of the Lucy mission are discussed in section5. In section6, 2019). we discuss the implications of our work in the context of the next The premise of the cladistical method is that characteristics generation of wide-field surveys that are coming online in the next are inherited through descent. It is then inferred that organisms decade. Finally, we draw our conclusions in section7.

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 5

2 DATASETS AND METHODS and Centaur populations (e.g. Horner & Wyn Evans 2006). It should be noted that stability for 1 × 106 years does not equate to, or Here we present an overview of the cladistical methodology used even imply, stability on timescales comparable to the age of the in a planetary science context. For a more detailed overview of the Solar system (Levison et al. 1997; Tsiganis et al. 2005a; Horner techniques involved, we direct the interested reader to Holt et al. et al. 2012; Di Sisto et al. 2014, 2019; Holt et al. 2020a). We use (2018). this stability level to exclude objects temporarily captured near the Jovian Lagrange points, such as P/2019 LD2 (Hsieh et al. 2021; Steckloff et al. 2020; Bolin et al. 2021). 2.1 Matrix and Characteristics In addition to the proper elements obtained from AstDyS, Each analysis begins with the creation of a 2-d matrix that contains we also include information on the libration of the Jovian Trojans all known information about the objects of interest – in this case, the around their host Lagrange point. To obtain these libration values, Jovian Trojans. Individual object are allocated a row in that matrix. we performed 1 × 104 year integrations of the orbital evolution of The columns of the matrix contain information on a different char- the Trojans under the influence of the Sun and four giant planets, acteristic of the objects studied – including their physical properties using the REBOUND WHFAST integrator (Rein & Liu 2012). For and orbital elements. these integrations, we used a timestep of 0.3954 years, and wrote The great advantages of using the cladistical methodology is out the instantaneous orbital elements of all objects simulated every that it can take a wide and disparate set of characteristics for a group 10 years. From these, we were able to calculate the amplitude of of objects, and can cope with incomplete datasets. To illustrate the libration, as well as the mean angle in the Jovian reference frame. breadth of characteristics that can be incorporated into a cladistical Similar physical properties, such as albedos and colours, would study, in this work we bring together the proper elements of the also be suggestive of analogous formation scenarios. We chose to Jovian Trojans, retrieved from AstDyS (Knežević & Milani 2017), not include mass, or any properties related to mass, as character- geometric albedos from NASA HORIZONS (Giorgini et al. 1996), istics in the analysis. Their inclusion could hide any relationships simulated libration properties, the WISE albedos (Grav et al. 2011), between a massive object and any daughter objects, the result of SDSS (Carvano et al. 2010) colours, Gaia DR2 G-band color (Spoto collisions resulting in families. We do include visual geometric et al. 2018) and MOVIS colours (Morate et al. 2018; Popescu et al. albedo (Giorgini et al. 1996), as this represents analogous physical 2016, 2018). properties. Due to the unique dynamics of the Jovian Trojans, the instan- In Holt et al.(2018), the presence or absence of various chem- taneous osculating orbital elements can not be used for taxonomic ical species were used as characteristics in the cladistical analy- proposes (e.g., Beauge & Roig 2001; Brož & Rozehnal 2011). The sis. This information requires detailed spectral analysis, which is AstDyS database (Knežević & Milani 2017) provides a set of robust only currently available for two Trojans, 624 Hektor (1907 XM) proper elements, in semi-major axis, eccentricity and inclination, (Marchis et al. 2014; Perna et al. 2018) and 911 Agamemnon (1919 for the Jovian Trojans. Those proper elements are generated from FD) (Perna et al. 2018), although it is likely that this situation will the results of 1 × 106 year simulations, from which the osculating change in the coming decade as a result of both the Lucy mission elements of the target objects are output at regular intervals. The and observations with the James Webb Space Telescope. As a proxy resulting database of osculating elements are then processed using for composition, broadband colours can be used in astrocladistics, Fourier Transform analysis. This technique removes oscillations due as has been undertaken by Fraix-Burnet et al.(2010) in their studies to planetary perturbations, with the final result being three proper of galaxies. elements (Δ푎 푝: proper delta in semi-major axis to the Jovian mean Several of the Jovian Trojans have been imaged by large all- (5.2 au), 푒 푝; proper eccentricity; sin푖 푝: sine of the proper inclina- sky surveys, with data available from the Sloan Digital Sky Survey tion. By moving from an instantaneous value for the objects orbit to (SDSS) (Szabo et al. 2007), the Wide-field Infrared Survey Explorer one that has been modified to take account of the periodic motion (WISE)(Grav et al. 2012), Gaia DR2 (Spoto et al. 2018) and MOVIS of the Trojans around the Lagrange points, these proper elements (Popescu et al. 2016). The wide range of wavelengths represented provide a much more accurate insight into a given object’s prove- by these datasets are shown in Fig.2. We include these colours as nance. Two objects with a common origin would be expected, in characteristics in our analysis, in addition to the dynamical dataset the absence of any major chaotic scattering events, to have similar described above. In total, combining the dynamical and observa- proper elements, but might, at any given instant, be at a different tional data, this results in a maximum of 17 characteristics being part of their libration cycle, and hence have markedly different os- included for each Trojan studied in this work. Each of these char- culating elements. These proper elements can therefore, unlike the acteristics, along with their coefficient of determination (푅2) and osculating elements, inform us about long term orbital relationships ranges, are presented in appendixA. in the population. Once all characteristics are collated for our objects of inter- The Jovian Trojans are unique in that they are trapped in 1:1 est, they are binned to give each object a unique integer value mean-motion resonance with Jupiter, which means that their proper for each characteristic. This was carried out using a Python pro- semi-major axes lie very close to that of Jupiter, approximately gram developed for Holt et al.(2018) 3. The binning of the data 5.2 au. The proper semi-major axis for the Trojans is therefore has multiple benefits. The primary reason for binning is the re- expressed, in this work, as a distance from the 5.2 au baseline quirement the cladistical methodology to have whole numbers for (훿푎 푝). An additional benefit to using these elements is that, due analysis, representing character states. This has the added benefit of to the requirement that the object’s exhibit 1 × 106 years of stable normalising each of the independent datasets. By normalising the osculations around their host Lagrange point in simulations of their datasets, the binning program also reduces the heterogeneity seen dynamical evolution, the AstDyS database represents a dataset of Jovian Trojans that are at least relatively dynamically stable, and should exclude any objects that have otherwise been mis-classified, 3 Available from https://github.com/TimHoltastro/ such as objects temporarily captured from the Jupiter family comet holt-etal-2021-Jovian-Trojan-astrocladistics.git.

MNRAS 000,1–26 (2020) 6 T. R. Holt et al. in the colours of the population (Grav et al. 2011, 2012; DeMeo & Carry 2013; DeMeo et al. 2014), mitigating some of the effects of the ‘information content’ (Milani et al. 2014) from each catalogue. The maximum number of bins for each characteristic, is set at 15, though if a co-efficient of determination (푅2) of greater than 0.99 is reached, a smaller number is used, shown in appendixA. Those characteristics with a smaller number are then weighted, to stan- dardise their contribution to the analysis. All binned characteristics have 푅2 values larger than 0.95. The binned matrices are then im- ported into Mesquite (Maddison & Maddison 2017), a program used for management of cladistical matrices and trees, for further analysis. The dynamical characteristics and albedo are ordered as in Holt et al.(2018) and Fraix-Burnet et al.(2006), with the colours Figure 3. Size-Frequency distribution (SFD) of the Jovian Trojan population (black solid), L (black dashed) and L (black dot) swarms. We show the unordered. The reasoning behind the ordering of dynamical charac- 4 5 SFD of objects used in this work in blue, showing a completeness to 25km. teristics is related to the stability of the Jovian Trojans. In dynamical A estimated complete SFD distribution of the Jovian Trojans (red) is also space, the Jovian Trojans are relatively stable (e.g. Nesvorný 2002; shown (Nesvorný 2018). Robutel & Gabern 2006; Emery et al. 2015; Holt et al. 2020a), and therefore any changes in dynamical properties represent large dif- ferences. In contrast to this, the colour ratios represent estimations in proper Δ semi-major axis (Δ푎 푝), eccentricity (푒 푝) and sine in- in compositional structure of the objects. These broad-band colours clination (sin푖 푝). The calculated mean libration values would be at ◦ ◦ can be affected by single changes in mineralogy (e.g. DeMeo et al. the closest approach to Jupiter (56.42 and 285.72 for the L4and ◦ 2015; Reddy et al. 2015), and are thus unordered. L5swarms respectively), with low libration amplitudes (L4: 4.044 , Simulations have suggested that some of the Jovian Trojans L5: 2.73◦). These values represent a very stable area of the parame- are unstable on relatively short timescales (e.g. Levison et al. 1997; ter space. In terms of albedo (L4: 0.024, L5: 0.031) and colours, the Tsiganis et al. 2005a; Di Sisto et al. 2014, 2019; Holt et al. 2020a). object would be very dark, and have a featureless spectrum. Based In order to account for this, we use only those objects that are on these parameters the ougroup served the purpose of rooting each present in the AstDyS database (Knežević & Milani 2017). As consensus tree without being too close and considered part of the the creation of proper elements requires a degree of stability (e.g. ingroups, or too far away so that the relationship to the populations Knežević & Milani 2003), these objects are stable in the swarms of interest were lost. for at least 1 × 106 years. In this initial phase, we also only select Each matrix is available in the online supplemental material4 those Trojans that have available observational data from at least in binned and unbinned form. one of the four surveys, WISE, SDSS, Gaia or MOVIS. The result of this is the generation of two distinct matrices, one for each of the two Jovian Swarms. The L4 dataset is smaller with 398 objects, 2.2 Trees whilst the L5 matrix contains 407 objects. Though these subsets Each Mesquite taxon-character matrix is then used to create a are markedly smaller than the total known populations of the two set of phylogenetic trees using Tree analysis using New swarms, they offer a significant advantage over a possible HCM set. Technology (TNT) v1.5 (Goloboff et al. 2008; Goloboff & Cata- For comparison, in the L4 swarm there are only five objects, 4060 lano 2016), via the Zephyr Mesquite package (Maddison & Mad- Deipylos (1987 YT1), 3793 Leonteus (1985 TE3), 5027 Androgeos dison 2015). This tree search is based on the concept of maximum (1988 BX1), 5284 Orsilocus (1989 CK2) and 4063 Euforbo (1989 parsimony (Maddison et al. 1984). Each tree generated in the block CG2), and one, 7352 (1994 CO), in the L5 that are present in all four has a length and in this case, is a characteristic of the tree itself, surveys. Even if only the largest photometric dataset (SDSS, Szabo and not of the individual branches. This tree length is calculated on et al. 2007) is considered, our subsets are nearly double those of a the bases of characteristics changing states, for example a change restricted HCM-type study (L4:176 objects, L5:232 objects). form a 0 to a 1 would constitute a 1 step value. In ordered charac- The objects in our subsets are shown in the context of the teristics, a change from 0 to 2 would be two steps, where as in the swarms in Fig.1. In selecting only those objects with observational unordered, would only be one step. A tree with more changes in data available from one or other of the named surveys, we acknowl- character state would have a longer tree length. The TNT algorithm edge that we are introducing a size bias, since larger objects are (Goloboff et al. 2008; Goloboff & Catalano 2016) rearranges the more likely to have been surveyed. We show the size-frequency dis- configuration of the trees, attempting to find the set of trees with tribution of our chosen objects in Fig.3. This shows that our subset the lowest tree length, creating a block of the most equally parsi- is complete to approximately 25km diameter. monious trees, those with the same minimum tree length. We use In addition to the Jovian Trojans, a fictitious outgroup object a drift algorithm (Goloboff 1996) search by generating 100 Wag- is created, with a base 0 for each of the characteristics. The function ner trees (Farris 1970), with 10 drifting trees per replicate. These of this outgroup is to root the trees. In the context of biological starting trees are then checked using a Tree bisection and reconnec- cladistics, a related clade, but one that is outside the group of in- tion (TBR) algorithm (Goloboff 1996) to generate a block of 10000 terest, is selected as the outgroup (Farris 1982). In doing this, the equality parsimonious dendritic trees. The Nexus files for both ma- outgroup sets the base character state for each characteristic. For trices, both with and without the tree blocks, are available on the astrocladistics of the Trojans, the dynamics make selection of the outgroup more difficult, as there is no true ancestral state from which ingroup characteristics are derived. For the synthetic outgroup cre- 4 https://github.com/TimHoltastro/ ated for this study, the dynamical characteristics are set close to 0 holt-etal-2021-Jovian-Trojan-astrocladistics.git

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 7

5 GITHUB repository . A 0.5 majority-rules consensus tree can be Table 1. Comparison of times taken to generate each 10,000 tree blocks, as constructed (Margush & McMorris 1981) once the tree block is described in section 2.2. (subset) are the matrices used in this work, where imported back into Mesquite (Maddison & Maddison 2017). This as (Pop) are the full known population at their respective Lagrange points. tree is then a hypothesis for the relationships between the Jovian No.: Number of objects in the matrix; 퐻푟푠푐 푝푢: number of CPU hours Trojans in the individual swarms. taken to generate tree block on a single core of Intel Xeon W-2133 CPU at As part of the consensus tree, each node (see Fig.5 and Fig. 3.60GHz; 퐿푡푟푒푒: Tree length; 퐼푐:consensus index (Brooks et al. 1986) of 6) shows the fraction of trees in the block that contain that node the 0.5 consensus tree; 퐼푟 :retention index (Naylor & Kraus 1995) of the 0.5 consensus tree. (퐹푛표푑푒). This fraction is tabulated in tables2 and3 for each subclan, clan and superclan. The higher the prevalence of the node, with No. 퐻푟푠 퐿 퐼 퐼 1.0000 indicating that the node is in all 10,000 trees, gives higher 푐 푝푢 푡푟푒푒 푐 푟 confidence in the grouping. L4 (subset) 398 10.72 1635.37 0.123 0.751 L5 (subset) 407 10.69 1984.79 0.113 0.712 L4 (Pop) 3620 420.15 3926 0.041 0.899 2.3 Dispersal velocities, Diameter calculations and Escape L5 (Pop) 1920 372.2 2794 0.054 0.883 analysis

The taxonomic clusters produced by the cladistical methodology database, combined with an estimate of the mean geometric albedo can be verified using the established inverse Gauss equations (e.g. values for the population (푃푣 = 0.075) using equation1(Fowler & Zappala et al. 1996; Turrini et al. 2008; Holt et al. 2018), in much JR Chillemi 1992). the same way that asteroid collisional families are identified and confirmed (e.g. Nesvorný et al. 2015). Holt et al.(2018) provide a 1329 demonstration of the use of those equations in conjunction with their 퐷(푘푚) = √ 10−0.2퐻 (1) cladistical analysis of the Jovian and Saturnian satellite systems. In 푃푣 that work, the inverse Gauss equations are used to comment on It should be noted that it is highly likely that most Jovian the relative timing of creation and validity of the clusters in the Trojans, particularly the smaller members of the population, are irregular satellites identified by astrocladistics. The rationale for markedly aspherical. Indeed, shapes inferred from occultation ob- this is that clusters with low dispersal velocities would most likely servations suggest that several of the targets for the Lucy mission indicate families produced by recent breakups, with larger velocities are likely irregular in shape (Buie et al. 2015; Mottola et al. 2020). possibly indicating either more energetic disruptions of the family’s Given the known shapes in this size regime, from the Main belt parent body, or an older family that has had longer to disperse. and Near Earth populations (e.g., Durech et al. 2015), it is expected We extend the methodology used in Holt et al.(2018) to in- that other Jovian Trojans are also irregular in shape. From this our vestigate the mean dispersal velocity in the dynamical parameter calculated diameter values should only be taken as estimations, and 6 space of the clusters we identify in the Jovian Trojan population . are available in the Github associated with this study. In the traditional methodology, the largest object is used as a point As part of our analyses, we track the dynamical evolution of the of reference for the parameters used in the calculations (specifi- chosen objects, using data presented in Holt et al.(2020a) which cally 푎푟 , 푒푟 , 푖푟 and 푛푟 in equations 5-6 in Holt et al. 2018). In presented escape fractions of the Trojan swarms and collisional this work we calculate two different dispersal velocities for each families on a timescale of 4.5 × 109 years. The best fit orbital Jovian Trojan. As in the original work, we determine the dispersal solution for each Jovian Trojan studied in that work was integrated velocity of each object in a given cluster to the largest object in forwards in time under the gravitational influence of the Sun and that cluster (Δ푉ref). In addition, we calculate the dispersal velocity four giant planets for 4.5 × 109 years. In addition, eight ’clones’ of from a fictitious centroid at the mean of the cluster proper element each object were studied, with initial orbital parameters perturbed space (Δ푎prop, 푒 푝, sin푖 푝 and period 푛: Δ푉푚cent). The inverse Gauss from the best fit solution along the Cartesian uncertainties presented equations also require knowledge of the values of 휔 and 휔 + 푓 at the in the HORIZONS database. We use this information to comment on initial point of disruption (e.g. Zappala et al. 1996; Nesvorný et al. the stability of the individual members, and each cluster as a whole. 2004, 2015). For ease of comparison, we have used 휔 as 90◦ and 휔 + 푓 as 45◦ . Datasets for each of the clusters are available from the Github repository 7. 2.4 Full population analysis Only 1857 of the 5553 (33.44 per cent) canonical Trojan have In addition to the subset analysis, we also conducted an analysis of measured albedos, and therefore reliable diameters in the NASA the full L swarm (3620 objects) and full L swarm (1920 objects), HORIZONS database. In order to investigate the size distribution of 4 5 using same techniques presented in section2. Since many of the ob- each swarm, we created an estimate of the diameter and volume of jects in each swarm remain poorly characterised, with many lacking each of the 5553 Jovian Trojans in the AstDyS database (Knežević for any information other than an apparent magnitude and orbital & Milani 2017). The unknown diameters (D) were calculated from solution, there is insufficient information in the matrices for us to the absolute magnitude (퐻) of the object in the NASA HORIZONS place great weight in the results of this additional analysis. We only include this as a computational note for future work, as presented in Table1. 5 Available from https://github.com/TimHoltastro/ holt-etal-2021-Jovian-Trojan-astrocladistics.git 6 Python 3 program is available from the GITHUB repository: https://github.com/TimHoltastro/ 3 RESULTS AND DISCUSSION holt-etal-2021-Jovian-Trojan-astrocladistics.git 7 https://github.com/TimHoltastro/ Here, we present the taxonomic trees resulting from our cladistical holt-etal-2021-Jovian-Trojan-astrocladistics.git analysis of the Jovian Trojan swarms. Each swarm is presented and

MNRAS 000,1–26 (2020) 8 T. R. Holt et al.

100619 (1997 TK14) 4086 Podalirius (1985 VK2) 3.1 L Swarm 11 4 11 9857 (1991 EN) Ajax 11 1404 Ajax (1936 QW) 0.929 11 Subclan 23135 (2000 AN146) In the L Trojan swarm, we analyse a total of 398 objects using the 0.929 0.97940.9794 4 0.929 0.97940.9794 7119 Hiera (1989 AV2) 11 11 9431 (1996 PS1) Hiera astrocladistical methodology. A total of 10,000 equally parsimo- 11 24403 (2000 AX193) 11 Ajax 0.97940.9794 11 0.97940.9794 25911 (2001 BC76) Subclan nious trees were generated, a process that took 10 hrs, 43 min using 316158 (2009 UW26) Clan 0.97940.9794 0.9570.957 0.97940.9794 207749 (2007 RC286) 2002 CQ a single core of Intel Xeon W-2133 CPU at 3.60GHz. The resulting 0.97940.9794 134 42367 (2002 CQ134) 0.97940.9794 55578 (2002 GK105) Subclan consensus tree is presented in Fig.5. The tree has a consistency 42554 (1996 RJ28) 55568 (2002 CU15) index of 0.123 (Brooks et al. 1986) and a retention index of 0.751 11 0.97740.9774 316550 (2010 XE81) 12917 (1998 TG16) D (F2007) (Naylor & Kraus 1995). The consensus tree has a length of 1635.37 0.97740.9774 0.9010.901 5258 (1989 AU1) DX (B2004) 0.97740.9774 0.9010.901 11 8 111932 (2002 GG33) Anius . 11 8060 Anius (1973 SD1) 0.99960.9996 Subclan 0.97740.9774 18060 (1999 XJ156) X (F2007) The superclans, clans and subclans identified in the L4 swarm 39793 (1997 SZ23) 0.98050.9805 Eurybates 137879 (2000 AJ114) are listed in Table2. In the L 4 swarm, we identify a total of ten 0.90070.9007 312457 (2008 QH42) Clan 0.90090.9009 315208 (2007 RS22) unaffiliated clans and eight superclans containing an additional sev- 0.97810.9781 3548 Eurybates (1973 SO) L C (F2007) Eurybates 0.99980.9998 enteen clans. Each of these trees are shown in detail in Appendix 39285 (2001 BP75) 0.98030.9803 C (F2007) 24380 (2000 AA160) C (F2007) Subclan 11 B. 28958 (2001 CQ42) C (F2007) In the L4swarm, there are four canonical collisional families Figure 4. Consensus trees of Greater Ajax superclan, including Ajax and (Nesvorný et al. 2015). Here three are represented in the subset, Eurybates clans. An example of trees shown in AppendixB. Letters asso- the 1996 RJ, Hektor and Eurybates families. All members of the ciate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), Eurybates, 1996 RJ and Hektor families in the canonical set used in classified by associated reference T1989: Tholen(1989); B2004: Bendjoya this study are also in Rozehnal et al.(2016) and Vinogradova(2015). et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confi- There are no representatives of the canonical Arkesilaos family, dence rating: Hasselmann et al.(2012). L indicates objects to be visited by though Vinogradova(2015) associated this family with their Epeios the Lucy spacecraft (Levison et al. 2017). Green highlights are members of non-canonical family, of which the largest member, 2148 Epeios the Eurybates collisional family. (1976 UW) is the type object of the Epeios clan. The only member of the Hektor family, 624 Hektor (1907 XM), is the type object of the Hektor clan, in the Greater Hektor superclan. The Eurybates discussed separately, and we compare our results to the previously collisional family provides some place for comment. Seven of the identified collisional families (Nesvorný et al. 2015). In order to thirteen identified members are clustered the Ajax clan, around 3548 avoid confusion with a specific cluster identified in our cladistics Eurybates (1973 SO), the type object. There are two other clusters analysis, we use the term clan to identify the groups of objects of Eurybates family members, three objects in the Philoctetes Clan, that share a similar heritage. We borrow two conventions from the and another three that are unassociated with any clan. The fact biological Linnean taxonomy (Linnaeus 1758), namely the inclusion that these are clustered, but separated in the consensus tree, may of a type object and the use of prefixes. Each clan is named after the indicate that they are victims of ‘chaining’ in HCM, and thus not member that was first discovered. This object is designated the type truly members of the collisional family. object. Due to observational bias, in most cases, the type object is the largest member of the clan. The largest member of the group is used as a reference point for the dispersal velocities explained 3.1.1 Unaffiliated L4 clans in section 2.3, and termed the reference object. It is important to note that the type object and the reference object in a clan can Our results reveal ten clans in the L4 swarm that are unaffiliated with be the same object, though this is not always the case. In order any identified superclan, presented in Fig. B1. None of the unaffili- to assist with any hierarchical grouping, we use the super and sub ated clans can be further split into subclans. Six of the unaffiliated prefixes, to denote higher and lower groups. To further improve the clans, namely the Stentor, 1998WR10, Periphas, Halitherses, Poly- clarity of the hierarchical clusters, the superclan’s have ’Greater’ poites and Ulysses clans, are located at the base of the L4 tree. Each affixed to the representative name. We choose five members as the of the ten unaffiliated clans in the L4 swarm contain at least one D- minimum number for a clan or subclan. This terminology forms a type object. The Agamemnon and Ulysses clans containing five and basis for future expansion of the small Solar system body taxonomic six D-type members respectively. The Halitherses clan contains one framework. X-type, 13475 Orestes (1973 SX), along with a single D-type, 13362 The Greater Ajax superclan, shown in Fig.4, highlights the (1998 UQ16), indicating that there may be some heterogeneity to hierarchical nature of this new terminology. The superclan is split these clans. into two clans, the Ajax and Eurybates clans. The type object of The dynamical stability of all members of the identified unaffil- both the Greater Ajax superclan and the Ajax clan is 1404 Ajax iated clan members was assessed by (Holt et al. 2020a). Comparing (1936 QW), whereas 3548 Eurybates (1973 SO) is the type object of the Eurybates clan. Within both clans, there are two subclans. In the Eurybates clan, there is the Anius subclan with type object 8060 8 The tree length, retention index and consistency index are measures of Anius (1973 SD1), and the Eurybates subclans, along with three how accuracy a tree represents the true relationships. A smaller tree length implies a more parsimonious, and thus likely tree (Goloboff 2015). The two other objects, namely 42554 (1996 RJ28), 55568 (2002 CU15), other indices are measures of homoplasy, the independent loss or gain of a 316550 (2010 XE81), not associated with either subclan. In this characteristic (Brandley et al. 2009). In both indices, a value of 1 indicates example set, the Trojan 3548 Eurybates (1973 SO) is therefore the no homoplasy, and thus no random events. The consistency index is the type object of both the Eurybates subclan and Eurybates clan, and ratio of the minimum number of changes in a tree, to the actual number is also a member of the Greater Ajax superclan. In this example, (Givnish & Sytsma 1997). The retention index is similar, but incorporates 3548 Eurybates (1973 SO) is also the reference object used in the maximum number of changes into the index (Farris 1989). We direct dispersal velocity calculations calculations for the Eurybates clan the interested reader to Gascuel(2005) for a more detailed analysis of the and subclan. mathematics behind these indices.

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 9

Outgroup 11 4902 Thessandrus (1989 AN2) D (H2012, 54) 11 15436 (1998 VU30) 11 2260 Neoptolemus (1975 WM1) DTU (T1989) 5284 Orsilocus (1989 CK2) 11 D (H2012, 91) 20729 (1999 XS143) 11 356893 (2011 XL3) 11 280072 (2002 CL218) 11 11 226027 (2002 EK127) 11 9799 (1996 RJ) 11 2146 Stentor (1976 UQ) 11 11 83983 (2002 GE39) 11 11 7641 (1986 TT6) 11 D (H2012, 92) 88225 (2001 BN27) Stentor Clan Fig. B1 38050 (1998 VR38) 5126 Achaemenides (1989 CH2) C (B2004) 11 11 41340 (1999 YO14) 0.76280.7628 85807 (1998 WR10) 11 0.90570.9057 0.90570.9057 162822 (2001 BD49) D (H2012, 61) 0.97980.9798 0.97980.9798 37301 (2001 CA39) 0.980.98 11 161024 (2002 FM7) 0.98130.9813 343174 (2009 SH333) 1998 WR Clan 0.98130.9813 351210 (2004 JD40) 0.8860.886 10 0.8860.886 23970 (1998 YP6) 195104 (2002 CN130) 0.86890.8689 0.86890.8689 24536 (2001 CN33) 0.92160.9216 37299 (2001 CN21) 0.88560.8856 0.92160.9216 15663 Periphas (4168 T-2) D (H2012, 53) 11 11 4833 Meges (1989 AL2) 11 D (B2004) 0.92080.9208 22014 (1999 XQ96) 24587 Kapaneus (4613 T-2) Periphas Clan 312782 (2010 VB46) 11 0.99960.9996 11 30102 (2000 FC1) 11 59049 (1998 TC31) 11 135547 (2002 EN14) 254669 (2005 LO19) 11 36259 (1999 XM74) D (H2012, 59) 13362 (1998 UQ16) D (H2012, 71) 11 254679 (2005 LU50) 11 0.94220.9422 0.96220.9622 0.94220.9422 0.96220.9622 5123 (1989 BL) 0.98130.9813 13387 Irus (1998 YW6) 0.94220.9422 0.94220.9422 38617 (2000 AY161) 11 0.98040.9804 11 63210 (2001 AH13) 0.88630.8863 0.88630.8863 13475 Orestes (1973 SX) X (H2012, 78) 0.92440.9244 12974 Halitherses (1973 SB2) 5436 Eumelos (1990 DK) 0.8310.831 11 89858 (2002 CK96) 0.98090.9809 Halitherses Clan 0.98090.9809 13366 (1998 US24) 11 0.99980.9998 9712 Nauplius (1973 SO1) 11 11 58473 (1996 RN7) 11 11 9807 (1997 SJ4) 11 65134 (2002 CH96) 65257 (2002 FU36) 0.97990.9799 3709 Polypoites (1985 TL3) D (B2004) 11 11 18062 (1999 XY187) 11 D (H2012, 78) 11 4035 (1986 WD) 11 D (B2004) 0.92290.9229 264154 (2009 VA107) 246147 (2007 PM16) Polypoites Clan 35272 (1996 RH10) D (H2012, 73) 13353 (1998 TU12) 0.88450.8845 0.99970.9997 15536 (2000 AG191) D (H2012, 87) 12238 Actor (1987 YU1) 0.92270.9227 13782 (1998 UM18) 0.96940.9694 (2011 YQ4) 0.96940.9694 4834 Thoas (1989 AM2) D (B2004) 20716 (1999 XG91) 0.96940.9694 11 0.92270.9227 21595 (1998 WJ5) 0.96940.9694 0.96940.9694 355768 (2008 RY57) 0.96940.9694 5254 Ulysses (1986 VG1) D (B2004) 5264 Telephus (1991 KC) 0.96940.9694 11 D (H2012, 99) 111819 (2002 DD1) 0.96940.9694 0.96940.9694 20424 (1998 VF30) D (H2012, 86) 0.98940.9894 0.92240.9224 23958 (1998 VD30) 0.98940.9894 24501 (2001 AN37) Ulysses Clan 0.98940.9894 63195 (2000 YN120) 0.98940.9894 310027 (2010 AH95) 0.98940.9894 11396 (1998 XZ77) 0.98940.9894 0.96930.9693 D (H2012, 95) 16099 (1999 VQ24) 0.98940.9894 21599 (1998 WA15) 0.97970.9797 D (H2012, 97) 252173 (2001 DL10) 83975 (2002 AD184) 11 11 21284 Pandion (1996 TC51) 11 11 24486 (2000 YR102) 11 63265 (2001 CP12) D (H2012, 53) 0.92240.9224 13385 (1998 XO79) 0.99870.9987 168364 (1996 TZ19) 0.95010.9501 0.99870.9987 5283 Pyrrhus (1989 BW) Neg (B2004) 0.99870.9987 Fig. B2 0.99870.9987 24519 (2001 CH) 0.99870.9987 38610 (2000 AU45) 0.99870.9987 65111 (2002 CG40) 0.99870.9987 312638 (2010 AP111) 0.94960.9496 0.99880.9988 0.99880.9988 12921 (1998 WZ5) X (F2007) Epeios Clan 0.99890.9989 0.99890.9989 2148 Epeios (1976 UW) 0.99970.9997 37710 (1996 RD12) 3564 Talthybius (1985 TC1) D (H2012, 91) 89829 (2002 BQ29) 0.95090.9509 588 Achilles (1906 TG) D (T1989) 55571 (2002 CP82) 0.97070.9707 0.99960.9996 0.95090.9509 116954 (2004 HS1) 0.95090.9509 0.97070.9707 160534 (1996 TA58) 0.97110.9711 38619 (2000 AW183) Greater Achilles Superclan 0.97110.9711 5259 Epeigeus (1989 BB1) D (H2012, 77) 0.95090.9509 0.97110.9711 0.95090.9509 0.97110.9711 33822 (2000 AA231) 0.97110.9711 0.97110.9711 3794 Sthenelos (1985 TF3) Achilles Clan 0.97110.9711 23075 (1999 XV83) 0.89270.8927 0.89270.8927 24312 (1999 YO22) 0.97990.9799 89844 (2002 CP64) 0.97990.9799 36267 (1999 XB211) 25895 (2000 XN9) 0.97990.9799 11 11 15527 (1999 YY2) 11 0.97990.9799 23480 (1991 EL) 162861 (2001 DY103) 0.97990.9799 0.97990.9799 166148 (2002 EU14) 1991 EL Clan 0.97990.9799 0.97990.9799 11395 (1998 XN77) 0.97990.9799 42187 (2001 CS32) 2759 Idomeneus (1980 GC) D (H2012, 96) 11 4063 Euforbo (1989 CG2) D (B2004) 11 0.97980.9798 24505 (2001 BZ) 11 22054 (2000 AP21) 0.97980.9798 0.97980.9798 3793 Leonteus (1985 TE3) 11 326125 (2011 YY61) Idomeneus Clan 160135 (2000 YB131) 11 Fig. B1 190268 (2007 XU3) 11 11 5028 Halaesus (1988 BY1) D (H2012, 72) 0.88430.8843 11 37297 (2001 BQ77) 11 0.97980.9798 20428 (1998 WG20) 23119 (2000 AP33) 11 13183 (1996 TW) 11 39369 (2002 CE13) 0.95990.9599 Halaesus Clan 90337 (2003 FQ97) 11 257405 (2009 SG330) 0.88430.8843 4836 Medon (1989 CK1) D (B2004) 13060 (1991 EJ) 0.95070.9507 3540 Protesilaos (1973 UF5) 0.97070.9707 202752 (2007 PX30) 0.95070.9507 23624 (1996 UX3) 20720 (1999 XP101) 0.93110.9311 0.980.98 60383 (2000 AR184) D (H2012, 71) 0.93110.9311 22056 (2000 AU31) Fig. B3 11 41268 (1999 XO64) 0.88430.8843 0.97070.9707 0.97070.9707 23968 (1998 XA13) 0.97070.9707 12972 Eumaios (1973 SF1) 0.97070.9707 24534 (2001 CX27) 0.97070.9707 63290 (2001 DS87) 0.97010.9701 11668 Balios (1997 VV1) 83978 (2002 CC202) 0.97010.9701 0.97010.9701 15521 (1999 XH133) 0.94030.9403 233925 (2009 UL2) 0.97070.9707 0.90130.9013 0.86520.8652 13182 (1996 SO8) 0.86520.8652 0.99980.9998 0.99980.9998 4057 Demophon (1985 TQ) 11 11 5012 Eurymedon (9507 P-L) C (H2012, 61) 0.93190.9319 11 Eurymedon Clan 15529 (2000 AA80) Greater Nestor Superclan 168033 (2005 JJ143) 0.97090.9709 659 Nestor (1908 CS) XC (T1989) 0.97930.9793 22203 Prothoenor (6020 P-L) 0.9590.959 15033 (1998 VY29) 0.97930.9793 0.97930.9793 22059 (2000 AD75) 0.9590.959 0.9590.959 4060 Deipylos (1987 YT1) D (B2004) 0.97890.9789 23152 (2000 CS8) Nestor Clan 22149 (2000 WD49) 0.97990.9799 350055 (2010 RE38) 275007 (2009 TW40) 4068 Menestheus (1973 SW) D (B2004) 100619 (1997 TK14) 0.9120.912 0.9120.912 4086 Podalirius (1985 VK2) 11 11 9857 (1991 EN) 11 11 1404 Ajax (1936 QW) 23135 (2000 AN146) 0.97940.9794 0.89280.8928 0.9290.929 0.97940.9794 7119 Hiera (1989 AV2) 11 11 9431 (1996 PS1) 11 11 24403 (2000 AX193) 0.97940.9794 11 Fig. B4 0.97940.9794 25911 (2001 BC76) 316158 (2009 UW26) Ajax Clan 0.97940.9794 0.9570.957 0.97940.9794 207749 (2007 RC286) 0.97940.9794 0.97940.9794 42367 (2002 CQ134) 0.97940.9794 0.9120.912 55578 (2002 GK105) 42554 (1996 RJ28) 55568 (2002 CU15) 11 0.97740.9774 316550 (2010 XE81) 12917 (1998 TG16)1 D (F2007) 0.97740.9774 0.9010.901 5258 (1989 AU1) 0.97740.9774 0.9010.901 11 111932 (2002 GG33) 11 8060 Anius (1973 SD1) 0.99960.9996 0.97740.9774 18060 (1999 XJ156) X (F2007) Greater Ajax Superclan 39793 (1997 SZ23) 0.98050.9805 137879 (2000 AJ114) 0.90070.9007 0.90070.9007 312457 (2008 QH42) 0.90090.9009 315208 (2007 RS22) Eurybates Clan 0.86610.8661 0.97810.9781 3548 Eurybates (1973 SO) 0.86610.8661 0.97810.9781 0.99980.9998 L C (F2007) 39285 (2001 BP75) 0.98030.9803 C (F2007) 24380 (2000 AA160) C (F2007) 11 28958 (2001 CQ42) C (F2007) 65194 (2002 CV264) D (H2012, 54) 38606 (1999 YC13) 173086 Nireus (2007 RS8) 0.97920.9792 200023 (2007 OU6) 0.97060.9706 0.95930.9593 0.97060.9706 1868 Thersites (2008 P-L) DX (B2004) 0.97080.9708 0.97080.9708 4946 Askalaphus (1988 BW1) D (H2012, 64) 11 0.99950.9995 266869 (2009 UZ151) 2797 Teucer (1981 LK) D (H2012, 87) 0.95930.9593 11 0.95930.9593 264155 (2009 VJ109) 11 Thersites Clan Fig. B5 20995 (1985 VY) 11 D (H2012, 71) 11 8317 Eurysaces (4523 P-L) 11 37298 (2001 BU80) 624 Hektor (1907 XM) D (T1989) 11 129602 (1997 WA12) 0.87910.8791 22035 (1999 XR170) 24275 (1999 XW167) 0.99870.9987 11 0.87080.8708 42230 (2001 DE108) 0.87080.8708 11 163702 (2003 FR72) 11 11429 Demodokus (4655 P-L) 11 6090 (1989 DJ) D (B2004) 11 4489 (1988 AK) D (H2012, 93) 11 6545 (1986 TR6) D (F2007) Greater Hektor Superclan 11 2920 Automedon (1981 JR) 11 41379 (2000 AS105) Hektor Clan 11 3801 Thrasymedes (1985 VS) 11 1583 Antilochus (1950 SA) D (T1989) 11 11 12916 Eteoneus (1998 TL15) 11 11 5285 Krethon (1989 EO11) 11 XD (B2004) 224020 (2005 JL160) 24537 (2001 CB35) 11 18063 (1999 XW211) 114710 (2003 GX7) 11 0.98030.9803 11 911 Agamemnon (1919 FD) D (T1989) 0.85180.8518 11 11 32498 (2000 XX37) D (H2012, 54) 3596 Meriones (1985 VO) 0.98030.9803 Fig. B1b 429970 (2013 AQ54) 0.98030.9803 15440 (1998 WX4) 0.98030.9803 24244 (1999 XY101) 5027 Androgeos (1988 BX1) 11 0.96080.9608 D (H2012, 81) 63294 (2001 DQ90) 0.94130.9413 312787 (2010 VA114) Agamemnon Clan 0.92180.9218 36279 (2000 BQ5) D (H2012, 71) 0.97990.9799 0.97990.9799 15398 (1997 UZ23) 0.97990.9799 0.97990.9799 51378 (2001 AT33) 0.98030.9803 D (H2012, 79) 55563 (2002 AW34) 65209 (2002 DB17) 0.97820.9782 31835 (2000 BK16) D (H2012, 61) 0.97860.9786 3391 Sinon (1977 DD3) 0.97880.9788 107004 (2000 YC112) 38607 (2000 AN6) 0.9790.979 0.9790.979 15094 Polymele (1999 WB2) L X 5041 Theotes (1973 SW1) 0.99980.9998 21271 (1996 RF33) Fig. B6 0.99980.9998 19725 (1999 WT4) X (H2012, 93) 0.99980.9998 13383 (1998 XS31) 0.99980.9998 0.99980.9998 11 0.99980.9998 24233 (1999 XD94) X (H2012, 66) 63291 (2001 DU87) 0.99980.9998 0.97990.9799 0.99980.9998 0.97990.9799 24420 (2000 BU22) 0.97990.9799 C (F2007) 0.89010.8901 111805 (2002 CZ256) 0.95130.9513 0.95130.9513 0.99980.9998 23144 (2000 AY182) 11 24426 (2000 CR12) 16152 (1999 YN12) 0.97970.9797 11 63202 (2000 YR131) 0.97970.9797 23963 (1998 WY8) X (H2012, 56) 0.97970.9797 11 166285 (2002 GY127) Philoctetes 0.97970.9797 65232 (2002 EO87) 19913 Aigyptios (1973 SU1) 0.97990.9799 0.97970.9797 1869 Philoctetes (4596 P-L) 0.99980.9998 24539 (2001 DP5) 0.99980.9998 0.97960.9796 42403 Andraimon (6844 P-L) 0.97960.9796 0.97960.9796 63286 (2001 DZ68) 0.97980.9798 11 8241 Agrius (1973 SE1) 0.97960.9796 11 Clan 9590 (1991 DK1) D (H2012, 73) 13184 Augeias (1996 TS49) 11 42168 (2001 CT13) 11 11 63259 (2001 BS81) 11 11 38574 (1999 WS4) 11 39692 (1996 RB32) 23285 (2000 YH119) D (H2012, 93) 24357 (2000 AC115) 11 0.95970.9597 24506 (2001 BS15) 0.92370.9237 8125 Tyndareus (5493 T-2) 12658 Peiraios (1973 SL) 0.94280.9428 0.97980.9798 0.94280.9428 57920 (2002 EL153) 10664 Phemios (5187 T-2) 0.97110.9711 11 14235 (1999 XA187) D (H2012, 68) 0.89010.8901 Greater Diomedes Superclan 161017 (2002 EP106) C (H2012, 55) 0.95090.9509 35673 (1998 VQ15) 5209 (1989 CW1) 0.97980.9798 0.87710.8771 18263 Anchialos (5167 T-2) 0.94270.9427 11351 Leucus (1997 TS25) L D (F2007) 0.98090.9809 11 83977 (2002 CE89) 11 4543 Phoinix (1989 CQ1) 11 Diomedes 11 43706 Iphiklos (1416 T-2) 11 21601 (1998 XO89) 11 1437 Diomedes (1937 PB) DX (T1989) 11 11 11 11397 (1998 XX93) 11 11 15539 (2000 CN3) 11 11 53436 (1999 VB154) 11 65228 (2002 EH58) 7214 Anticlus (1973 SM1) 11 Clan 23939 (1998 TV33) 0.98090.9809 0.98090.9809 23123 (2000 AU57) D (H2012, 70) 11 14707 (2000 CC20) D (F2007) 11 13062 Podarkes (1991 HN) 11 21593 (1998 VL27) 11 15651 Tlepolemos (9612 P-L) 11 13331 (1998 SU52) 0.980.98 107804 (2001 FV58) 13694 (1997 WW7) 11 Lycomedes 11 11 11 9694 Lycomedes (6581 P-L) 11 0.98010.9801 39287 (2001 CD14) 103508 (2000 BV1) 11 111785 (2002 CQ186) 13230 (1997 VG1) 11 11 23126 (2000 AK95) 11 22049 (1999 XW257) 11 11 17874 (1998 YM3) Clan 11 11 10247 Amphiaraos (6629 P-L) 11 103989 (2000 DC94) 130190 (2000 AG90) 42146 (2001 BN42) 11 11 4501 Eurypylos (1989 CJ3) 11 L D 0.97950.9795 21900 Orus (1999 VQ10) 353201 (2009 SP246) Fig. B1i 0.91080.9108 0.93990.9399 2456 Palamedes (1966 BA1) 0.93990.9399 14268 (2000 AK156) 0.93990.9399 11 24531 (2001 CE21) 0.99980.9998 24341 (2000 AJ87) C (F2007) 0.98030.9803 Thersander Clan 9817 Thersander (6540 P-L) 0.91060.9106 11 0.91060.9106 53477 (2000 AA54) 101466 (1998 WJ15) 0.95920.9592 0.95920.9592 43212 (2000 AL113) C (F2007) 0.93950.9395 0.93950.9395 9818 Eurymachos (6591 P-L) 11 X (F2007/H2012, 84) 65225 (2002 EK44) 80302 (1999 XC64) 0.91160.9116 160679 (2000 DB6) 7543 Prylis (1973 SY) 0.960.96 65000 (2002 AV63) 0.960.96 0.960.96 1749 Telamon (1949 SB) D (H2012, 97) 0.960.96 0.960.96 5244 Amphilochos (1973 SQ1) 0.85420.8542 0.86460.8646 11 21370 (1997 TB28) 39264 (2000 YQ139) Telamon Clan Fig. B7 0.9030.903 12714 Alkimos (1991 GX1) 4007 Euryalos (1973 SR) 0.9030.903 11 0.9030.903 136557 Neleus (5214 T-2) 0.85420.8542 162811 (2001 AG51) 0.85420.8542 0.88410.8841 163155 (2002 CL130) 11 7152 Euneus (1973 SH1) X (B2004) 0.88410.8841 0.88410.8841 11 4138 Kalchas (1973 SM) X (B2004) 11 11 89924 (2002 ED51) 11 11 22008 (1999 XM71) 0.86640.8664 11 24508 (2001 BL26) Kalchas Clan 11252 Laertes (1973 SA2) 0.93590.9359 0.93590.9359 13379 (1998 WX9) 0.97730.9773 0.8390.839 38052 (1998 XA7) 39278 (2001 BK9) Greater Telamon Superclan 0.85420.8542 0.85420.8542 0.88410.8841 24225 (1999 XV80) 0.88410.8841 38600 (1999 XR213) 5023 Agapenor (1985 TG3) X (H2012, 65) 0.8650.865 0.99980.9998 243484 (2009 TA23) 0.90290.9029 89871 (2002 CU143) 0.92270.9227 24498 (2001 AC25) Theoklymenos 0.92270.9227 10989 Dolios (1973 SL1) 0.52680.5268 0.92270.9227 0.52680.5268 20144 (1996 RA33) 0.99870.9987 0.99870.9987 5652 Amphimachus (1992 HS3) 0.98080.9808 0.92270.9227 65583 Theoklymenos (4646 T-2) 24390 (2000 AD177) D (F2007) 0.96910.9691 3063 Makhaon (1983 PV) 0.96910.9691 11 204911 (2008 QE5) 0.99990.9999 16974 (1998 WR21) Clan 11 17351 Pheidippos (1973 SV) 38614 (2000 AA113) 0.97010.9701 13463 Antiphos (5159 T-2) X (F2007) 0.97010.9701 15535 (2000 AT177) D (F2007) 0.97010.9701 24485 (2000 YL102) X (H2012, 64) 0.97010.9701 54678 (2000 YW47) 24530 (2001 CP18) 0.94980.9498 11 65224 (2002 EJ44) Fig. B8 0.94980.9498 0.94980.9498 22404 (1995 ME4) 0.94980.9498 128383 (2004 JW52) 0.97010.9701 22055 (2000 AS25) 79444 (1997 UM26) 0.97010.9701 23382 Epistrophos (4536 T-2) D (H2012, 65) 11 0.97970.9797 11 312643 (2010 BZ111) 11 11 38621 (2000 AG201) 11 11 39293 (2001 DQ10) D (H2012, 53) 0.97970.9797 11 360103 (2013 CW) 58479 (1996 RJ29) Epistrophos Clan 0.97970.9797 161027 (2002 FM38) 0.97970.9797 23706 (1997 SY32) 0.97970.9797 1647 Menelaus (1957 MK) 0.95990.9599 Greater Odysseus Superclan 0.95990.9599 1143 Odysseus (1930 BH) D (T1989) 0.95990.9599 14690 (2000 AR25) 0.97990.9799 24882 (1996 RK30) X (H2012, 73) 0.97990.9799 42179 (2001 CP25) 9713 Oceax (1973 SP1) 0.97970.9797 0.97950.9795 161020 (2002 EK158) 0.95960.9596 13372 (1998 VU6) 0.95960.9596 11 22009 (1999 XK77) 0.97990.9799 63272 (2001 CC49) Odysseus Clan 21372 (1997 TM28) C (H2012, 62) 0.97990.9799 0.97990.9799 36271 (2000 AV19) 11 22052 (2000 AQ14) 11 161044 (2002 GG181) 0.97990.9799 63292 (2001 DQ89) 11 11 5025 (1986 TS6) 11 63257 (2001 BJ79)

Figure 5. Consensus tree of cladistical analysis of 398 L4 Jovian Trojans. Numbers indicate the proportion of the 10000 generated trees where a given branch is present. Colours are indicative of previously identified collisional families: Green: Eurybates; Orange: Hektor; Red; 1996 RJ; after Nesvorný et al.(2015). Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), from different sources, T1989: Tholen(1989); B2004: Bendjoya et al. (2004); L2004: Lazzaro et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012). Lucy Targets are indicated by an L. A high resolution, expanded form of this figure is available in online supplemental material. Blue rectangles correspond to detailed figures in AppendixB.

MNRAS 000,1–26 (2020) 10 T. R. Holt et al.

members of the collisional family. The type object of this clan, Table 2. Clans, superclans and subclans identified in the L4 Trojan swarm. Name: Clan Name; 푁 : Number of objects; 퐷ref: Reference object diameter; 2146 Stentor (1976 UQ), is chosen over 9799 (1996 RJ), due to 푉esc: Escape velocity of reference object; 퐹esc: fraction of objects that escape it being discovered nearly 20 years earlier. In this clan, although the L4 Lagrange point, from Holt et al.(2018); Δ푉 푚ref: mean dispersal 2146 Stentor (1976 UQ) (50.76 km) is the type object, 7641 (1986 velocity calculated from inverse Gauss equations, see section 2.3, to the TT6) is used as the reference frame for our calculations of the clan reference object, with 1휎 standard deviation; Δ푉 푚 : as Δ푉 푚 , with cen ref member’s dispersion in Δ푉ref, as the available observational data calculations to the fictitious cluster center; 퐹푛표푑푒: faction of trees in the suggest that it has the largest diameter in the clan (71.84 km). block that contain the node. Unfortunately, no members of this clan have been classified

Name 푁 퐷ref 푉esc 퐹esc Δ푉 푚ref Δ푉 푚cen 퐹푛표푑푒 under the Bus-Demeo system. Almost all members of this clan km ms−1 ms−1 ms−1 were found to be dynamically stable in the simulations carried out L4-Stentor 8 71.84 24.02 0.07 11.38±7.85 10.25±6.51 1.0000 by Holt et al.(2020a), with the one exception being the clones of the L4-1998 WR10 5 34.95 11.69 0.02 26.02±8.11 10.61±5.33 0.7628 L4-Periphas 5 80.17 26.81 0.44 13.02±6.11 10.61±4.56 0.9216 type object, 2146 Stentor (1976 UQ). More than half of the clones of L4-Halitherses 15 37.7 12.61 0.01 21.53±12.28 15.63±9.9 0.9422 L4-Polypoites 5 68.73 22.98 0 30.67±9.95 15.49±8.5 0.9799 that object (56 per cent) escaped from the Jovian Trojan population L4-Ulysses 17 76.15 25.46 0.08 24.15±12.43 14.25±8.25 0.9694 over the 4.5 × 109 years of those simulations. The stability of the L4-Idomeneus 6 112.05 37.47 0 9.81±3.51 8.37±3.7 1.0000 L4-Halaesus 10 50.77 16.98 0.06 12.3±9.36 10.56±6.34 1.0000 remainder of the clan is likely the result of most of the members L4-Agamemnon 16 131.04 43.82 0.12 28.34±12.5 21.41±11.01 1.0000 ◦ L4-Thersander 10 65.92 22.04 0.14 21.82±10.93 17.5±12.43 0.9795 having low 훿푎prop (< 0.036 푎푢), mean libration angles (< 3.5 from the Lagrange point) and range (< 14◦). L4-Greater Achilles 35 130.1 43.51 0.06 16.91±11.24 14.4±8.6 0.9501 L4-Epeios 10 48.36 16.17 0 19.55±7.42 8.57±4.42 0.9987 The clan has relatively compact Gaia G magnitude values L4-Achilles 9 130.1 43.51 0.15 9.9±5.96 8.65±6.54 0.9707 (17.56 to 18.11 mag), though there are only two similar sized mem- L4-1991EL 10 68.98 23.07 0.06 17.37±13.76 12.69±8.48 0.9799 bers, 2146 Stentor (1976 UQ) and 9799 (1996 RJ), in the dataset. L4-Greater Nestor 27 112.32 37.56 0.63 34.04±20.11 29.81±12.31 0.9507 L4-Eurymedon 6 45.68 15.28 0.3 20.96±15.31 13.48±6.9 0.9013 Three additional objects, 7641 (1986 TT6), 83983 (2002 GE39) and L4-Nestor 7 112.32 37.56 0.4 20.71±13.1 14.84±5.4 0.9709 88225 (2001 BN27), have a corresponding SDSS (g - r) colour (0.57 L4-Greater Ajax 29 85.5 28.59 0.38 40.33±26.27 32.91±16.75 0.9290 to 0.7), indicating that perhaps there is a diagnostic feature for the L4-Ajax 12 85.5 28.59 0.6 18.06±14.39 16.82±10.65 0.9794 clan in the visible range. L4-Ajax Sub 4 85.5 28.59 0.64 11.29±0.93 7.34±2.62 1.0000 L4-Hiera Sub 4 59.15 19.78 0.36 8.31±1.19 4.35±0.85 1.0000 L4-2002 CQ134 Sub 4 32.16 10.75 0.81 36.08±17.87 20.26±11.97 0.9794 L4-Eurybates 16 63.88 21.36 0.23 32.58±28.94 24.59±14.67 0.9774 3.1.1.2 Idonmeneus Clan: The small Idomeneus clan (6 mem- L4-Anius Sub 5 53.28 17.82 0.27 12.61±10.34 10.42±4.62 0.9010 L4-Eurybates Sub 8 63.88 21.36 0.24 25.23±20.27 19.43±2.22 0.9007 bers), Fig. B1e contains two D-types, 2759 Idomeneus (1980 GC) and 4063 Euforbo (1989 CG2), along with a small Δ푉푚 L4-Greater Hektor 28 225 75.24 0.54 31.47±19.35 28.99±21.63 0.9593 −1 L4-Thersites 11 89.43 29.91 0.83 34.57±33.85 27.49±23.04 0.9792 (9.81±3.51 ms ), and large reference object, 3793 Leonteus (1985 L4-Hektor 17 225 75.24 0.35 31.43±16.53 27.93±16.05 1.0000 TE3). This clan also includes 4063 Euforbo (1989 CG2), a 95.62 km L4-Greater Diomedes 75 117.79 39.39 0.43 108.79±36.64 41.85±23.23 0.9782 object. The clan is entirely stable, with no clones of any member es- L4-Philoctetes 26 33.96 11.36 0.38 25.19±7.9 19.07±11.21 0.9998 L4-Andraimon Sub 10 33.96 11.36 0.77 27.48±6.64 23.91±7.2 0.9796 caping. The members have a relatively low range of reference angle L4-Diomedes 12 117.79 39.39 0.76 56.9±28.09 40.6±19.19 0.9427 values, fairly close to the 60◦ Lagrange point (60.44◦ to 61.77◦), L4-Lycomedes 20 31.74 10.61 0.45 33.18±16.71 29.44±16.14 0.9809 ◦ ◦ L4-Amphiaraos Sub 8 26.83 8.97 0.57 13.3±4.33 10.18±1.9 1.0000 though with a comparatively low libration range (19.43 to 29.64 ). The clan has a small spread of SDSS colours, particularly in the (u L4-Greater Telamon 35 111.66 37.34 0.05 27.16±15.83 21.68±11.82 0.8646 L4-Telamon 5 64.9 21.7 0.27 26.96±18.11 20.7±6.98 0.9600 - g) colour (1.23-1.51). In the MOVIS survey there are narrow (Y - L4-Kalchas 6 46.46 15.54 0 16.88±10.79 12.47±4.59 1.0000 L4-Theoklymenos 19 111.66 37.34 0.03 25.71±17.83 20.08±12.5 0.8390 J) (0.29 to 0.38) and (J - Ks) colour ratios (0.49 - 0.72). The nar- L4-Makhaon Sub 5 111.66 37.34 0.09 13.39±6.05 8.22±1.17 0.9691 row ranges indicate that the colours, along with the dynamics are

L4-Greater Odysseus 36 114.62 38.33 0.11 24.17±12.28 18.41±9.07 0.9701 diagnostic for this clan. L4-Epistrophos 5 24 8.02 0 8.32±3.94 6.99±2.47 1.0000 L4-Odysseus 20 114.62 38.33 0 17.6±11.75 12.54±8.43 0.9797 3.1.1.3 Thersander Clan: The Thersander clan, named after 9817 Thersander (6540 P-L) contains 10 objects, and is high- our list of those clans with the dynamical data from that work, we lighted in Fig. B1i. This unaffiliated clan, includes 21900 Orus find that most of the clans exhibit significant dynamic stability, at a (1999 VQ10), a provisionally allocated D-type that is the target of level that exceeds the mean stability of the L4 Trojan population as a the Lucy mission. In the clan, there is also 24341 (2000 AJ87), an whole (with the simulations described in Holt et al. 2020a yielding identified C-type (Fornasier et al. 2007). Close to this clan, there a mean escape fraction of 0.24 for the L4 cloud over the age of the are several members of the Eurybates family, 24341 (2000 AJ87), a Solar system). The exception is the Periphas clan, which displays a C-type, 9818 Eurymachos (6591 P-L), a P/X-type (Fornasier et al. higher escape fraction (0.44) over the course of those simulations. 2007; Hasselmann et al. 2012) and 65225 (2002 EK44). This could In the following sections, we discuss three of these unaffiliated have implications for classification of 21900 Orus (1999 VQ10), see clans, the Stentor, Idonmeneus and Thersander clans, highlighting section5 for discussion. The compact SDSS colours are due to only several interesting cases. The other seven clans, as shown in Fig. a single object, 53477 (2000 AA54), found in the survey. In terms B1, may contain objects of interest, though we leave further detail of escapes, a low number of clones escape the swarm, mainly from discussion for future research. 14268 (2000 AK156) and 24531 (2001 CE21). 3.1.1.1 Stentor Clan: The first clan identified in our consensus tree of the L Trojans (Figure5) is the Stentor clan, shown in more 4 3.1.2 Greater Achilles Superclan detail in Fig. B1h, after the type object 2146 Stentor (1976 UQ), and consists of a total of 8 objects. The clan includes the two identified The Greater Achilles superclan contains 35 objects, grouped into members of the 1996 RJ collisional family, 226027 (2002 EK127 three distinct groups, the Epeios (discussed bellow), 1991 El and and 9799 (1996 RJ), (Nesvorný et al. 2015), and it seems likely Achilles clans, as shown in Fig. B2. The type object, 588 Achilles that the other members of the clan represent previously undetected (1906 TG), has been classified as a DU-type (Tholen 1989). The

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 11 majority of the objects in the superclan are classified as D-type, stable members are located in the two clans, but though those clans with just two exceptions, both of which are members of the Epeios still exhibit escape fractions higher than the base L4 escape fraction clan: 12921 (1998 WZ5), a X-type, and 5283 Pyrrhus (1989 BW), (at 0.3 and 0.4, respectively). The superclan, as a whole, has an av- which is unclassified, but has an unusual negative spectral slope in erage 훿푎 range (0.03 to 0.11 au), with relatively high eccentricities Bendjoya et al.(2004). (0.07 to 0.17). If the more traditional 훿푉ref of the superclan is considered, the −1 −1 Eios (19.55 ± 7.42 ms ) and 1991El (17.37 ± 13.7 ms ) clans 3.1.3.1 Nestor clan: This clan contains 7 objects, two of which have larger dispersal velocities than the Greater Achilles superclan have been taxonomically identified, the XC-type 659 Nestor (1908 −1 −1 (16.91 ± 11.2 ms ), whilst the Epeios (8.57 ± 4.42 ms ) and CS), and D-type 4060 Deipylos (1987 YT )(Bendjoya et al. 2004). −1 1 Achilles (8.65 ± 6.54 ms ) clans have smaller Δ푉cent than the Holt et al.(2020a) noted a slightly larger escape rate amongst the −1 superclan (4.4 ± 8.6 ms ). X-types in the Trojans, and this is reflected in this clan. The Nestor The Greater Achilles superclan is relatively stable (0.057 퐹esc). Clan has a relatively high escape fraction (0.4), versus that of the Only 160534 (1996 TA ), a member of the Achilles clan, has a high 58 L4 swarm (0.23) as a whole. The members of the clan all display escape fraction (0.78). This is not surprising, as the superclan has a centres of libration that are slightly ahead of the 60◦ point (60.44◦ to ◦ low range of 훿푎prop (0.0 to 0.05 au), and is close to the 60 Lagrange 64.43◦), though the range of amplitudes is relatively small (14.33◦ ◦ ◦ point (59.1 to 63.1 ). to 24.54◦). With the diversity of taxonomic types within the clan, it is not surprising that the members also display a wide range of 3.1.2.1 Epeios Clan: The Epeios clan, named for 2148 Epeios SDSS colours ,(b - v):0.65 - 0.99, (u - g): 1.62 - 2.29, (g - r): 0.43 (1976 UW), contains 10 members. The type object was also in the - 0.77, (r - i): 0.18 - 0.27. The narrow range of MOVIS values are non-canonical Epeios collisional family (Vinogradova 2015). This due to only a single representative of the clan, 4060 Deipylos (1987 non-canonical family was associated with the canonical Arkesilaos YT1),(Y - J):0.241, (J - Ks):0.547, (H - Ks):0.137, in the survey. family (Nesvorný et al. 2015), of which we have no members rep- resented. This could indicate with further characterisation in future surveys, members of the Arkesilaos family could form part of this 3.1.4 Greater Ajax Superclan clan. This is supported by the fact that both the Epeios clan and Epeios collisional family (Vinogradova 2015) contain X-type ob- The 29 objects in this superclan, and the associated Ajax and Eu- jects. rybates clans, are shown in Fig.4. We use this superclan, and the In this clan, 5283 Pyrrhus (1989 BW) was unclassified, though following detailed discussion of both clans, as examples for the it has an interesting negative slope in Bendjoya et al.(2004). Also, rest of the consensus trees, found in AppendixB. This superclan within this clan is 12921 (1998 WZ5), an identified X-type (For- includes the many members of the Eurybates collisional family. nasier et al. 2007). The Epeios clan is entirely stable, with no un- The cluster is not named the ‘Eurybates superclan’, as 1404 Ajax stable members. There are a narrow range of SDSS colours, though (1936 QW) was discovered in 1936 (Wyse 1938), nearly 40 years there are only two members, 37710 (1996 RD12) and 168364 (1996 before 3548 Eurybates (1973 SO). This superclan is one of the TZ19), in the survey. Dynamically, this clan is close to the Lagrange most complex in the L4 swarm, with multiple subclans in each clan. ◦ ◦ ◦ point (59.1 to 61.77 ), with small libration amplitudes (4.04 to Apart from one unassociated object, 100619 (1997 TK14), all ob- 14.33◦) and eccentricities (0.01 to 0.1). jects are in one of the clans. In terms of escapes, the Greater Ajax This clan may contain a dynamical pair of objects, 258656 superclan is has a higher escape fraction (0.38) than the L4 swarm (2002 ES76) and 2013 CC41 (Holt et al. 2020b), the first such objects as a whole. The group is dynamically diverse, though they have a ◦ ◦ identified in the Trojan population. Unfortunately neither of these compact 훿푎prop range (0.07 to 0.11 ). Relatively compact SDSS objects are included in this analysis, due to their lack of presence in values, (b - v):0.65-0.93, (u - g): 1.25-1.72, (g - r): 0.43-0.7, (r - i): wide-field surveys. The Epeios clan does not include any D-types, 0.15-0.29, may be an actual feature of this superclan, as eight of the but has a X-type, 12921 (1998 WZ5)(Fornasier et al. 2007), and 29 superclan objects are represented in the SDSS survey, though the an object with a potential negative slope, 5283 Pyrrhus (1989 BW) (i - z) color has quite a wide range (-0.03-0.26). (Bendjoya et al. 2004). These associations are an indication that the 258656-2013 C41 pair may have different properties to the majority 3.1.4.1 Ajax clan: In this clan there are three subclans (Ajax, of the Jovian Trojans. Hiera and 2002 CQ134), each consisting of four objects in a branch- ing format. The Hiera and 2002 CQ134 subclans form a sister group to the Ajax subclan. Unfortunately, there are no taxonomically iden- 3.1.3 Greater Nestor Superclan tified members of this clan. With the close association to the Eu- The Great Nestor superclan consists of 37 objects shown in Fig.4 rybates family, this makes the three largest members of the clan, and includes two distinct clans, Eurymedon and Nestor, as well as 1404 Ajax (1936 QW), 4086 Podalirius (1985 VK2) and 7119 Hi- several additional members that are not associated with any individ- era (1989 AV2), all of which have a absolute H-magnitude greater ual clan. We discuss the Nestor clan in detail below. Whilst most of than 9, of particular interest for future telescope observations, see the Trojans are D-types (72.2 per cent), the Greater Nestor superclan section4. Most of the escapes in the Greater Ajax superclan come contains two large members of other taxonomic types, 659 Nestor from this clan. The 2002 CQ134 subclan has a large escape fraction (1908 CS), a XC-type (Tholen 1989) and 5012 Eurymedon (9507 (0.81), with all members having an escape fraction over 0.65. P-L), a C-type (Hasselmann et al. 2012), each is the type object of The clan is located well ahead of the 60◦ point, with mean their respective clan. Based on the simulations described in Holt libration angle between 63.1◦ and 65.76◦. The clan does have a rel- et al.(2020a), the Greater Nestor superclan has the largest escape atively narrow range of dynamical values (Δ푎prop:0.09 au-0.11 au, fraction of any superclan in the L4 swarm, with fully 63 per cent of 푒prop:0.03-0.08, sin푖prop:0.28-0.49), that could be diagnostic. In all test particles generated based on clan members escaping from addition, some of the SDSS values may also be diagnostic, (b - the Trojan population on a timescale of 4 × 109 years. The more v):0.86-0.93, (u - g):1.44-1.63, (g - r):0.63-0.7, (r - i):0.15-0.24,

MNRAS 000,1–26 (2020) 12 T. R. Holt et al. with three members of the clan represented, 4086 Podalirius (1985 3.1.5.1 Thersites clan: As with the superclan, almost all mem- VK2), 24403 (2000 AX193) and 42367 (2002 CQ134). Two addi- bers of this clan are identified as D-types (1868 Thersites (2008 P- tional members , 207749 (2007 RC286) and 316158 (2009 UW26), L), 4946 Askalaphus (1988 BW1), 2797 Teucer (1981 LK), 20995 are represented in the MOVIS dataset with similar values, (Y - J): (1985 VY), Bendjoya et al. 2004; Hasselmann et al. 2012). Most of 0.469-0.494, (J - Ks): 0.608-0.712. The range of Gaia values from the unstable members of the Hektor superclan are in the Thersites six different sized members is broader (17.29-18.93 mag), high- clan, with six members of the clan having all nine clones escape, lighting the need for further investigations into members of this 2797 Teucer (1981 LK), 4946 Askalaphus (1988 BW1), 8317 Eu- clan. rysaces (4523 P-L), 20995 (1985 VY), 37298 (2001 BU80) and 266869 (2009 UZ151). This clan has higher eccentricity (0.03 to ◦ ◦ 3.1.4.2 Eurybates clan: There are two subclans (Anius and 0.11) and libration range (39.85 -60.27 ) compared with the Hek- Eurybates) in this clan. The Anius subclan has five members, with tor clan. As with the superclan, the SDSS colours are compact, (b two duos and a single object, in a 1:2:2 format. The Eurybates - v):0.79-0.86, (u - g):1.35-1.53, (g - r):0.57-0.63, (r - i):0.23-0.29, subclan (eight members), as expected for the group containing many (i - z): 0.09-0.2, and with four members in the survey, 2797 Teucer members of the Eurybates collisional family (Brož & Rozehnal (1981 LK), 4946 Askalaphus (1988 BW1), 20995 (1985 VY) and 2011; Nesvorný et al. 2015), has a comparatively complex structure 38606 (1999 YC13), could be diagnostic. There are three members (three duos and two singles in 2:1:1:2:2 format). The type object of represented in MOVIS, 173086 Nireus (2007 RS8), 200023 (2007 Eurybates clan, 3548 Eurybates (1973 SO) is a target for the Lucy OU6), 264155 (2009 VJ109) and 266869 (2009 UZ151), though mission. There are three other Eurybates family members, 39285 264155 (2009 VJ109), has quite different colours, (Y - J):0.294, (J - Ks):1.004, compared to the other three, (Y - J):0.398-0.492, (J - (2001 BP75), 24380 (2000 AA160), 28958 (2001 CQ42), all C-types (Fornasier et al. 2007), in close association under the Eurybates Ks):0.309-0.909. subclan. The other four members of the Eurybates subclan, 39793 3.1.5.2 Hektor clan: The type object of this clan, 624 Hektor (1997 SZ23), 137879 (2000 AJ114), 312457 (2008 QH42), 315208 (1907 XM), is the largest object in the Jovian Trojan population (2007 RS22), and possibly two in the Anoius subclan, 12917 (1998 (225km, Marchis et al. 2014). It is also the largest member of the TG16) and 111932 (2002 GG33), are likely previously unidentified members of the collisional family. The age of this collisional family Hektor collisional family (Rozehnal et al. 2016). Unfortunately, has been identified as approximately,1.045±0.364×109 years (Holt 624 Hektor (1907 XM) is the only member of the collisional family et al. 2020a). With that long an age, the possibility for interlopers is studied in this analysis, therefore any conclusions about potential quite high, as the true members of the collisional family disperse. family memberships are speculative at best. Most of the instability in this clan in confined to two members, 24275 (1999 XW ) 18060 (1999 XJ156) is a X-type in Fornasier et al.(2007), and the 167 corresponding SDSS colours, (b - v):0.70, (u - g):1.69, (g - r):0.48, (r and 42230 (2001 DE108), both of which have only a single clone - i):0.21, (i - z):0.06, are different to other members. The Eurybates remaining at the end of the Holt et al.(2020a) simulations. The clan clan, which includes members of the Eurybates collisional family, as a reasonably high Δ푎prop values (0.09 au - 0.12 au). As with the has a lower escape fraction (0.23) than the superclan as a whole Hektor superclan, most of the SDSS colours, (b - v):0.72-0.86, (u - (0.38). The clan escape fraction (0.23) is similar to the escape g):1.16-1.63, (g - r):0.5-0.63, (i - z):0.09-0.2, are compact, with a fraction of the Eurybates collisional family (0.1881) found by Holt range of (r - i) (0.18-0.29), MOVIS, (Y - J):0.02-0.46, (J - Ks):0.49- et al.(2020a). If we disregard the X-type (18060 (1999 XJ156), (g 1.18, and Gaia (15.11-18.38 mag) values. The type object, 624 - r):0.48), the SDSS (g - r) colour is contained within a single bin, Hektor (1907 XM), shows a level of heterogeneity in the spectra (g - r): 0.633-0.7. (Perna et al. 2018), agreeing with the compact values for the clan. Interestingly, 1583 Antilochus (1950 SA) and 3801 Thrasymedes (1985 VS), were identified as potential asteroid pair (Milani 1993), though this was not confirmed by Holt et al.(2020b). In our analysis 3.1.5 Greater Hektor superclan these two objects are next to one another in the dendritic tree (Fig. This superclan contains the only member of the Hektor collisional B5), lending strength to our analysis. family (Rozehnal et al. 2016), 624 Hektor (1907 XM), considered in our analysis. The supercaln also contains many other objects iden- 3.1.6 Greater Diomedes superclan tified as D-type (Roig et al. 2008; Rozehnal et al. 2016). The excep- tion, 5285 Krethon (1989 EO11), is a XD-type (Bendjoya et al. 2004) This is the largest superclan in the L4 swarm, with 71 members. It −1 in the Thersites clan, which with further examination could be rei- also has the largest Δ푉ref of any superclan (108.79 ± 36.64 ms ). −1 dentified as a true D-type. In the superclan, the Δ푉ref and Δ푉cent are The Δ푉cent is more reasonable (41.85 ± 23.23 ms ), closer to the −1 −1 −1 similar (31.47 ± 19.35 ms and 28.99 ± 21.63 ms ), as well as in 푉esc of 1437 Diomedes (1937 PB) (39.3 ms ), the type object of the both clans (Thersites clan: 34.5733.85 ms−1 and 27.4923.04 ms−1, superclan. The superclan includes two Lucy targets, 11351 Leucus −1 −1 Hektor clan: 31.43 ± 16.53 ms and 27.93 ± 16.05 ms ), with (1997 TS25) and 15094 Polymele (1999 WB2). They are both pro- each of mean velocities being smaller than the 푉esc of 624 Hektor visionally classified differently, with 15094 Polymele (1999 WB2) (1907 XM) (75.24 ms−1). being a X-type (Buie et al. 2018; Souza-Feliciano et al. 2020) and Dynamically, the superclan is ahead of the Lagrange point 11351 Leucus (1997 TS25) a D-type (Buie et al. 2018). They are ◦ ◦ ◦ ◦ (63.1 to 68.4 ), with a fairly high libration range (34.75 to 60.27 ) in two separate clusters, with 5094 Polymele (1999 WB2) not in and 훿푎prop (0.09 au to 0.12 au). Some of the compact range of any clan, and 11351 Leucus (1997 TS25) in the Diomedes clan with SDSS values, (b - v):0.72-0.86, (u - g):1.16-1.63, (g - r):0.5-0.63, another DX-type, 1437 Diomedes (1937 PB). The dynamical stabil- (i - z):0.09-0.2, could be diagnostic, but a wider range of other ity of the different clans within the superclan is markedly variable, colours, (r - i):0.18-0.29), MOVIS, (Y - J):0.02-0.46, (J - Ks):0.37- with some significantly less stable than others (e.g. Diomedes clan 1.18, and Gaia (15.11-18.38 mag) are indicative of heterogeneity which has an escape fraction of 0.76, compared to the Philoctetes in the superclan. clan, with an escape fraction of 0.38). The escape rates within each

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 13 clan, however, are relatively consistent - so all objects within an as well as the Theoklymenos clan. The SDSS values are relatively unstable clan are similarly unstable, whilst those in the stable clans diverse, (b - v):0.65-0.93, (u - g):1.35-1.72, (g - r):0.43-0.7, (i - are all relatively stable, and each of theses clans has a larger escape z):-0.03-0.26), particularly the (r - i) color (0.16-0.34). fraction than that of the overall L4 swarm (0.2335). 3.1.7.1 Kalachas clan: The Kalachas clan contains two X-type 3.1.6.1 Philoctetes clan: This clan with 26 members, displays objects, 4138 Kalchas (1973 SM) and 7152 Euneus (1973 SH1) a high diversity of taxonomic types, three X-types (19725 (1999 (Bendjoya et al. 2004), both of similar size (46.46 km and 45.52 km WT4), 24233 (1999 XD94) and 23963 (1998 WY8); Hasselmann respectively). The smaller of the two, 7152 Euneus (1973 SH1) −1 et al. 2012), a C-type (24420 (2000 BU22), Fornasier et al. 2007), has a low Δ푉ref (5.4ms ) to 138 Kalchas (1973 SM), which is the and a D-type (9590 (1991 DK1); Hasselmann et al. 2012) in the reference object for the clan. Even though they were not identified in Andraimon subclan. This clan also contains three members of the Holt et al.(2020b), their Δ푉ref, similar properties and sizes, indicate Eurybates family (24420 (2000 BU22), 111805 (2002 CZ256) and that these two large objects could be an ancient disrupted binary pair 24426 (2000 CR12), Nesvorný et al. 2015), and a fourth non- (Vokrouhlický & Nesvorný 2008; Pravec et al. 2019). canonical member (63291 (2001 DU87), Rozehnal et al. 2016). All members of this clan are stable over the life of the Solar A large fraction of this clan is represented in the SDSS database system (Holt et al. 2020a). The clan has very low proper eccen- (0.6923), with relatively compact colours, (b - v):0.58-0.93, (u - tricities (0.0161-0.0532) and sin푖 (0.0102-0.119) values, and with g):1.16-1.63, (g - r):0.37-0.7, (i - z):-0.03-0.2, though there is a mid-range 훿푎prop values, places the clan within the stable param- wide (r - i) range (0.1-0.24). There is only a single representative eter space (Nesvorný 2002; Di Sisto et al. 2014; Hellmich et al. of the clan in the Gaia survey (19725 (1999 WT4), 18.67 mag), 2019; Holt et al. 2020a). The Δ푉ref of the clan is relatively small −1 so the value range here is only indicative. As the largest object in (16.88 ± 10.7 ms ), and close to the 푉esc of 4138 Kalchas (1973 −1 the clan, 1869 Philoctetes is relatively small (33.96 km), the 푉esc SM) (15.5 ms ). With a relatively high fraction of objects (50 per −1 −1 (11.36 ms ) is lower than the Δ푉ref (25.1 ± 7.9 ms ). cent) represented in the SDSS catalogue, the (b - v), (u - g), (g - r) and (i - z) colours are possibly diagnostic, (b - v):0.72-0.86, (u 3.1.6.2 Diomedes clan: This mid-sized (12 members) clan, con- - g):1.44-1.72, (g - r):0.5-0.7, (i - z):0.09-0.15. The range of (r - i) tains 11351 Leucus (1997 TS25), a D-type (Fornasier et al. 2007) SDSS colours (0.16-0.23) are mainly due to 89924 (2002 ED51), (r Lucy target. The type object of the clan, 1437 Diomedes (1937 PB) - i): 0.225 being a possible outlier. is also classified as a DX-type (Tholen 1989). The Δ푉cent for the −1 clan is relatively high (56.9 ± 28.09 ms ), though close to the 푉esc −1 of the large type object (39.3 ms ). With relatively high Δ푎prop 3.1.8 Greater Odysseus superclan values (0.11 to 0.16 au) and mean center of libration values (67.09◦ to 73.74◦; Amplitude: 50.06◦ to 75.59◦), it is unsurprising that this The Odysseus superclan (36 members) contains two clans, clan has a high escape rate (0.76). In the SDSS dataset, there are Epistrophs (5 members) and Odysseus (20 members), neither of which is discussed here in detail. There is a diversity of taxonomic only three members represented, 5209 (1989 CW1), 43706 Iphik- types in this superclan. The type object, 1143 Odysseus (1930 BH) los (1416 T-2) and 83977 (2002 CE89), and with only two in the is classified as a D-type (Tholen 1989), though there are two other MOVIS database, 11397 (1998 XX93) and 65228 (2002 EH58), it is difficult to make any conclusions regarding colour distribution. objects with taxonomic classifications, namely 24882 (1996 RK30) The wide range of WISE (W1:0.08-0.26, W2:0.06-0.28) albedos which is an X-type, and 21372 (1997 TM28) classified as a C- indicate that there is a variety of compositions in this clan. type (Hasselmann et al. 2012). The Epistrophos clan contains two D-types (39293 (2001 DQ10) and 23382 Epistrophos (4536 T-2) Hasselmann et al. 2012). There is a X-type (13463 Antiphos (5159 T-2) Fornasier et al. 2007), another D-type (15535 (2000 AT ) 3.1.7 Greater Telamon superclan 177 Fornasier et al. 2007), and a X-type (24485 (2000 YL102) Hassel- The Greater Telamon superclan which has 35 members, including mann et al. 2012), that are not associated with any clan. three separated clans, Telmon, Kalchas and Theoklymenos. The The range of albedos and colours reflect the diversity in the su- Telmon and Kalchas clans are relativly small, with 5 and 6 members perclan. Much of this can, however, be explained by several outliers, respectively. The Theoklymenos clan is larger, at 19 members, and for example, 9713 Oceax (1973 SP1)in the Odysseus clan has high contains a X-type (5023 Agapenor (1985 TG3) Hasselmann et al. WISE (W1:0.336 , W2:0.336) and geometric (0.168) albedos com- 2012), and two D-types (24390 (2000 AD177 and 3063 Makhaon pared with the rest of the objects. A particularly interesting object (1983 PV) Fornasier et al. 2007; Lazzaro et al. 2004). We discuss is 128383 (2004 JW52), in terms of its colours. The SDSS colours the Kalachas clan in more detail below. for 128383 (2004 JW52) are high for (b - v) (1.55) and (g - r) (1.3), This is one of the most stable superclans (퐹esc: 0.05) in the but low for (i - z), (-0.55), the opposite of the rest of the superclan, Trojan population. Most of the escape values in the superclan orig- (b - v):0.649-0.857, (g - r):0.433-0.7, (i - z):-0.0167-0.25. This one inate with the type object, 1749 Telamon (1949 SB), where all nine outlier accounts for much of the SDSS variation. −1 particles escape (Holt et al. 2020a). Within this only supercaln 3063 The superclan (Δ푉cent : 18.41 ± 9.07 ms ) and clans −1 Makhaon (1983 PV) has a higher escape fraction (0.33) higher than (Odysseus: Δ푉cent : 12.54 ± 8.43 ms ) are fairly compact, par- −1 the L4 swarm (0.23). ticularly the Epistrophos clan (Δ푉cent : 6.99 ± 2.47 ms ). This Other superclan members have all nine clones stay in the L4 superclan is also quite stable (퐹esc: 0.11), with the majority of the Trojan region. With moderate Δ푎 values (0.04-0.09 au) and a loca- instability coming form the unaffiliated superclan members, such as ◦ ◦ tion near the Lagrange point (59.61 to 64.43 ), this stability is not 22404 (1995 ME4), where all the clones escape. The Epistrophos surprising. In general, the clan has low WISE albedos (W1:0.102- and Odyssesus clan members are all completely stable, due to both 0.239 , W2:0.102-0.251). The exception is 24225 (1999 XV80) sets being close to the Lagrange point (60.44◦ to 61.77◦ and 59.1◦ (W1:0.378, W2:0.378), which extends the ranges of the superclan to 61.77◦ respectively).

MNRAS 000,1–26 (2020) 14 T. R. Holt et al.

3.2 L Swarm 5 Table 3. Clans, superclans and subclans identified in the L5 Trojan swarm. In our analysis of the L swarm, we present a consensus tree of 407 푁 푎푚푒: Family Name; 푁 : Number of members; 퐷ref: Reference object 5 diameter; 푉 : Escape velocity of reference object; 퐹 : fraction of objects objects in Fig.6. A total of 10,000 equally parsimonious trees took esc esc that escape the L5 Lagrange point, from Holt et al.(2018); Δ푉ref: dispersal approximately 10 hrs 26 minutes to find using a single core of Intel velocity relative to the reference object (calculated using the inverse Gauss Xeon W-2133 CPU at 3.60GHz. The consensus tree has a length of equations; see section 2.3), with 1휎 standard deviation; Δ푉cent: as Δ푉ref, 1984.79, with a consensus index of 0.113 (Brooks et al. 1986) and with calculations to the fictitious cluster center; 퐹푛표푑푒: faction of trees in retention index of 0.712 (Naylor & Kraus 1995). The superclans, the block that contain the node. clans and sublclans identified in the L5 swarm are listed in Table3. In 푁 푎푚푒 푁 표. 퐷푟푒 푓 표푏 푗 푉푒푠푐 퐹푒푠푐 Δ푉푟푒 푓 Δ푉푐푒푛푡. 퐹푛표푑푒 the L5 swarm, there are seven clans unaffiliated with any superclan km 푚푠−1 푚푠−1 푚푠−1 with six subclans within them. There is a small number of large L5-Asteropaios 17 57.65 19.28 0.06 25.94±11.96 15.48±6.14 0.9304 superclans (three), compared with the L swarm, and each superclan L5-Lykaon Sub 5 50.87 17.01 0.07 10.22±2.14 7.06±1.84 0.9588 4 L5-1988 RS10 Sub 7 32.14 10.75 0.02 9.97±6.12 8.31±5.99 0.8942 contains a larger number of clans and subclans. In total there are L5-Dolon 20 42.52 14.22 0.31 46.28±27.85 34.71±19.81 0.9999 14 clans containing a total of 14 subclans. Overall, the L5 swarm L5-Erichthonios Sub 5 27.53 9.21 0.04 13.36±10.86 9.95±6.73 0.9999 L5-Dolon Sub 11 42.52 14.22 0.35 25.77±13.42 23.52±14.58 1.0000 contains more hierarchical structure than the L4 swarm, shown in Fig.6. L5-Apisaon 9 40.67 13.6 0.67 26.29±7.75 20.31±7.29 0.9794 In the L5 swarm, there are two canonical collisional fami- L5-Khryses 8 53.2 17.79 0.53 14.41±5.08 8.02±3.15 0.9784 lies, 2001 UV209 and the larger Ennomos family (Nesvorný et al. L5-1999 RU12 5 24.01 8.03 0.84 29.24±11.18 17.87±4.84 1.0000 2015). Vinogradova(2015) questioned the existence of any colli- L5-1990 VU1 21 63.19 21.13 0.52 28.35±28.23 24.87±18.96 0.9391 sional families in the L5swarm, thought they did note some clus- L5-1990 VU1 Sub 7 59.3 19.83 0.73 61.38±30.9 31.94±9.74 0.9788 L5-Idaios Sub 8 44.55 14.9 0.38 13.72±5.31 8.93±3.59 0.9395 tering around 247341 2001 UV209, 11487 (1988 RG10), and 4709 L5-Anchises 8 99.55 33.29 0.88 32.88±10.82 22.51±13.02 0.9612 Ennomos (1988 TU2). Rozehnal et al.(2016) has a similar dataset to the canonical one, with a few extra objects. The non-canonical L5-Greater Patroclus 133 140.36 46.94 0.1 31.57±20.49 31.62±15.09 0.8377 L5-Memnon 23 118.79 39.72 0.11 15.31±7.57 15.05±6.59 0.9534 2001 UV209 and several Ennomos family members are in the Ce- L5-Memnon Sub 9 118.79 39.72 0.15 16.02±7.97 12.24±7.9 0.9332 L5-Amphios Sub 9 38.36 12.83 0.14 14.06±8.13 13.04±7.89 0.9727 briones and Troilus clans of the Greater Patroclus superclan, along L5-1971 FV1 18 75.66 25.3 0.07 12.76±7.58 9.43±5.5 0.9065 with the two canonical Ennomos family members. The Ennomos L5-Lampos Sub 6 35.39 11.83 0.22 21.47±4.71 11.11±1.99 1.0000 L5-1971 FV1 Sub 8 75.66 25.3 0 6.35±0.93 5.28±2.55 0.9801 family is more problematic. In our subset, there are nine mem- L5-1989 TX11 5 28.26 9.45 0 10.8±1.35 4.33±2.38 0.9248 L5-Phereclos 17 94.62 31.64 0.01 9.97±5.41 8.14±3.84 0.8886 bers, spread throughout the L5swarm. There is a small cluster of L5-Pandarus Sub 5 82.03 27.43 0.04 18.61±0.94 7.48±3.44 0.9996 L5-Phereclos Sub 12 94.62 31.64 0 10.61±5.66 7.29±3.49 0.889 three members in the Aneas clan, though the largest member of L5-Troilus 13 100.48 33.6 0.09 18.95±7.41 12.88±5.81 1.0000 the collisional family, 4709 Ennomos (1988 TU2), is located in the L5-Troilus Sub 5 100.48 33.6 0 15.95±5.0 8.2±4.36 1.0000 L5-1988 RY11 Sub 5 39.75 13.29 0.2 22.58±6.65 10.33±4.42 1.0000 Cebriones clan, Greater Pratoclus superclan, with two other non- L5-Cebriones 17 95.98 32.09 0.23 24.9±10.97 19.04±7.42 1.0000 L5-Bitias Sub 7 47.99 16.05 0.35 23.47±9.83 13.74±4.09 0.9798 canonical members. The hierarchical structure seen in the L5 swarm through astrocladistics could indicated that the dynamical history of L5-Greater Aneas 64 118.22 39.53 0.2 65.85±34.23 38.7±20.27 0.8884 L5-1988 RH13 6 53.1 17.76 0.65 36.74±22.51 23.44±15.43 0.9350 the swarm is more complex than can be reliably identified by HCM, L5-1994 CO 5 47.73 15.96 0.13 28.95±5.47 21.4±11.93 0.9997 L5-1989 UQ5 5 25.91 8.66 0 25.34±4.92 9.72±7.17 1.0000 and as indicated by the lack of confident clusters in Vinogradova L5-Sarpedon 17 77.48 25.91 0.04 23.15±13.77 18.98±6.16 0.9596 (2015). L5-Hippokoon Sub 5 18.43 6.16 0 12.03±4.65 9.9±5.74 1.0000 L5-Sarpedon Sub 11 77.48 25.91 0.04 16.65±13.65 15.97±9.07 0.9596 L5-Aneas 26 118.22 39.53 0.2 34.55±18.97 22.42±13.03 0.9544 L5-Helicaon Sub 5 32.54 10.88 0.27 8.95±3.27 7.18±3.51 1.0000 L5-Iphidamas Sub 5 49.53 16.56 0.33 15.8±6.57 13.08±5.2 0.9795 L5-Aneas Sub 8 118.02 39.47 0.07 30.7±20.66 23.17±13.27 0.9744 3.2.1 Unaffiliated L5 clans L5-Greater Astyanax 80 126.29 42.23 0.45 92.28±43.46 50.89±28.51 0.9647 There are seven clans that are unaffiliated with any superclan in L5-Mentor 20 126.29 42.23 0.41 48.51±24.27 32.58±18.62 0.9732 L5-1988 RR10 Sub 5 29.08 9.72 0 19.21±3.39 9.84±4.86 1.0000 the L5 swarm. In this section we discuss the Dolan (20 members), L5-Mentor Sub 10 126.29 42.23 0.58 36.72±8.02 24.68±11.69 0.9732 L5-Helenos 11 34.05 11.39 0.12 40.81±19.19 21.03±11.21 1.0000 1990 VU1 (21 members) and Anchises (8 members) clans. The L5-Astyanax 41 53.98 18.05 0.55 141.79±42.59 42.8±28.01 0.9735 values for the other four clans, Asteropaios (17 members), Apisaon L5-Ophelestes Sub 5 32.39 10.83 0.18 20.79±12.53 13.7±6.25 1.0000 L5-Astyanax Sub 6 53.98 18.05 0.54 99.92±57.95 55.04±28.89 0.9796 (9 members), Khryses (8 members) and 1990 VU1 are available in L5-Acamas Sub 6 43.86 14.67 0.74 102.44±11.67 31.58±31.34 1.0000 the Github repository9. In the superclan, the Asteropaios, Dolan and L5-1989 UX5 Sub 9 32.19 10.76 0.56 15.28±8.38 12.97±7.93 0.9735 1990 VU1 each have have two subclans, shown in Fig. B9, unlike the L4 clans. All unaffiliated clans in the L5 swarm are located (1993 BZ12), 32482 (2000 ST354) and 29314 Eurydamas (1994 between the Patroclus and Aneas superclans in the tree. Except CR18); Hasselmann et al. 2012), along with two D-types (9430 for the 1999 RU2 clan, which does not contain any taxonomically Erichthonios (1996 HU10) and 11488 (1988 RM11); Fornasier et al. identified objects, each clan contains at least one D-type object. 2004; Hasselmann et al. 2012), both located in the Erichthonios Most of the unaffiliated clans have escape fractions higher than that subclan. This diversity in types is reflected in the geometric (0.03- of the L5 swarm (0.2489 Holt et al. 2020a). The exception is the 0.14) and WISE (W1:0.07-0.29, W2:0.08-0.3) albedo ranges of the ◦ ◦ stable Asteropaios clan (퐹esc:0.06). The 1992 RU2 (퐹esc:0.84) and clan. The clan is close (295.12 to 297.46 ) to the L5 Lagrange point ◦ Anchises clans (퐹esc: 0.88) are particularly unstable. (300 ) resulting in an overall escape fraction (퐹esc:0.31) similar to the overall L5 swarm (0.2489 Holt et al. 2020a), though the 3.2.1.1 Dolon Clan: This clan contains 55419 (2001 TF19), Erichthonios subclan is much more stable (퐹esc:0.04). The overall −1 which is a member of the Ennomos collisional family (Nesvorný Δ푉ref and Δ푉cent of the clan are relatively high (46.28 ± 27.85 ms et al. 2015). In this clan there are three X-type objects (11554 Asios and 34.71 ± 19.81 ms−1 respectively), in comparison to the small −1 reference object (푉esc : 14.22 ms ). The SDSS (u - g) (1.51-1.62), (g - r) (0.48-0.64) and (i - z) (0.01-0.18) as well as the MOVIS (J 9 https://github.com/TimHoltastro/ - Ks) (0.53-0.9) colours are compact and fairly diagnostic for the holt-etal-2021-Jovian-Trojan-astrocladistics.git clan.

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 15

Outgroup 1 32720 Simoeisios (2131 T-3) 1 31821 (1999 RK225) D (F2007) 1 155427 (1997 LO5) 1 51357 (2000 RM88) 1 57626 (2001 TE165) 1 24018 (1999 RU134) 0.9805 55496 (2001 UC73) 51344 (2000 QA127) 0.9502 73641 (1977 UK3) 0.9421 0.8094 117446 (2005 AV45) 0.9421 0.9037 0.9037 24467 (2000 SS165) 0.9998 D (F2007) 0.9042 186128 (2001 TP154) 51362 (2000 SY247) 1870 Glaukos (1971 FE) 1 D (H2012, 87) 0.9406 62201 (2000 SW54) D (H2012, 66) 6998 Tithonus (3108 T-3) D (F2007) 0.9594 0.9594 1 17417 (1988 RY10) 110829 (2001 UT54) 376869 (2001 TQ260) 0.9594 0.9592157470 (2005 AG61) 483014 (2014 UJ170) 3240 Laocoon (1978 VG6) D (H2012, 66) 1 0.9594 52275 (1988 RS12) 0.9792 884 Priamus (1917 CQ) D (T1989) 124985 (2001 TK131) 0.8377 0.8377 4832 Palinurus (1988 TU1) D (H2012, 80) 0.8566 2241 Alcathous (1979 WM) D (T1989) 0.8566 1873 Agenor (1971 FH) 23987 (1999 NB63) 0.9594 0.8566 1 343161 (2009 KH3) 0.8319 0.8319 63955 (2001 SP65) D (H2012, 54) 0.8566 73795 (1995 FH8) 0.8566 11509 Thersilochos (1990 VL6) Fig. B10 6997 Laomedon (3104 T-3) D (H2012, 55) 0.8566 617 Patroclus (1906 VY) L X (T1989) 5119 (1988 RA1) 0.8322 0.8322 6002 (1988 RO) 155337 (2006 KH89) 0.9735 295336 (2008 HY8) 0.8566 1 0.9394 1 106060 (2000 SS316) 0.9534 1 125159 (2001 UV93) 11887 Echemmon (1990 TV12) 0.9525 34642 (2000 WN2) 0.9534 0.8569 0.95340.9332 0.8569 32437 (2000 RR97) D (H2012, 59) 0.98 1 30505 (2000 RW82) 369886 (2012 RM6) 0.9802 0.9802 2895 Memnon (1981 AE1) C (B2004) 0.9802 0.9802 3317 Paris (1984 KF) D (B2004) 0.907 1 1 62426 (2000 SX186) 80119 (1999 RY138) D (H2012, 65) 0.9732 11275 (1988 SL3) 0.801 37519 Amphios (3040 T-3) 0.9727 32475 (2000 SD234) Memnon Clan 0.9727 1 32501 (2000 YV135) 0.9997 0.9997105808 (2000 SZ135) D (H2012, 68) 131447 (2001 QZ113) 0.9997 31806 (1999 NE11) 1 1 19844 (2000 ST317) 1 24449 (2000 QL63) 0.9594 0.9594 76837 (2000 SL316) 0.9732 122460 (2000 QB146) 0.9732 1 31342 (1998 MU31) 76826 (2000 SW131) 0.7955 19020 (2000 SC6) D (H2012, 74) 343996 (2011 QK3) 343896 (2011 JK8) 0.9065 30504 (2000 RS80) 0.8568 0.9458 4722 Agelaos (4271 T-3) 52273 (1988 RQ10) D (H2012, 70) 0.972 0.972 32339 (2000 QA88) D (H2012, 80) 0.9723 1 0.9735 16667 (1993 XM1) D (H2012, 88) 51345 (2000 QH137) 0.8198 0.947 D (H2012, 79) 55678 Lampos (3291 T-1) 0.9999 1 0.9999 1 156237 (2001 UH146) 156250 (2001 UM198) 51994 (2001 TJ58) D (H2012, 56) 0.9801 284433 (2007 DU52) 0.9592 155789 (2000 TD9) 1971 FV Clan 0.9594 3708 (1974 FV1) 1 0.8385 0.9798 110380 (2001 SO343) 0.9598 122391 (2000 QZ75) 1 1 32356 (2000 QM124) 99328 (2001 UY123) D (F2007) 157741 (2006 BE202) 0.9248 23463 (1989 TX11) 0.92480.947 154990 (2005 AA66) 0.905 0.9779 51359 (2000 SC17) D (F2007) 57714 (2001 UY124) 4348 Poulydamas (1988 RU) X (B2004) 0.9996 1989 TX Clan 30806 (1989 UP5) 0.9996 17423 (1988 SK2) 11 0.9996 0.9996 2674 Pandarus (1982 BC3) D (T1989) 0.8313 0.8886 1 0.8313 158333 (2001 WW25) 157471 (2005 AX71) 0.889 160164 (2001 TW252) 185906 (2000 SF94) 0.889 0.9609 0.9594 283519 (2001 TP47) 0.889 0.889 0.9732 56976 (2000 SS161) D (H2012, 58) 125059 (2001 TB233) 0.7649 0.952 54646 (2000 SS291) 0.7649 D (T1989) 0.9793 0.9996 2357 Phereclos (1981 AC) Phereclos Clan 110832 (2001 UA58) 0.9591 156294 (2001 WU66) 0.9592 D (H2012, 55) 1 30499 (2000 QE169) Patroclus Superclan 55460 (2001 TW148) 127534 (2002 WR17) 119528 (2001 US179) 0.8681 0.9719 0.9719 52511 (1996 GH12) 0.8681 58084 Hiketaon (1197 T-3) 38257 (1999 RC13) 0.8945 56968 (2000 SA92) D (F2007) 24452 (2000 QU167) 0.8692 0.9592 D (F2007) 105896 (2000 SG187) 0.8692 99311 (2001 SQ282) 18037 (1999 NA38) 1 0.9747 1 18278 Drymas (4035 T-3) 1 1 5511 Cloanthus (1988 TH1) D (F2007) 1 0.9747 122581 (2000 RJ24) 17365 (1978 VF11) 17420 (1988 RL13) 0.9747 0.9741 0.9747 0.9741 11869 (1989 TS2) 1 D (H2012, 56) 0.9747 120454 (1988 SJ2) 18268 Dardanos (2140 T-3) D (F2004) 0.8621 51350 (2000 QU176) 0.8621 62692 (2000 TE24) 105746 (2000 SP92) 0.9494 0.9494 30708 Echepolos (4101 T-3) 51365 (2000 TA42) 1 1 76867 (2000 YM5) 1 122592 (2000 RE29) 129153 (2005 EL140) 1 1 1 1208 Troilus (1931 YA) 1 1 1 FCU (T1989) 1 299491 (2006 BY198) 1 17172 (1999 NZ41) 1 117447 (2005 AX46) 1 1 29977 (1999 NH11) 32480 (2000 SG348) 1 32464 (2000 SB132) 1 Troilus Clan 1 22180 (2000 YZ) 1 30791 (1988 RY11) 19018 (2000 RL100) 9023 Mnesthus (1988 RG1) 1 1 17415 (1988 RO10) 1 17171 (1999 NB38) 2363 Cebriones (1977 TJ3) D (T1989) 1 0.9141 4709 Ennomos (1988 TU2) 1 24470 (2000 SJ310) 53419 (1999 PJ4) 0.9279 0.9141 0.9279 32496 (2000 WX182) 0.999 51910 (2001 QQ60) 0.9735 1 5120 Bitias (1988 TZ1) 16956 (1998 MQ11) 0.9798 Cebriones Clan 54656 (2000 SX362) 1 51969 (2001 QZ292) 1 1 32440 (2000 RC100) 1 1 29603 (1998 MO44) 1 129135 (2005 AD21) 23549 Epicles (1994 ES6) D (F2007) 1 153708 (2001 UK76) 0.9304 291327 (2006 BQ194) 4805 Asteropaios (1990 VH7) 0.9126 1 4828 Misenus (1988 RV) 97893 (2000 QV65) 0.892 0.9588 4792 Lykaon (1988 RK1)11 0.8994 D (B2004) 0.8994 39474 (1978 VC7) 0.9803 D (H2012, 52) 0.9516 1 106001 (2000 SR283) 284443 (2007 EE51) 0.9347 158231 (2001 SJ256) 0.8942 Asteropaios Clan 0.8942 32397 (2000 QL214) 0.952 54582 (2000 QU179) 0.952 5257 (1988 RS10) 0.952 0.952 153758 (2001 UQ214) 0.9998 0.9997 11487 (1988 RG10) 185485 (2007 EL68) 77897 (2001 TE64) 0.9794 9142 Rhesus (5191 T-3) 0.9256 58931 Palmys (1998 MK47) 42277 (2001 SQ51) Fig. B9 0.9266 0.9521 0.9319 5233 (1988 RL10) 160465 (2006 BL226) 0.9068 12649 Ascanios (2035 T-3) 13402 (1999 RV165) 0.9339 76840 (2000 TU3) 62714 (2000 TB43) 0.9999 51354 (2000 RX25) 0.9339 0.9999 178268 (2008 AH32) 11554 Asios (1993 BZ12) X (H2012, 93) 0.9999 284882 (2009 FY59) 0.9999 0.9999 124696 (2001 SC137) 0.9339 0.9999 0.9999 0.9999 9430 Erichthonios (1996 HU10) D (F2004) 0.9999 0.9999 0.9999 11488 (1988 RM11) XD/D (F2007, H2012, 51) 30498 (2000 QK100) 32482 (2000 ST354) X (H2012, 72) 1 17442 (1989 UO5) 29314 Eurydamas (1994 CR18) 1 1 X (H2012, 66) 30704 Phegeus (3250 T-3) Dolon Clan 0.9535 1 156125 (2001 SH347) 1 414468 (2009 KM14) 1 7815 Dolon (1987 QN) 1 24472 (2000 SY317) 1 55060 (2001 QM73) 1 1 55419 (2001 TF19) 248550 (2005 XS92) 157468 (2004 XS184) 32794 (1989 UE5) DX (F2007) 0.9794 32499 (2000 YS11) D (H2012, 89) 0.9794 11663 (1997 GO24) DX (F2007) 0.9534 0.9534 1 76812 (2000 QQ84) 1 24451 (2000 QS104) 1 32811 Apisaon (1990 TP12) X (H2012, 59) 1 1 51962 (2001 QH267) 0.9534 1 1 18493 Demoleon (1996 HV9) DX (F2007) Apisaon Clan 1 122733 (2000 SK47) D (H2012, 58) 61610 (2000 QK95) 34298 (2000 QH159) D (H2012, 54) 0.9784 0.9996 4707 Khryses (1988 PY) C (F2007) 0.9737 47967 (2000 SL298) D (F2007, H2012) 0.9737 0.9784 17418 (1988 RT12) 0.9788 110359 (2001 SA318) 0.9788 0.9737 31037 Mydon (1996 HZ25) 0.9737 1 1 12126 (1999 RM11) Khryses Clan 1 45822 (2000 QQ116) 17314 Aisakos (1024 T-1) 333412 (2002 WE29) 0.9532 5638 Deikoon (1988 TA3) 0.9532 76824 (2000 SA89) 1 22808 (1999 RU12) 1 1 1 55457 (2001 TH133) 0.9532 1 1 77891 (2001 SM232) 99943 (2005 AS2) 116439 (2003 YN162) 1999 RU Clan 16070 (1999 RB101) D (H2012, 69) 0.9532 2 0.9391 76820 (2000 RW105) 32435 (2000 RZ96) 0.9794 0.9391 0.9794 30506 (2000 RO85) 0.9794 301760 (2010 JP42) 0.9391 58008 (2002 TW240) D (H2012, 58) 0.9532 129145 (2005 CE) 0.9788 5648 (1990 VU1) 0.9593 XD (B2004) 0.9593 0.9788 51935 (2001 QK134) 0.9788 118815 (2000 SM108) 0.9788 18228 Hyperenor (3163 T-1) 0.9189 1 1 5907 (1989 TU5) 29196 (1990 YY) 0.9532 187476 (2006 BB213) 0.9395 73677 (1988 SA3) 1990 VU Clan 0.9594 15977 (1998 MA11) D (F2004) 1 0.9803 24459 (2000 RF103) 0.9803 30705 Idaios (3365 T-3) 0.98030.9803 D (H2012, 69) 128299 (2003 YL61) 0.9803 1 47969 (2000 TG64) D (H2012, 58) 56962 (2000 SW65) 371911 (2008 DB47) 284192 (2006 BR12) 155332 (2006 BA157) 0.9612 88775 (2001 SY76) 0.9346 0.9735 11552 Boucolion (1993 BD4) D (H2012, 66) 0.9735 36425 (2000 PM5) 0.9735 1173 Anchises (1930 UB) 0.97350.9735 X (T1989) 0.9735 11273 (1988 RN11) 0.9343 1 11089 (1994 CS8) X (F2004) Anchises Clan 161646 (2006 BL56) 4827 Dares (1988 QE) D (H2012, 89) 116134 (2003 WZ142) 0.8095 319282 (2006 BY73) 0.935 0.935 15502 (1999 NV27) D (F2004) 0.9794 184988 (2006 FF12) 0.9794 0.9794 17419 (1988 RH13) C (H2012, 62) 0.9346 0.9794 0.8884 68519 (2001 VW15) 1988 RH Clan 2207 Antenor (1977 QH1) D (T1989) 0.9787 Fig. B11 125106 (2001 UR39) 13 4708 Polydoros (1988 RT) 0.5379 D (H2012, 74) 0.5379 127532 (2002 WH9) 0.9997 7352 (1994 CO) D/X (B2004, F2004) 1 0.9547 1 98153 (2000 SY68) 1 0.9732 18940 (2000 QV49) D (F2004) 31820 (1999 RT186) D (F2007) 1994 CO Clan 0.9547 24448 (2000 QE42) D (H2012, 64) 1 150876 (2001 SA220) 1 30807 (1989 UQ5) D (H2012, 62) 1 0.897 1 110859 (2001 UW79) 179902 (2002 VO4) 0.9546 4754 Panthoos (5010 T-3) 1989 UQ Clan 64270 (2001 TA197) 51346 (2000 QX158) D (H2012, 59) 5 0.9546 105720 (2000 SR79) 0.9546 1 0.9596 1 98037 (2000 RE20) 1 36922 (2000 SN209) 1 1 30698 Hippokoon (2299 T-3) D (F2007, H2012) 0.9546 0.9594 1 0.9546 106091 (2000 SZ361) 32370 (2000 QY151) 0.9596 154992 (2005 CV68) 0.9594 77902 (2001 TY141) 0.9596 54653 (2000 SB350) 0.9394 0.9546 0.9394 47963 (2000 SO56) Aneas Superclan 0.9546 0.9394 2223 Sarpedon (1977 TL3) DU/D (T1989, B2004, F2004) Sarpedon Clan 0.9598 84709 (2002 VW120) D (F2004) 0.9598 18054 (1999 SW7) 0.95980.9799 D (H2012, 74) 0.9598 54655 (2000 SQ362) 0.8971 0.9598 0.92 370105 (2001 TA132) 491611 (2012 TX51) 17414 (1988 RN10) 2893 Peiroos (1975 QD) 0.9544 D (T1989) 36624 (2000 QA157) 1 34746 (2001 QE91) 0.954 1 1 1867 Deiphobus (1971 EA) 1 247967 (2003 YD149) 0.9744 0.9744 114208 (2002 VH107) D (H2012, 59) 24458 (2000 RP100) 1 155786 (2000 SD358) 0.954 1 1 48764 (1997 JJ10) 1 1 30942 Helicaon (1994 CX13) D (H2012, 59) 0.9542 47962 (2000 RU69) 53418 (1999 PY3) 76857 (2000 WE132) 0.9795 0.9544 0.9795 24446 (2000 PR25) D (H2012, 59) 0.9544 1 Aneas Clan 4791 Iphidamas (1988 PB1) 1 1 29976 (1999 NE9) D (H2012, 81) 0.9544 105803 (2000 SH132) 25347 (1999 RQ116) 0.9747 D (B2004) 0.9747 1172 Aneas (1930 UA) D (T1989) 0.9744 129147 (2005 CY70) 117389 (2004 YD23) 0.9997 4867 Polites (1989 SZ) 0.9997 0.9997 12444 Prothoon (1996 GE19) 0.9997 0.9997 12929 (1999 TZ1) 18046 (1999 RN116) D (H2012, 89) 65590 Archeptolemos (1305 T-3) 282198 (2001 UM166) 0.9647 12052 Aretaon (1997 JB16) 5130 Ilioneus (1989 SC7) D (F2004) 1 109549 (2001 QM257) 0.9735 0.9732 125045 (2001 TK211) 17416 (1988 RR10) D (F2004) 0.9732 1 133853 (2003 YQ133) 1 153141 (2000 SP203) 1 0.9735 1 34785 (2001 RG87) 1 X (F2004) 0.9732 114345 (2002 XN72) Fig. B12 1 5476 (1989 TO11) 47957 (2000 QN116) 0.9732 34521 (2000 SA191) 0.9732 25883 (2000 RD88) Mentor Clan 0.9732 3451 Mentor (1984 HA1) X (H2012, 96) 0.9735 0.9732 1 289501 (2005 EJ133) 1 1 5637 Gyas (1988 RF1) 1 99334 (2001 VC92) 1 68444 (2001 RH142) 1 133862 (2004 BR38) 1 1 12242 Koon (1988 QY) 48438 (1989 WJ2) 57013 (2000 TD39) 1 1 4715 (1989 TS1) D (B2004) 25344 (1999 RN72) 0.947 55267 (2001 RP132) 31819 (1999 RS150) 24453 (2000 QG173) 0.9735 1 0.9735 184983 (2006 CS19) 1 1 246114 (2007 GR70) 0.9795 47959 (2000 QP168) 0.9735 0.9795 Astyanax Superclan 161664 (2006 DM16) 0.9795 1 1 1872 Helenos (1971 FG) 0.9795 283173 (2009 HZ62) 4829 Sergestus (1988 RM1) XD (F2004) 0.9735 1 Helenos Clan 0.9735 47955 (2000 QZ73) 1 1 31814 (1999 RW70) 161916 (2007 EO34) 152297 (2005 TH49) 106160 (2000 TG61) 1 117385 (2004 YN20) 0.9735 1 52767 Ophelestes (1998 MW41) 1 1 23694 (1997 KZ3) D (F2007) 32430 (2000 RQ83) D (F2004) 0.9735 216409 (2008 GM84) 1 98143 (2000 SS60) 1 1 51340 (2000 QJ12) 122962 (2000 SG215) 32420 (2000 RS40) 0.9735 1 1 24444 (2000 OP32) 99309 (2001 SH264) 64326 (2001 UX46) 0.9592 0.9592 1871 Astyanax (1971 FF) D (F2004) 0.9735 1 0.9796 76804 (2000 QE) D (F2007) 153500 (2001 RN122) 1 1 17492 Hippasos (1991 XG1) 0.9735 98362 (2000 SA363) 1 31344 (1998 OM12) 77906 (2001 TU162) 0.9735 32615 (2001 QU277) D (F2004) 0.9735 106143 (2000 TU44) 51958 (2001 QJ256) 0.9735 1 0.9735 187456 (2005 XK5) Astyanax Clan 0.9735 18137 (2000 OU30) D (F2004) 99306 (2001 SC101) 1 0.9735 24454 (2000 QF198) CX (H2012, 57) 0.9798 151883 (2003 WQ25) 0.9395 0.9395 16560 Daitor (1991 VZ5) CX (H2012, 77) 0.9735 0.9998 1 2594 Acamas (1978 TB) 48604 (1995 CV) 48249 (2001 SY345) D (F2004) 0.9735 77860 (2001 RQ133) 0.9735 34835 (2001 SZ249) 0.9735 9030 (1989 UX5) D (F2007) 0.9735 111198 (2001 WX20) 0.9735 131635 (2001 XW71) 0.9735 51351 (2000 QO218) 0.9509 0.9509 54596 (2000 QD225) 0.9774 182522 (2001 SZ337)

Figure 6. Consensus tree of cladistical analysis of 407 L5 Jovian Trojans. Numbers indicate fraction of 10000 trees where branch is present. Colours are indicative of previously identified collisional families: Brown: Ennomos; Purple: 2001 UV209 after Nesvorný et al.(2015). Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009) from different sources, T1989: Tholen(1989); B2004: Bendjoya et al.(2004); F2004: (Fornasier et al. 2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012). Lucy Targets are indicated by an L. A high resolution, expanded form of this figure is available in online supplemental material. Blue rectangles correspond to detailed figures in AppendixB.

MNRAS 000,1–26 (2020) 16 T. R. Holt et al.

3.2.1.2 1990 VU1 clan: There are two identified subclans (1990 with any clan in this analysis. The binary 617 Patroclus (1906 VY) VU1 and Idaios subclans) in this clan. The type object, 1990 VU1 (Merline et al. 2001) is currently the only Lucy target in the L5 −1 has been identified as a XD-type (Bendjoya et al. 2004), with five swarm. The Δ푉ref to 617 Patroclus (1906 VY) (31.57±20.49 ms ) −1 other D-types (16070 (1999 RB101), 58008 (2002 TW240), 15977 is smaller than the 푉esc (46.94 ms ) and similar to the Δ푉cent −1 (1998 MA11), 30705 Idaios (3365 T-3) and 47969 (2000 TG64) (31.62 ± 15.09 ms ). Fornasier et al. 2004; Hasselmann et al. 2012) present in the clan. In terms of stability, this clan has an escape fraction (0.52), nearly 3.2.2.1 Memnon clan: The Memnon clan has several D-types double that of the L5 swarm as a whole (Holt et al. 2020a, 0.2489). (30505 (2000 RW82), 3317 Paris (1984 KF), 80119 (1999 RY138) There is a wide variety of escape fraction of members this clan, with and 105808 (2000 SZ135) Bendjoya et al. 2004; Hasselmann et al. all 9 particles of the type object 1990 VU1 escaping, but two other 2012), though the type object, 2895 Memnon (1981 AE1) is a C- members, 30705 Idaios (3365 T-3) and 301760 (2010 JP42), being type (Bendjoya et al. 2004). As with the superclan, this clan is stable ◦ ◦ completely stable. This range of stability is not unexpected, as the (퐹esc: 0.11) and close to the L5 Lagrange point (296.29 -303.31 ). −1 clan has a wide variance in Δ푉cent (24.87±18.96 ms ), 푒prop (0.04- A representative of the 2001 UV209 collisional family (37519 0.14) and sin푖prop (0.01-0.43). The Gaia G magnitude is constrained Amphios (3040 T-3) Nesvorný et al. 2015), is within this clan, and (17.67-18.19 mag), with only four similar sized objects represented, is the the type object of the Amphios subclan, which has a small −1 −1 more analysis is needed. The (i - z) SDSS colour (0.05-0.317) has a Δ푉ref (14.06 ± 8.13 ms ) and Δ푉cent (13.04 ± 7.89 ms ), close −1 narrow range in this clan. to the 푉esc (12.83 ms ). The objects in this subclan may represent unidentified members of the 2001 UV209 collisional family, or at 3.2.1.3 Anchises clan: This clan is unstable (퐹esc: 0.88), includ- least closely associated objects. ing all clones of the type object 1173 Anchises (1930 UB). This The clan has mid range (b - v) (0.74-0.93), (u - g) (1.18-1.73) particular object was studied by Horner et al.(2012), who found and (g - r) (0.52-0.7) SDSS colours, with high (i - z) values (0.12- that it will most likely escape the Trojan population and evolve to 0.34). The two MOVIS objects 295336 (2008 HY8), (Y - J):0.559373, become either a Centaur or Jupiter family comet on hundred-million (J - Ks):0.973755, (H - Ks):0.407764, and 369886 (2012 RM6), (Y - year timescales. The clan is located a few degrees from the 300◦ J):0.318022, (J - Ks):0.585282, show quite different colours. Further Lagrange point (291.6◦ to 296.29◦) with a decent range (32.05◦ to characterisation of the large objects in the clan, 2895 Memnon (1981 ◦ 51.55 ) and 훿푎prop (0.08 to 0.12). The type object 1173 Anchises AE1), 3317 Paris (1984 KF) and 37519 Amphios (3040 T-3), would (1930 UB), along with 11089 (1994 CS8) are X-types (Tholen be required to resolve this dichotomy in the colours. 1989; Fornasier et al. 2004). There is also a D-type, (11552 Bouco- lion (1993 BD4) Hasselmann et al. 2012) in this clan. In the Gaia G 3.2.2.2 Troilus clan: Within the clan there are two small sub- band, 1173 Anchises (1930 UB) shows a different value (16.75 mag) clans, the Troilus and 1988 RY11 subclans. The Troilus subclan, to the other two smaller, measured objects, 11089 (1994 CS8) and which in includes the type object, 1208 Troilus (1931 YA), of the 11552 Boucolion (1993 BD4) (18.47 and 18.32 mag respectively). clan, is entirely stable. The members of the 1988 RY11 subclan have Unfortunately, 1173 Anchises (1930 UB) was not observed in ei- a higher escape fraction (퐹esc: 0.2), though even this is lower than ther of SDSS or MOVIS surveys. This is of note, as the SDSS (b - v) the over all L5 escape fraction (0.2489). (0.69-0.93), (g - r) (0.48-0.7), (r - i) (0.2-0.27), as well as the MOVIS The type object, 1208 Troilus (1931 YA), is an interesting (Y - J) (0.23-0.32) and (J - Ks) (0.44-0.53) colours are plausibly case. It is the type object of the Troilus clan, which also contains diagnostic of the clan. a single member of the Ennomos collisional family (76867 (2000 YM5) Nesvorný et al. 2015). It is classified as FCU-type (Tholen 1989), designating it as an unusual object. It is the only ’F-type’ 3.2.2 Greater Patroclus Superclan in the Trojan swarm. This type was degenerated under the modern This large (133 members) superclan contains six clans, as shown in Bus-Demeo system (Bus 2002) into the B-types, closely associated with the other C-types in the Trojans. As the type object is relatively Fig. B10. Of these, we discuss the Memnon (23 members), Troilus −1 −1 large, the Δ푉ref (18.95±7.41 ms ) and Δ푉cent (12.88±5.81 ms ) (13 members) and Cebriones (17 members) clans in the following −1 of the clan is lower than the 푉esc (33.6 ms ). The clan is clustered sections. The details of the other clans, 1971 FV1 (18 members), ◦ ◦ centrally around the L5 Lagrange point (298.63 to 302.14 ), which 1989 TX11 (5 members) and Phereclos (17 members), are available on the Github repository10. There is a diversity of taxonomic types likely indicates that it dates back to the time the Jovian Trojans were represented in this superclan, though as with other superclans, the captured. The SDSS (b - v) (0.72-0.91), (g - r) (0.5-0.7) and (i - z) members are predominantly D-types. Overall, the superclan is more (0.07-0.23) colours are relatively constrained. An initial tight MOVIS bin is due to only a single object (299491 (2006 BY198) Popescu stable (퐹esc: 0.1) than the L5 swarm as a whole. Each of the clans et al. 2018). has a lower escape rate than the L5 swarm, with several having no escapees, see Table3, for details. The clan is clustered close to the ◦ ◦ ◦ 3.2.2.3 Cebriones clan: 4709 Ennomos (1988 TU ), the largest 300 Lagrange point (296.29 -303.31 ), with relatively low 훿푎prop 2 (0.0-0.11 au). member of the Ennomos collisional family, is in the Cebriones clan The largest member of the Ennomos collisional family (4709 (Nesvorný et al. 2015). Again, 4709 Ennomos (1988 TU2) is not used as the type object, as the chosen type object, 2363 Cebriones Ennomos (1988 TU2) Nesvorný et al. 2015), is within this superclan, though it is not used as the type object. The actual type object, 617 (1977 TJ3) was discovered earlier. A non-canonical family member, Patroclus (1906 VY) was discovered over 80 years earlier and thus 32496 (2000 WX182) (32496 (2000 WX182) Rozehnal et al. 2016), is considered the type for the superclan, though it is not associated is also in the clan. This is complicated by two members of the non-canonical 2001 UV209 family (17171 (1999 NB38) and 24470 (2000 SJ310), Rozehnal et al. 2016) that are also present in the clan. 10 https://github.com/TimHoltastro/ 2363 Cebriones (1977 TJ3) is a D-type object (Tholen 1989), holt-etal-2021-Jovian-Trojan-astrocladistics.git and the only classified member of the clan. This clan has the highest

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 17 escape rate in the Greater Patroclus superclan (퐹esc: 0.23), and even This superclan has a diversity of taxonomic types. The major- this is lower than that of the overall L5 swarm (0.2489 Holt et al. ity of the superclan is D-types, but the type object of the Mentor 2020a). In terms of colours, there are an insufficient number of clan, 3451 Mentor (1984 HA1) is a well recognised X-type (Bus multi-spectral observations to ascertain any trends, with only two 2002; Hasselmann et al. 2012). There are also two CX-types in the members represented in the SDSS data, 17415 (1988 RO10) and Astyanax clan (24454 (2000 QF198) and 16560 Daitor (1991 VZ5) 129135 (2005 AD21), and two different objects in MOVIS, 51969 Hasselmann et al. 2012). The Helenos clan contains one taxonomic (2001 QZ292) and 53419 (1999 PJ4). identified member, 4829 Sergestus (1988 RM1), an XD-type (For- nasier et al. 2004). This diversity of taxonomic types is reflected in the wide range of all colour values (W1:0.07-0.4, W2:0.03-0.4, 3.2.3 Greater Aneas Superclan G-mag:15.86-18.7 mag, (b - v):0.65-0.91, (u - g):1.18-1.95, (g - r):0.44-0.68, (r - i):0.07-0.4, (i - z):-0.26-0.29, (Y - J):0.05-0.46, (J - This superclan (64 members) contains five clans, 1988 RH13 (6 members), 1994 CO (5 members), 1989 UQ (5 members), Sarpe- Ks):0.07-1.18, (H - Ks):0.04-0.81). The superclan has a large Δ푉ref 5 −1 don (17 members) and Aneas (26 members) clans, with subclans (92.28 ± 43.46 ms ) compared to the 푉esc of the largest member, −1 −1 in the Aneas clan (Hippokoon and Sarpendon subclans) and Aneas 3451 Mentor (42.2 ms ), though the Δ푉cent (50.89 ± 28.51 ms ) clans (Helicaon, Iphidamas and Aneas subclans). The only clan dis- is more reasonable. The escape fraction of the supergroup (0.42) cussed in detail here is the Aneas clan. Almost all taxonomically is higher than the L5 swarm. The superclan has a large range of identified members of this superclan are D-types (Tholen 1989; high 훿푎prop values (0.07 au - 0.15 au), though the smaller values Bendjoya et al. 2004; Fornasier et al. 2004; Hasselmann et al. 2012). are limited to the 1988RR10 subclan (훿푎prop:0.07-0.11) within the Mentor clan. The only exception is 17419 (1988 RH13), the type object of the 1988 RH13 Clan, a C-type, though with a comparatively low con- fidence score (62, Hasselmann et al. 2012). Over-all the superclan 3.2.4.1 Mentor Clan: 3451 Mentor (1984 HA1), the type ob- has a relatively low escape rate (퐹esc: 0.2), when compared with ject of the Mentor clan, is a large (126.29km) X-type (Bus 2002; the L5 swarm (0.2489 Holt et al. 2020a). Within the Greater Aneas Hasselmann et al. 2012). There is also a X-type (34785 (2001 superclan, the majority of unstable members are in the 1988 RH13 RG87) Fornasier et al. 2004), and two D-types (5130 Ilioneus (1989 Clan, which has an escape rate of 0.65. Other clans have a simi- SC7) and 17416 (1988 RR10) Fornasier et al. 2004). The Δ푉ref −1 lar or lower escape rate than the superclan. Though 1172 Anease (48.51±24.27 ms ) is close to the 퐹esc of 3451 Mentor (1984 HA1) −1 −1 (1930 UA) is a large object (118.02km), the reference object for the (42.23 ms ), and the Δ푉cent (32.58 ± 18.62 ms ). Even amongst dispersal velocities in the superclan is 1867 Deiphobus (1971 EA) the Trojans, which are some of the darkest objects in the Solar sys- −1 (118.22km). The Δ푉ref (65.85 ± 34.23 ms ) is high. The Δ푉cent tem (Grav et al. 2012), the Mentor clan has a range of low geomet- −1 (38.7 ± 20.27 ms ), though still quite high, is closer to the 푉esc ric (0.0367-0.107) and WISE (W1:0.0557-0.171, W2:0.0276-0.177 (39.53 ms−1). Grav et al. 2011, 2012) albedos. Unfortunately, there are only two representatives in the SDSS dataset: 3451 Mentor (1984 HA1) and 3.2.3.1 Aneas clan: The Aneas clan contains several D-type 133862 (2004 BR38), and only a single representative in the MOVIS objects, including the type object 1172 Aneas (1930 UA) (Tholen database, 289501 (2005 EJ133), and therefore any comments on 1989). The three members of the Ennomos collisional family present colours are preliminary. in the clan (36624 (2000 QA157), 1867 Deiphobus (1971 EA) and 247967 (2003 YD149) Nesvorný et al. 2015) form a cluster with 3.2.4.2 Astyanax Clan: This is one of the largest clans in 34746 2001 QE91, however this does not fulfill the minimum re- our analysis and at 41 members is larger than some superclans. −1 quirements for a subclan (five objects). There are three other sub- Consequently, it does have a large Δ푉ref (141.79 ± 42.59 ms ) −1 −1 clans Helicaon, Iphidamas and Aneas subclans, each containing at and Δ푉cent (42.8 ± 28.01 ms ) relative to the 푉esc (18.05 ms ) least one D-type. As in the Greater Anease superclan, 1172 Aneas of the small type object (1871 Astyanax (1971 FF), 53.98km). −1 (1930 UA) is the dynamical reference object for Δ푉ref calculations. Two of the subclans, Ophelestes (Δ푉ref : 20.79 ± 12.5 ms , −1 The over all escape fraction of the clan (퐹esc:0.2) is similar to the Δ푉cent : 3.7 ± 6.25 ms ) and 1989 UX (Δ푉ref : 15.28 ± 8.38, −1 Greater Aneas superclan (퐹esc:0.2), though the Helicaon (0.27 퐹esc) Δ푉cent : 12.97 ± 7.93 ms ), have low dispersal velocities, though and Iphidamas (0.33 퐹esc) subclans have a slightly higher rates. In these are higher than the 푉esc of the respective type objects −1 the SDSS colours, (b - v) (0.649-0.857), (g - r) (0.5-0.633)and (i (52767 Ophelestes (1998 MW41):10.83 ms and 9030 (1989 −1 - z) (-0.0167-0.25) are relatively constrained. The (u - g) (1.294- UX5):10.76 ms respectively). Within this clan, there are two 1.847) and (r - i) (0.0682-0.267) values would also be relatively members of the Enominos collisional family in this clan (17492 compact, except for the outlier 129147 (2005 CY70), which has Hippasos (1991 XG1) and 98362 (2000 SA363) Nesvorný et al. comparatively high values, (u - g):2.28, (r - i):0.37. 2015) clustered close together in the Astyanax subclan. The small Gaia range (17.836-18.381 mag) is due to only two objects being represented, 16560 Daitor (1991 VZ5) and 17492 Hippasos(1991 3.2.4 Greater Astyanax Superclan XG1). The majority of the objects (60.09 per cent) are in the SDSS colour set. The (b - v) (0.649-0.926) and (g - r) (1.183-1.958) values This is the terminal superclan in the L5 tree. It contains 809 mem- bers, of which 41 are in the Astyanax clan, discussed in detail below. are low and constrained, where as the (u - g) (0.5-0.633) and (i - The Mentor clan (20 members) is also discussed. The remaining He- z)(-0.15-0.317) are on the high end and broad. lenos clan contains 11 members, and the values are presented in the Github repository11. 4 IDENTIFIED PRIORITY TARGETS

11 https://github.com/TimHoltastro/ One of the outcomes of this work is to identify priority targets for holt-etal-2021-Jovian-Trojan-astrocladistics.git future observations. Here, we collate these objects and describe the

MNRAS 000,1–26 (2020) 18 T. R. Holt et al. rationale for their selection. A summary of these objects is presented 2895 Memnon (1981 AE1) and 37519 Amphios (3040 T-3): Both in Table4. of these objects are located in the stable L5 Memnon clan, part of the Greater Patroclus superclan. One of only two members of the 1404 Ajax (1936 QW), 4086 Podalirius (1985 VK2) and 7119 2001 UV209 collisional family included in this analysis, is 37519 Hiera (1989 AV2): These three objects are located in the Ajax clan. Amphios (3040 T-3) (Nesvorný et al. 2015), also in the Memnon All three are fairly large, with H magnitudes brighter than 9. They clan. The objects are the type of their respective subclans. The are of interest due to a lack of taxonomically identified objects in the Memnon clan is also the closest clan to 617 Patroclus (1906 VY), a Ajax clan. This clan is close to the Eurybates clan, which contains Lucy target not affiliated with any clan. Both of these objects could multiple members of the Eurybates collisional family, along with provide additional information about the context of 617 Patroclus 3548 Eurybates (1973 SO), a Lucy target. (1906 VY), though 2895 Memnon (1981 AE1) is the cladistically closer object. 37519 Amphios (3040 T-3) is an interesting object in its own right, due to it’s affiliation with the 2001 UV209 collisional 2456 Palamedes (1966 BA1): The largest object (H magnitude of 9.3) for the Thersites clan, which contains 21900 Orus (1999 family, and may be the largest remnant of the collision that created that family. VQ10), a Lucy target. Only a single member of the clan, 53477 (2000 AA54), has SDSS colour values. Further classification and 1208 Troilus (1931 YA): A relatively large object (H mag 8.99), observations of 2456 Palamedes (1966 BA1) would help to provide 1208 Troilus (1931 YA) is the only F/B-type object identified in context for the smaller Lucy target, 21900 Orus (1999 VQ10), and the clan as a whole. the Trojan swarm (Tholen 1989; Bus 2002). Though this taxonomic type is associated with the C-types, there are none identified in the 5283 Pyrrhus (1989 BW): This object is the largest in the Epeios Troilus clan. This could indicate that the object is unique in the Tro- clan. In Bendjoya et al.(2004), it is reported as having a nega- jan population. Further detailed observations could help to place tive spectral slope. Unfortunately, it not represented in either of the this object in a wider small Solar system body context, and pos- multi-band surveys. This clan is of interest, as the only taxonom- sibly identify previously unknown associations between the Jovian Trojans and other populations. ically identified object, 12921 (1998 WZ5), a X-type amongst the prominently D-types of the Greater Achilles superclan. The 258656 4709 Ennomos (1988 TU ): The largest member of the Ennomos (2002 ES76)-(2013 CC41) pair identified by Holt et al.(2020b) is 2 also potentially in the Epeios clan, close to 5283 Pyrrhus (1989 collisional family (Brož & Rozehnal 2011). The object is a member BW). of the Cebriones clan, which has limited colour information. Further characterisation of this object would help to understand the diversity of collisional family members in the Jovian Trojans. 659 Nestor (1908 CS): An XC-type amongst the mostly D-types of the L4 Trojan swarm. It is also one of the largest members of the population (with a H magnitude of 8.99), and is the type 128383 (2004 JW52): This relatively small object (H mag 13.1) member of the Greater Nestor superclan, which has a variety of was removed at the binning stage from the analysis, due to due to taxonomic types. Additional observations of this object would help its anomalous colour. If the object was included, the SDSS colours to understand the diversity of objects in the Trojan population. would consist of two bins, this object and everything else. The object has high (b - v) and (g - r) colours (1.55 and 1.3 respectively) in comparison to the rest of the Jovian Trojan population ( 0.10-1.275 1437 Diomedes (1937 PB): This is the type object of the Diomedes and 0.300-1.045), as well as low (i - z) values (-0.55, compared with - clan, which includes 11351 Leucus (1997 TS ), a small Lucy target. 25 0.37-0.45). These anomalous values could be explained if the object Further observations of this object could provide more details on was an interloper in the Trojan population, but this is contradicted by 11351 Leucus (1997 TS25) (H mag: 10.7), and being a brighter the stability. The object has an approximately 0.55 fractional escape object (with an absolute magnitude of 8.3), is able to be observed rate, though only after spending an average of 3.7 × 109 in the more easily. Like 2456 Palamedes (1966 BA ), 1437 Diomedes 1 L Trojan swarm (Holt et al. 2020a). Further characterisation and (1937 PB) offers an opportunity to provide some context, prior to 4 investigations into this object could help to resolve this discrepancy visitation of a related object by Lucy. and discover the history of the object.

4138 Kalchas (1973 SM) and 7152 Euneus (1973 SH1): These objects are identified X-types in a very stable clan, with absolute 5 LUCY CONTEXT magnitudes of 10.1 and 10.2, respectively. Another large X-type in the population, 617 Patroclus (1906 VY), is part of a binary, and At the time of writing, five of the Jovian Trojans have been selected a Lucy target. Though not in the same clan, further investigations as targets to be visited by the Lucy spacecraft in the late 2020’s on 4138 Kalchas (1973 SM) and 7152 Euneus (1973 SH1) could to early 2030’s (Levison et al. 2017). Each of these objects are provide some details on other X-types in a stable configuration. included in our astrocladistical analysis, which allows us to provide additional information on the context of those targets, in advance of 1173 Anchises (1930 UB): The subject of dynamical and thermo- the mission. physical studies by Horner et al.(2012) and the type object of the unaffiliated L5 Anchises clan. This object is one of the darkest ob- 3548 Eurybates (1973 SO) is the largest fragment of the Eurybates jects (0.05 albedo) in the Trojan population, though it is quite large, collisional family (Brož & Rozehnal 2011), and a member of the over 100km, and has an H-magnitude of 8.89. We echo the call of Greater Ajax superclan, as described in section 3.1.4. Six other Horner et al.(2012) for further investigation into this object, par- members of the preciously identified Eurybates collisional family, ticularly in broadband colours, as the object is not represented in are also located within the clan. The majority of the objects that SDSS or MOVIS databases. are thought to be closely associated with 3548 Eurybates (1973

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 19

Table 4. Physical and observational parameters for the priority targets iden- in the clan, 24341 (2000 AJ87), is a C-type (Fornasier et al. 2007). tified in this work, taken from the Asteroid Lightcurve Database (http:// In addition, there are several other closely associated C-types. This www.minorplanet.info/lightcurvedatabase.html, retrieved 2020 could suggest that 21900 Orus (1999 VQ10) has a different compo- October 22, Warner et al. 2009). Here, P denotes the rotation period of the sition to 11351 Leucus (1997 TS25), despite both being designated asteroid, and 퐴min and 퐴max are the minimum and maximum amplitudes of D-types. This further highlights the diversity of taxonomic types the asteroid’s lightcurve. 퐻 is the absolute magnitude of the asteroid, and in the Trojan swarms, and could be confirmed with analysis of the 푝푉 the geometric albedo. Lucy data, as it becomes available. Indications of the differences between 21900 Orus (1999 VQ10) and 121351 Leucus (1997 TS25) Ast푛표. P 퐴min 퐴max 퐻 푝푉 could be investigated using observations of 2456 Palamedes (1966 hrs mag mag mag BA1), the largest object in the Thersander clan, of which 21900 659 15.98 0.22 0.31 8.71 0.040±0.004 Orus (1999 VQ10) is a member. 1173 11.60 0.16 0.73 8.91 0.035±0.002 1208 56.17 - 0.20 9.00 0.037±0.002 The 617 Patroclus (1906 VY)/Menoetius binary system is, so far ± 1404 29.38 - 0.30 9.41 0.050 0.003 the only Lucy target in the L swarm. Being a large object, it is very 1437 24.49 0.34 0.70 8.21 0.028±0.001 5 well studied (Merline et al. 2001; Marchis et al. 2006), and has a well 2456 7.24 0.05 0.27 9.37 0.026±0.002 2895 7.52 0.08 0.48 10.14 - established taxonomy as a X-type (Tholen 1989), though we note 4086 10.43 0.08 0.16 9.29 0.056±0.004 that in the original classification, as well as the Lucy documentation 4138 29.20 0.10 0.40 10.12 0.057±0.007 (Levison et al. 2017), it is a ’P-type’. In our analysis, 617 Patroculus 4709 12.28 0.31 0.47 8.77 0.078±0.005 (1906 VY) is the type object for the Greater Patroclus superclan. 5283 7.32 - 0.11 9.76 0.072±0.007 The binary is not, itself, associated with any of the clans, although 7119 400.00 - 0.10 9.85 0.036±0.005 it is close to the Memnon clan. Part of the issue is that in our 7152 9.73 - 0.09 10.34 - analysis 617 Patroclus (1906 VY) is not represented in the SDSS 37519 50.93 - 0.30 11.10 - catalogue. The inclusion of these data could potentially bring the object into the Memnon clan. Being close to the Memnon clan may associate it with other large members, 2895 Memnon (1981 AE1) SO) can be found in the Eurybates subclan, and are all classified and 37519 Amphios (3040 T-3), though neither of these have any as as C-types (Fornasier et al. 2007). The C-types are relatively colour values, beyond the size dependent Gaia G magnitudes. The rare in the Trojan population, comprising only approximately 12.79 relatively large 37519 Amphios (3040 T-3) is interesting due to it’s per cent by number, compared with over 60, by mass in the Main inclusion in the 2001 UV209 collisional family. While inclusion of Belt (DeMeo & Carry 2013). Other members of the Eurybates clan 617 Patroclus (1906 VY) in the family would be unreasonable, as the include two D-types, 12917 (1998 TG16)(Fornasier et al. 2007) and family creation event would have disrupted the binary (Nesvorný & 5258 (1989 AU1)(Bendjoya et al. 2004), and a X-type, 18060 (1999 Vokrouhlický 2019), this may indicate a link between the family and XJ156)(Fornasier et al. 2007), with all three in the Anius subclan, a the binary. Further analysis of several of these objects, as discussed sister subclan to the Eurybates subclan. This complexity of closely in section4, could help further classify these objects, and place 617 associate subclans, may indicates that 3548 Eurybates (1973 SO) Patroclus (1906 VY) in context prior to Lucy’s arrival, in 2033. may be different to other C-types.

15094 Polymele (1999 WB2) is a member of the Greater Diomedes superclan, as described in section 3.1.6, along with 11351 Leuchus 6 FUTURE SURVEYS (1997 TS25). It is not associated with any clan, though it is worth noting that if falls relatively close to the Philoctetes clan, which In this work, we use astrocladistics to investigate the Jovian Trojan contains several X-types, a C-type, a D-type, and three members of population, drawing upon observational data obtained by the latest the Eurybates collisional family. The diversity in this superclan, and generation of wide-field surveys. In the coming decade, several new the associated Philoctetes clan, means that it is hard to anticipate the surveys will come online, providing a wealth of new data that could physical nature of 15094 Polymele. It may have a shared heritage be incorporated in future studies. Here, we comment on the potential with any of the other members of the clan, and observations by Lucy for the use of the astrocladistical methodology in the analysis of that may well shed new light on its true nature and affiliation. data, and discuss how those surveys will improve our understanding of the Jovian Trojan population. 11351 Leucus (1997 TS25) , like 15094 Polymele (1999 WB2), is a member of the Greater Diomedes superclan. Specifically, 11351 Gaia DR3: In this work we use single G-band (330 to 1050 nm) data Leucus (1997 TS25) is located well within the Diomedes clan, and taken from Gaia DR2 (Spoto et al. 2018). Whilst this single band the type object 1437 Diomedes (1937 PB) (Tholen 1989) is a well data can provide some information about the objects, The Gaia G- recognised DX-type. This suggests that 11351 Leucus (1997 TS25) band magnitudes are clearly linked to size, to first approximation, is representative of the majority of D-type Jovian Trojans (Fornasier but also to some extent albedo and distance. Albedos within the et al. 2007). This close association could imply that 11351 Leucus Jovian Trojans are low, and relatively consistent (Romanishin & (1997 TS25) has a common origin and physical composition to that Tegler 2018). Distance is also normalised somewhat, due to the larger object, and as such, that Lucy’s visit will provide valuable librations of the population around the Lagrange points. In the Gaia data on an object that could be representative of the majority of the DR2 dataset, there are two additional two bands, G퐵푃-band (330- Trojan population that is associated with the D-types. 680 nm) and G푅푃-band (630-1050 nm) (Evans et al. 2018) for stellar objects, but data in these bands is not available for Solar system 21900 Orus (1999 VQ10) , located in the unaffiliated Thersander objects. These data are expected to be included in the full Gaia Clan, is another provisional D-type. The only other classified object DR3 release, which is currently scheduled for release in early 2022,

MNRAS 000,1–26 (2020) 20 T. R. Holt et al. and once available, could be incorporated into future astrocladistical et al.(2018). Using the wide-filed imaging system, in the near-IR surveys in a similar way to the SDSS and MOVIS colours. (0.6-2.0 휇m), RST will be able to observe the majority of the cur- rently known Jovian Trojans. In conjunction with the broadband The Vera Rubin Observatory, with the Legacy Survey of Space Rubin Observatory LSST colours, those observations will yield a and Time (Rubin Obs. LSST), is expected to receive first light in large database of Jovian Trojan characteristics. As computational 2023. During the first few years that Vera Rubin is active, estimates capabilities and algorithm optimisations increases prior to launch, suggest that more than 280,000 Jovian Trojans are expected to be astrocladistics will provide a tool capable of analysing such large discovered (LSST Science Collaboration et al. 2009). Of those ob- datasets. jects, it is likely that more than 150 observations will be made of at least 50,000, which will be sufficient for those objects to be char- acterised in five broadband colours (LSST Science Collaboration 7 CONCLUSION et al. 2009). This will provide a much larger context for taxonomy in the Jovian Trojan population, and small Solar system bodies in In this work we apply the new astrocladistical technique to the Jo- general. Astrocladistics is a tool that could be used to further anal- vian Trojans. We combine dynamical characteristics with colour yse these data, and that is ideally suited to the analysis of such information from the Sloan Digital Sky Survey (SDSS), WISE, vast and sprawling datasets. Assuming that the currently observed Gaia DR2 and MOVIS, into a holistic taxonomic analysis. We create L4/L5 numerical asymmetry holds (Jewitt et al. 2000; Nakamura & two matrices, one for the L4 and one the L5 Trojans, comprised Yoshida 2008; Yoshida & Nakamura 2008; Vinogradova & Cher- of 398 and 407 objects respectively. As part of this analysis, we netenko 2015), it is expected that those observations would yield find clustering beyond the previously identified collisional families results for approximately 33,000 objects in the vicinity of L4, and (Nesvorný et al. 2015). These clusters we term ‘clans’, which pro- 17,000 around L5. Given that the computational requirements for vide the beginnings of a taxonomic framework, the results of which / cladistical analysis increases approximately with a trend of 푛3 2 are presented visually using a consensus dendritic tree. Our results (Goloboff et al. 2008; Goloboff & Catalano 2016), we estimate that, yield a hierarchical structure, with individual clans often congregat- using current computational architecture, the analysis of such large ing within a larger ‘superclan’, and with other clans being further datasets would require approximately 2700 CPU-hours for the L5 broken down into one or more ‘subclans’. These subclans, clans and analysis and 7500 CPU-hours for the population around L4. In order super clans form clusters of objects with a possible common origin. for this to be feasible, further testing into the TNT 1.5 parallelisation With the next generation wide-field surveys and the Lucy mission, (Goloboff & Catalano 2016) will be required. these clusters will be able to be placed in a wider context under the new paradigm. The James Web Space Telescope (JWST) is currently scheduled In our analysis of the members of the L4 swarm, we identify for launch in 2021. The telescope will provide detailed analysis of a total of ten unaffiliated clans and eight superclans that, in turn, many Solar system objects (Rivkin et al. 2020). In contrast to the contain an additional seventeen clans. Within our analysis, we in- work of Gaia and the Vera Rubin observatory, which are undertak- clude 13 members of the Eurybates collisional family (Nesvorný ing wide ranging surveys, the JSWT is instead a targeted mission, et al. 2015), the largest in the Trojan population. Seven of these, providing detailed IR spectra on specific objects, rather than broad- including 3548 Eurybates (1973 SO), a Lucy target, cluster into the band colours on many objects. Whilst the time required for such Eurybates clan, a part of the Greater Ajax superclan. Other canoni- observations will doubtless be incredibly highly sought after, two cal family members cluster together, though are separated, possibly members of the Jovian Trojan population, 617 Patroclus (1906 VY) indicating that they are not true collisional family members, but and 624 Hektor (1907 XM), have already been approved for study suffer from one of the inherent issues with the methodology used to under the Guaranteed Time Observations program (Rivkin et al. identify families. 2020). Once those observations are complete, the results can be The L5 swarm shows more hierarchical structure: seven un- placed in a wider context due to this work. As JWST is a lim- affiliated clans, with six subclans within them. The L5 swarm is ited time mission, we recommend the prioritisation of those targets found to contain at least three large superclans, with each superclan identified in section4 to provide the most benefit. containing a larger number of clans and subclans. In total, there are 14 clans containing 14 subclans in the L5 swarm. The only Lucy Twinkle is a low-cost, community funded, space telescope, sched- target in the L5 swarm, 617 Patroclus (1906 VY), is the type object uled for launch in 2023 or 2024 (Savini et al. 2018). The mission will of the Greater Patroculus superclan, thought it is not specifically provide spectral analysis in three bands in the visible and near-IR part of any clan, it is close to the Memnon clan, which includes (0.4-1 휇m, 1.3-2.42 휇m, and 2.42-4.5 휇m). In terms of the Jovian 2001 UV209 collisional family member, 37519 Amphios (3040 T- Trojans, the mission will be able to provide detailed observations 3). The other members of the larger Ennominos collisional family down to approximately 15th magnitude. Over the seven year ini- (Nesvorný et al. 2015) are distributed throughout the dendritic tree, tial lifetime, Twinkle is expected to observe 50 or so of the largest indicating that perhaps the original HCM (Zappala et al. 1990) is Trojans (Edwards et al. 2019b,a), all of which are included in this inappropriate for describing the history of the swarm. work. This will provide further characterisation of these bodies, A key outcome of our astrocladistical analysis is that we iden- particularly in the IR range. Astrocladistics can offer added value to tify 15 high priority targets for follow-up observations. These are analysis of Twinkle observations, through associations within clans. all comparatively large and bright objects that should be observed to provide further context for the Jovian Trojan swarms as a whole. The Nancy Grace Roman Space Telescope (RST, formally Several are closely related to Lucy targets that could provide addi- WFIRST) is currently in development, with an expected launch tional information in preparation for in-situ observations. date in 2025. Once launched, there will a number of opportuni- All of the future Lucy targets (Levison et al. 2017) are included ties for small body Solar system science using RST, including the in our analysis. Our results therefore provide a taxonomic context the ability to obtain a wealth of data for the Jovian Trojans Holler for the mission, and extend the value of discoveries made. By asso-

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 21 ciating the Lucy targets with other clan members, inferences can be Carruba V., Domingos R. C., Nesvorný D., Roig F., Huaman M. E., Souami made about their nearest relatives, and the swarms as a whole. D., 2013, Mon. Not. R. Astron. Soc., 433, 2075 Whilst the focus of this work is on the current generation of Carvano J. M., Hasselmann P. H., Lazzaro D., Mothé-Diniz T., 2010, Astron. wide-field surveys, several new observatories will be coming on Astrophys., 510, A43 line in the next few decades. The Vera Rubin Observatory, with Chamberlain A., Wood B., 1987, J. Hum. Evol., 16, 119 the Legacy Survey of Space and Time (Rubin Obs. LSST), the Continuum Analytics 2016, Anaconda Software Distribution. Version 2.4.0, https://continuum.io James Web Space Telescope (JWST), Twinkle and the Nancy Grace Darwin C., 1859, On the Origin of the Species by Natural Selection. Murray, Roman Space Telescope (RST, formerly WFIRST) will all be able to London, UK observe the Jovian Trojan population and further characterise these DeMeo F. E., Carry B., 2013, Icarus, 226, 723 objects. Astrocladistics offers a method of analysis that will allow a DeMeo F. E., Carry B., 2014, Nature, 505, 629 timely and detailed analysis of the relationships between the Jovian DeMeo F. E., Binzel R. P., Slivan S. M., Bus S. J., 2009, Icarus, 202, 160 Trojans, based on the observations made by these next generation DeMeo F. E., Binzel R. P., Carry B., Polishook D., Moskovitz N. A., 2014, telescopes, and helps to identify high priority targets for competitive Icarus, 229, 392 observational time. The Jovian Trojans are the remnants of the early DeMeo F. E., Alexander C. M. O., Walsh K. J., Chapman C. R., Solar system, held dynamically stable for the past 4.5 × 109 years. Binzel R. P., 2015, in Michel P., DeMeo F. E., Bottke W. F., They are vital clues to this early period in the story of the Solar eds, , Asteroids IV. University of Arizona Press, pp 13–41 (arXiv:1506.04805), doi:10.2458/azu_uapress_9780816532131- system. Astrocladistical analysis of these objects provides us with ch002, http://arxiv.org/abs/1506.04805http://dx.doi. insights into their history and how they are related to one another. org/10.2458/azu{_}uapress{_}9780816532131-ch002 Deienno R., Morbidelli A., Gomes R., Nesvorný D., 2017, Astron. J., 153, 153 DATA AVAILABILITY Deienno R., Walsh K. J., Delbo M., 2020, Icarus, 357, 114218 Di Sisto R. P., Ramos X. S., Beaugé C., 2014, Icarus, 243, 287 A GitHub repository has been created for this Di Sisto R. P., Ramos X. S., Gallardo T., 2019, Icarus, 319, 828 study https://github.com/TimHoltastro/ Dotto E., et al., 2006, Icarus, 183, 420 holt-etal-2021-Jovian-Trojan-astrocladistics.git, Durech J., Carry B., Delbo M., Kaasalainen M., Viikinkoski M., 2015, and is publicly available. Matrices, trees and clan dispersal velocity in Michel P., DeMeo F. E., Bottke W. F., eds, , Asteroids IV. datasets are stored in this repository. The Python 3 binning and University of Arizona Press, pp 183–202 (arXiv:1502.04816), doi:10.2458/azu_uapress_9780816532131-ch010, http://www. dispersal velocity programs, as well as the tree-search parameters minorplanet.info/http://muse.jhu.edu/chapter/1705164 and nexis (.nex) files containing the tree-banks are also available. Ebell M., 1909, Astron. Nachrichten, 180, 213 Edwards B., Savini G., Tinetti G., Tessenyi M., Arena C., Lindsay S., Bowles N., 2019a, J. Astron. Telesc. Instruments, Syst., 5, 1 ACKNOWLEDGEMENTS Edwards B., Lindsay S., Savini G., Tinetti G., Arena C., Bowles N., Tessenyi M., 2019b, J. Astron. Telesc. Instruments, Syst., 5, 1 This research was in part supported by the University of South- Emery J. P., Brown R. H., 2003, Icarus, 164, 104 ern Queensland’s Strategic Research Initiative program. TRH was Emery J. P., Cruikshank D. P., Van Cleve J., 2006, Icarus, 182, 496 supported by the Australian Government Research Training Pro- Emery J. P., Burr D. M., Cruikshank D. P., 2011, Astron. J., 141, 25 gram Scholarship. Dr. Pablo Goloboff provided assistance with TNT, Emery J. P.,Marzari F., Morbidelli A., French L. M., Grav T., 2015, in Michel which is subsidized by the Willi Hennig Society, as well as addi- P.,DeMeo F., Bottke W., eds, , Asteroids IV.University of Arizona Press, tional comments on the methodology. We thank Dr. Didier Fraix- Tucson, AZ„ pp 203–220, doi:10.2458/azu_uapress_9780816532131- ch011, http://muse.jhu.edu/chapter/1705165 Burnet and an anonymous reviewer for their comments in improving Evans D. W., et al., 2018, Astron. Astrophys., 616, A4 this manuscript. Some analysis was conducted in Python 3.7 under Farris J. S., 1970, Syst. Biol., 19, 83 the Anaconda software environment (Continuum Analytics 2016). Farris J. S., 1982, Syst. Biol., 31, 328 Farris J. S., 1989, Cladistics, 5, 417 Fornasier S., Dotto E., Marzari F., Barucci M., Boehnhardt H., Hainaut O., REFERENCES Debergh C., 2004, Icarus, 172, 221 Fornasier S., Dotto E., Hainaut O., Marzari F., Boehnhardt H., Deluise F., Beauge C., Roig F., 2001, Icarus, 153, 391 Barucci M., 2007, Icarus, 190, 622 Bendjoya P., Cellino A., Di Martino M., Saba L., 2004, Icarus, 168, 374 Fowler J., JR Chillemi 1992, in Tedesco E. F., ed., , IRAS Minor planet Surv., Bolin B. T., Delbó M., Morbidelli A., Walsh K. J., 2017, Icarus, 282, 290 tech. repo edn, Philips Laboratory, Hanscom Air Force Base, MA. Bolin B. T., Walsh K. J., Morbidelli A., Delbó M., 2018, Mon. Not. R. USA, https://scholar.google.com.au/scholar?cluster= Astron. Soc., 473, 3949 9441480019698545315{&}hl=en{&}as{_}sdt=4005{&}sciodt= Bolin B. T., et al., 2021, Astron. J., 161, 116 0,6 Bottke W. F., Vokrouhlický D., Rubincam D., Nesvorný D., 2006, Annu. Fraix-Burnet D., Choler P., Douzery E. J. P., 2006, Astron. Astrophys., 455, Rev. Earth Planet. Sci., 34, 157 845 Brandley M. C., Warren D. L., Leaché A. D., McGuire J. A., 2009, Syst. Fraix-Burnet D., Dugué M., Chattopadhyay T., Chattopadhyay A. K., Biol., 58, 184 Davoust E., 2010, Mon. Not. R. Astron. Soc., 407, 2207 Brooks D. R., O’Grady R. T., Wiley E. O., 1986, Syst. Zool., 35, 571 Fukugita M., Ichikawa T., Gunn J. E., Doi M., Shimasaku K., Schneider Brož M., Rozehnal J., 2011, Mon. Not. R. Astron. Soc., 414, 565 D. P., 1996, Astron. J., 111, 1748 Buie M. W., et al., 2015, Astron. J., 149, 113 Gascuel O., 2005, Mathematics of Evolution and Phylogeny.. OUP Oxford, Buie M. W., Zangari A. M., Marchi S., Levison H. F., Mottola S., 2018, Oxford, UK Astron. J., 155, 245 Giorgini J. D., et al., 1996, in AAS/Division Planet. Sci. Meet. Abstr. #28. Bus S. J., 2002, Icarus, 158, 146 p. 1158 Cardone V. F., Fraix-Burnet D., 2013, Mon. Not. R. Astron. Soc., 434, 1930 Givnish T., Sytsma K., 1997, Mol. Phylogenet. Evol., 7, 320 Carruba V., Michtchenko T. A., 2007, Astron. Astrophys., 475, 1145 Goloboff P. A., 1996, Cladistics, 12, 199

MNRAS 000,1–26 (2020) 22 T. R. Holt et al.

Goloboff P. A., 2015, Cladistics, 31, 210 Morate D., Licandro J., Popescu M., de León J., 2018, Astron. Astrophys., Goloboff P. A., Catalano S. A., 2016, Cladistics, 32, 221 617, A72 Goloboff P. A., Farris J. S., Nixon K. C., 2008, Cladistics, 24, 774 Morbidelli A., 2010, Comptes Rendus Phys., 11, 651 Grav T., et al., 2011, Astrophys. J., 742, 40 Morbidelli A., Levison H. F., Tsiganis K., Gomes R., 2005, Nature, 435, 462 Grav T., Mainzer A. K., Bauer J. M., Masiero J. R., Nugent C. R., 2012, Mottola S., Hellmich S., Buie M. W., Zangari A. M., Marchi S., Brown Astrophys. J., 759, 49 M. E., Levison H. F., 2020, Planet. Sci. J. Press Hasselmann P. H., Carvano J. M., Lazzaro D., 2012, NASA Planet. Data Nakamura T., Yoshida F., 2008, Publ. Astron. Soc. Japan, 60, 293 Syst. Naylor G., Kraus F., 1995, Syst. Biol., 44, 559 Heinrich V., 1907, Astron. Nachrichten, 176, 193 Nesvorný D., 2002, Icarus, 160, 271 Hellmich S., Mottola S., Hahn G., Kührt E., de Niem D., 2019, Astron. Nesvorný D., 2018, Annu. Rev. Astron. Astrophys., 56, 137 Astrophys., 630, A148 Nesvorný D., Morbidelli A., 2012, Astron. J., 144, 117 Hennig W., 1965, Annu. Rev. Entomol., 10, 97 Nesvorný D., Vokrouhlický D., 2019, Icarus, 331, 49 Holler B. J., Milam S. N., Bauer J. M., Alcock C., Bannister M. T., Bjoraker Nesvorný D., Beaug C., Dones L., 2004, Astron. J., 127, 1768 G. L., 2018, J. Astron. Telesc. Instruments, Syst., 4, 1 Nesvorný D., Vokrouhlický D., Morbidelli A., 2013, Astrophys. J., 768, 45 Holt T. R., Brown A. J., Nesvorný D., Horner J., Carter B. D., 2018, Astro- Nesvorný D., Brož M., Carruba V., 2015, in Michel P., DeMeo phys. J., 859, 97 F. E., Bottke W. F., eds, , Asteroids IV. University of Ari- Holt T. R., et al., 2020a, Mon. Not. R. Astron. Soc., 495, 4085 zona Press, Tucson, AZ, pp 297–321 (arXiv:1502.01628), Holt T. R., Vokrouhlický D., Nesvorný D., Brož M., Horner J., 2020b, Mon. doi:10.2458/azu_uapress_9780816532131-ch016, http: Not. R. Astron. Soc., 499, 3630 //arxiv.org/abs/1502.01628http://dx.doi.org/10. Horner J., Wyn Evans N., 2006, Mon. Not. R. Astron. Soc. Lett., 367, L20 2458/azu{_}uapress{_}9780816532131-ch016http: Horner J., Müller T. G., Lykawka P. S., 2012, Mon. Not. R. Astron. Soc., //muse.jhu.edu/chapter/1705170 423, 2587 Nicholson S. B., 1961, Astron. Soc. Pacific Leafl., 8, 239 Horner J., et al., 2020, Publ. Astron. Soc. Pacific, 132, 102001 Parins-Fukuchi C., Greiner E., MacLatchy L. M., Fisher D. C., 2019, Pale- Hsieh H. H., Fitzsimmons A., Novaković B., Denneau L., Heinze A. N., obiology, 45, 378 2021, Icarus, 354, 114019 Parker A. H., Ivezić Ž., Jurić M., Lupton R. H., Sekora M., Kowalski A., Hug L. A., et al., 2016, Nat. Microbiol., 1, 16048 2008, Icarus, 198, 138 Ivezić Ž., et al., 2002, Astron. J., 124, 2943 Perna D., Bott N., Hromakina T., Mazzotta Epifani E., Dotto E., Dores- Jewitt D. C., Trujillo C. A., Luu J. X., 2000, Astron. J., 120, 1140 soundiram A., 2018, Mon. Not. R. Astron. Soc., 475, 974 Jofré P., Das P., Bertranpetit J., Foley R., 2017, Mon. Not. R. Astron. Soc., Pirani S., Johansen A., Bitsch B., Mustill A. J., Turrini D., 2019a, Astron. 467, 1140 Astrophys., 623, A169 Johanson D., White T., 1979, Science (80-. )., 203, 321 Pirani S., Johansen A., Mustill A. J., 2019b, Astron. Astrophys., 631, A89 Karlsson O., Lagerkvist C., Davidsson B., 2009, Icarus, 199, 106 Popescu M., et al., 2016, Astron. Astrophys., 591, A115 Knežević Z., Milani A., 2003, Astron. Astrophys., 403, 1165 Popescu M., et al., 2018, Astron. Astrophys., 617, A12 Knežević Z., Milani A., 2017, AstDys: Synthetic proper elements 5553 Pravec P., et al., 2019, Icarus, 333, 429 numbered and multiopposition Trojans, https://newton.spacedys. Radović V., Novaković B., Carruba V., Marčeta D., 2017, Mon. Not. R. com/{~}astdys2/propsynth/tro.syn Astron. Soc., 470, 576 LSST Science Collaboration et al., 2009, preprint (arXiv:0912.0201) Reddy V., Dunn T. L., Thomas C. A., Moskovitz N. A., Burbine T. H., 2015, Lazzaro D., Angeli C. A., Carvano J. M., Mothé-Diniz T., Duffard R., in Michel P., DeMeo F. E., Bottke W. F., eds, , Asteroids IV.University of Florczak M., 2004, Icarus, 172, 179 Arizona Press, Tucson, AZ, doi:10.2458/azu_uapress_9780816532131- Levison H. F., Shoemaker E. M., Shoemaker C. S., 1997, Nature, 385, 42 ch003, http://muse.jhu.edu/chapter/1705157 Levison H. F., Bottke W. F., Gounelle M., Morbidelli A., Nesvorný D., Rein H., Liu S.-F., 2012, Astron. Astrophys., 537, A128 Tsiganis K., 2009, Nature, 460, 364 Rein H., Tamayo D., 2015, Mon. Not. R. Astron. Soc., 452, 376 Levison H. F., Morbidelli A., Tsiganis K., Nesvorný D., Gomes R., 2011, Rivkin A. S., Marchis F., Stansberry J. A., Takir D., Thomas C., Group t. J. Astron. J., 142, 152 A. F., 2016, Publ. Astron. Soc. Pacific, 128, 018003 Levison H. F., Olkin C. B., Noll K., Marchi S., Lucy Team 2017, in Lu- Rivkin A. S., Milam, Stefanie N., Thomas C. A., 2020, STScI: Web nar Planet. Sci. Conf.. p. 2025, http://adsabs.harvard.edu/abs/ Observing Program: GTO 1244, https://www.stsci.edu/jwst/ 2017LPI....48.2025L observing-programs/program-information?id=1244 Linnaeus C., 1758, Systema Naturae per regna tria naturae, secundum Robutel P., Gabern F., 2006, Mon. Not. R. Astron. Soc., 372, 1463 classes, ordines, genera, species, cum characteribus, differentiis, syn- Roig F., Nesvorný D., 2015, Astron. J., 150, 186 onymis, locis Roig F., Ribeiro A. O., Gil-Hutton R., 2008, Astron. Astrophys., 483, 911 Lykawka P. S., Horner J., 2010, Mon. Not. R. Astron. Soc., 405, 1375 Romanishin W., Tegler S. C., 2018, Astron. J., 156, 19 Maddison W. P., Maddison D. R., 2015, Zephyr: a Mesquite package for Rozehnal J., Brož M., Nesvorný D., Durda D. D., Walsh K. J., Richardson interacting with external phylogeny inference programs. Version 1.1, D. C., Asphaug E., 2016, Mon. Not. R. Astron. Soc., 462, 2319 https://mesquitezephyr.wikispaces.com Savini G., et al., 2018, Sp. Telesc. Instrum. 2016 Opt. Infrared, Millim. Maddison W. P., Maddison D. R., 2017, Mesquite: a modular system for Wave, 9904, 175 evolutionary analysis. Version 3.20, http://mesquiteproject.org Slyusarev I. G., Belskaya I. N., 2014, SoSyR, 48, 139 Maddison W. P., Donoghue M. J., Maddison D. R., 1984, SystBio, 33, 83 Souza-Feliciano A. C., et al., 2020, Icarus, 338, 113463 Marchis F., et al., 2006, Nature, 439, 565 Spoto F., et al., 2018, Astron. Astrophys., 616, A13 Marchis F., et al., 2014, Astrophys. J., 783, L37 Steckloff J. K., Sarid G., Volk K., Kareta T., Womack M., Harris W., Wood- Margush T., McMorris F. R., 1981, Bull. Math. Biol., 43, 239 ney L., Schambeau C., 2020, Astrophys. J., 904, L20 Masiero J. R., et al., 2011, Astrophys. J., 741, 68 Strömgren E., 1908, Astron. Nachrichten, 177, 123 Merline W. J., et al., 2001, Int. Astron. Union Circ., 7741 Sutherland W., et al., 2015, Astron. Astrophys., 575, A25 Milam S. N., Stansberry J. A., Sonneborn G., Thomas C., 2016, Publ. Astron. Szabo G. M., Ivezić Ž., Jurić M., Lupton R. H., 2007, Mon. Not. R. Astron. Soc. Pacific, 128, 018001 Soc., 377, 1393 Milani A., 1993, Celest. Mech. Dyn. Astron., 57, 59 Tholen D. J., 1984, PhD thesis, University of Arizona, Tucson, http:// Milani A., Cellino A., Knežević Z., Novaković B., Spoto F., Paolicchi P., adsabs.harvard.edu/abs/1984PhDT...... 3T 2014, Icarus, 239, 46 Tholen D. J., 1989, in , Asteroids II. University of Arizona Press, p. 1139

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Tsiganis K., Varvoglis H., Dvorak R., 2005a, Celest. Mech. Dyn. Astron., L4 푅2 value: 0.9900 92, 71 L4 Bin deliminators: [0.0035364 0.01460667 0.02551333 0.03642 Tsiganis K., Gomes R., Morbidelli A., Levison H. F., 2005b, Nature, 435, 0.04732667 0.05823333 0.06914 0.08004667 0.09095333 0.10186 459 0.11276667 0.12367333 0.13458 0.14548667 0.15639333 0.1673 ] Turrini D., Marzari F., Beust H., 2008, Mon. Not. R. Astron. Soc., 391, 1029 L5 Bin Number: 15 Vinogradova T. A., 2015, Mon. Not. R. Astron. Soc., 454, 2436 L5 푅2 value: 0.9876 Vinogradova T. A., Chernetenko Y. A., 2015, Sol. Syst. Res., 49, 391 Vokrouhlický D., Nesvorný D., 2008, Astron. J., 136, 280 L5Bin deliminators: [0.0041151 0.01662667 0.02895333 0.04128 Walsh K. J., Delbó M., Bottke W. F., Vokrouhlický D., Lauretta D. S., 2013, 0.05360667 0.06593333 0.07826 0.09058667 0.10291333 0.11524 Icarus, 225, 283 0.12756667 0.13989333 0.15222 0.16454667 0.17687333 0.1892 ] Wang X., Hou X., 2017, Mon. Not. R. Astron. Soc., 471, 243 Warner B. D., Harris A. W., Pravec P., 2009, Icarus, 202, 134 Wolf M., 1907, Astron. Nachrichten, 174, 47 Wong I., Brown M. E., 2017, Astron. J., 153, 69 A3 sin푖 푝 Wyse A., 1938, Astron. Soc. Pacific Leafl., 3, 113 Yoshida F., Nakamura T., 2008, Publ. Astron. Soc. Japan, 60, 297 Sine of the proper inclination of the object. From AsyDys database Zappala V., Cellino A., Farinella P., Knežević Z., 1990, Astron. J., 100, 2030 https://newton.spacedys.com/astdys/ Zappala V., Cellino A., Dell’Oro A., Migliorini F., Paolicchi P., 1996, Icarus, Units: n/a 124, 156 Reference: Knežević & Milani(2017) L4 Bin Number: 15 L4푅2 value: 0.9870 L4 Bin deliminators: [0.0101936 0.06476 0.11852 0.17228 APPENDIX A: CHARACTERISTICS USED IN THE 0.22604 0.2798 0.33356 0.38732 0.44108 0.49484 0.5486 0.60236 MATRIX 0.65612 0.70988 0.76364 0.8174 ] This appendix details the characteristics used in the analysis. L5 Bin Number: 13 In total there are 17 values that are binned using the Python L5 푅2 value: 0.9901 3 (Continuum Analytics 2016) program, available at the as- L5 Bin deliminators: [0.012521 0.06543077 0.11766154 sociated Github (https://github.com/TimHoltastro/ 0.16989231 0.22212308 0.27435385 0.32658462 0.37881538 holt-etal-2021-Jovian-Trojan-astrocladistics.git). 0.43104615 0.48327692 0.53550769 0.58773846 0.63996923 This binning program is based on one developed in Holt et al. 0.6922 ] (2018). 푅2 values are the correlation between the binned values and the original data. The binning program sets the number of bins once an 푅2 value greater than 0.99 is reached, or the maximum number of bins, 15 is reached. Each characteristic is binned independently A4 MeanLib for the L4 and L5 Trojan matrices. Mean libration value, relative to Jupiter. Calculated using REBOUND (Rein & Liu 2012; Rein & Tamayo 2015) as outlined in section 2.1 of the text. A1 Δ푎 푝 Units: degree Proper Δ semi-major axis of the object. From AsyDys database Reference: n/a https://newton.spacedys.com/astdys/ L4 Bin Number: 15 Reference: Knežević & Milani(2017) L4 푅2 value: 0.9838 Units: au L4 Bin deliminators: [56.4248396 57.77509172 59.10538938 L4 Bin Number: 13 60.43568704 61.7659847 63.09628236 64.42658001 65.75687767 L4 푅2 value: 0.9902 67.08717533 68.41747299 69.74777065 71.07806831 L4 Bin deliminators: [0.0004417 0.01277692 0.02495385 72.40836597 73.73866362 75.06896128 76.39925894] 0.03713077 0.04930769 0.06148462 0.07366154 0.08583846 L5 Bin Number: 14 0.09801538 0.11019231 0.12236923 0.13454615 0.14672308 L5 푅2 value: 0.9908 L5 Bin deliminators: [285.72582824 0.1589 ] 286.91482596 288.0862523 289.25767863 290.42910496 L5 Bin Number: 13 291.60053129 292.77195762 293.94338395 295.11481029 L5 푅2 value: 0.9902 296.28623662 297.45766295 298.62908928 299.80051561 L5 Bin deliminators: [0.0041526 0.01563846 0.02697692 300.97194195 302.14336828 303.31479461] 0.03831538 0.04965385 0.06099231 0.07233077 0.08366923 0.09500769 0.10634615 0.11768462 0.12902308 0.14036154 0.1517 ] A5 LibRange Range of the objects libration, relative to Jupiter. Calculated using REBOUND (Rein & Liu 2012; Rein & Tamayo 2015) as outlined in A2 푒 푝 section 2.1 of the text. Proper eccentricity of the object. From AsyDys database Units: degree https://newton.spacedys.com/astdys/ Reference: n/a Units: n/a L4 Bin Number: 14 Reference: Knežević & Milani(2017) L4 푅2 value: 0.9904 L4 Bin Number: 15 L4 Bin deliminators: [ 4.04450175 9.22096281 14.325954

MNRAS 000,1–26 (2020) 24 T. R. Holt et al.

19.43094519 24.53593638 29.64092757 34.74591876 L5 Bin deliminators: [0.027628 0.0528 0.0776 0.1024 0.1272 39.85090995 44.95590114 50.06089233 55.16588352 0.152 0.1768 0.2016 0.2264 0.2512 0.276 0.3008 0.3256 0.3504 60.27087471 65.3758659 70.48085709 75.58584828] 0.3752 0.4 ] L5 Bin Number: 14 L5 푅2 value: 0.9908 L5 Bin deliminators: [ 2.7354308 7.67859255 12.55350552 17.42841848 22.30333145 27.17824441 32.05315738 A9 g -mean 36.92807035 41.80298331 46.67789628 51.55280924 푚푎푔 56.42772221 61.30263518 66.17754814 71.05246111] Mean G-band magnitude from the GAIA survey. Filter passband from 330 nm to 1050 nm Evans et al.(2018). Units: magnitude Reference: Spoto et al.(2018) L4 Bin Number: 15 A6 albedo L4 푅2 value: 0.9894 Geometric albedo of the object. From NASA-JPL HORIZONS Solar L4 Bin deliminators: [15.10926146 15.38560874 15.65787207 System Dynamics Database https://ssd.jpl.nasa.gov/ 15.9301354 16.20239873 16.47466206 16.74692539 17.01918872 Giorgini et al.(1996). 17.29145205 17.56371538 17.83597871 18.10824204 Units: n/a 18.38050537 18.65276871 18.92503204 19.19729537] Reference: Giorgini et al.(1996) L5 Bin Number: 12 2 L4 Bin Number: 15 L5 푅 value: 0.9904 L4 푅2 value: 0.9830 L5 Bin deliminators: [15.85627031 16.11791172 16.37645066 L4 Bin deliminators: [0.024827 0.03653333 0.04806667 0.0596 16.6349896 16.89352854 17.15206747 17.41060641 0.07113333 0.08266667 0.0942 0.10573333 0.11726667 0.1288 17.66914535 17.92768429 18.18622323 18.44476217 18.7033011 0.14033333 0.15186667 0.1634 0.17493333 0.18646667 0.198 ] 18.96184004] L5 Bin Number: 15 L5 푅2 value: 0.9817 L5 Bin deliminators: [0.030831 0.04226667 0.05353333 0.0648 0.07606667 0.08733333 0.0986 0.10986667 0.12113333 0.1324 A10 (b - v) 0.14366667 0.15493333 0.1662 0.17746667 0.18873333 0.2 ] Index of Johnson B (442nm) and Johnson V (540nm) band magnitudes, calculated from SDSS photometry (Fukugita et al. 1996). A7 W1Alb Units: magnitude Reference: Szabo et al.(2007) Near Infrared values from the WISE survey using the W1 filter L4 Bin Number: 15 (3.4휇푚). L4 푅2 value: 0.9591 Units: magnitude L4 Bin deliminators: [0.50896 0.57933333 0.64866667 0.718 Reference: Grav et al.(2011, 2012) 0.78733333 0.85666667 0.926 0.99533333 1.06466667 1.134 L4 Bin Number: 15 1.20333333 1.27266667 1.342 1.41133333 1.48066667 1.55 ] 2 L4 푅 value: 0.9824 L5 Bin Number: 15 L4 Bin deliminators: [0.055661 0.0786 0.1012 0.1238 0.1464 L5 푅2 value: 0.9878 0.169 0.1916 0.2142 0.2368 0.2594 0.282 0.3046 0.3272 0.3498 L5 Bin deliminators: [0.60968 0.63133333 0.65266667 0.674 0.3724 0.395 ] 0.69533333 0.71666667 0.738 0.75933333 0.78066667 0.802 L5 Bin Number: 15 0.82333333 0.84466667 0.866 0.88733333 0.90866667 0.93 ] L5 푅2 value: 0.9794 L5 Bin deliminators: [0.065666 0.08826667 0.11053333 0.1328 0.15506667 0.17733333 0.1996 0.22186667 0.24413333 0.2664 0.28866667 0.31093333 0.3332 0.35546667 0.37773333 0.4 ] A11 (u - g) Index of U (354.3 nm) and G (477 nm) band magnitudes taken from the SDSS (Fukugita et al. 1996). A8 W2Alb Units: magnitude Near Infrared values from the WISE survey using the W2 filter Reference: Szabo et al.(2007) (4.6휇푚). L4 Bin Number: 15 Units: magnitude L4 푅2 value: 0.9656 Reference: Grav et al.(2011, 2012) L4 Bin deliminators: [0.873585 0.96933333 1.06366667 1.158 L4 Bin Number: 15 1.25233333 1.34666667 1.441 1.53533333 1.62966667 1.724 L4 푅2 value: 0.9838 1.81833333 1.91266667 2.007 2.10133333 2.19566667 2.29 ] L4 Bin deliminators: [0.035641 0.05993333 0.08386667 0.1078 L5 Bin Number: 15 0.13173333 0.15566667 0.1796 0.20353333 0.22746667 0.2514 L5 푅2 value: 0.9724 0.27533333 0.29926667 0.3232 0.34713333 0.37106667 0.395 ] L5 Bin deliminators: [0.62835 0.74 0.85 0.96 1.07 1.18 1.29 1.4 L5 Bin Number: 15 1.51 1.62 1.73 1.84 1.95 2.06 2.17 2.28 ] L5 푅2 value: 0.9773

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 25

A12 (g - r) 0.1983819 0.242659 0.2869361 0.3312132 0.3754903 0.4197674 0.4640445 0.5083216 0.5525987 0.5968758 0.6411529 0.68543 ] Index of G (477 nm) and R (623.1 nm) band magnitudes taken L5 Bin Number: 15 from the SDSS (Fukugita et al. 1996). L5 푅2 value: 0.9886 Units: magnitude L5 Bin deliminators: [0.05425359 0.09975333 0.14458067 Reference: Szabo et al.(2007) 0.189408 0.23423533 0.27906267 0.32389 0.36871733 L4 Bin Number: 15 0.41354467 0.458372 0.50319933 0.54802667 0.592854 L4 푅2 value: 0.9560 0.63768133 0.68250867 0.727336 ] L4 Bin deliminators: [0.299 0.36666667 0.43333333 0.5 0.56666667 0.63333333 0.7 0.76666667 0.83333333 0.9 0.96666667 1.03333333 1.1 1.16666667 1.23333333 1.3 ] L5 Bin Number: 15 A16 (J - Ks) L5 푅2 value: 0.9851 L5 Bin deliminators: [0.4197 0.44 0.46 0.48 0.5 0.52 0.54 0.56 Index of J (1.25 휇푚) and K (2.15 휇푚) band magnitudes from the 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72 ] VISTA survey (Sutherland et al. 2015), in the MOVIS database (Popescu et al. 2016). Units: magnitude Reference: Popescu et al.(2018) A13 (r - i) L4 Bin Number: 15 L4 푅2 value: 0.9846 Index of R (623.1 nm) and I (762.5 nm) band magnitudes taken L4 Bin deliminators: [0.14045928 0.25723273 0.37228047 from the SDSS (Fukugita et al. 1996). 0.4873282 0.60237593 0.71742367 0.8324714 0.94751913 Units: magnitude 1.06256687 1.1776146 1.29266233 1.40771007 1.5227578 Reference: Szabo et al.(2007) 1.63780553 1.75285327 1.867901 ] L4 Bin Number: 15 L5 Bin Number: 15 L4 푅2 value: 0.9890 L5 푅2 value: 0.9890 L4 Bin deliminators: [0.09976 0.116 0.132 0.148 0.164 0.18 0.196 L5 Bin deliminators: [0.06778045 0.16160333 0.25403967 0.212 0.228 0.244 0.26 0.276 0.292 0.308 0.324 0.34 ] 0.346476 0.43891233 0.53134867 0.623785 0.71622133 L5 Bin Number: 15 0.80865767 0.901094 0.99353033 1.08596667 1.178403 L5 푅2 value: 0.9841 1.27083933 1.36327567 1.455712 ] L5 Bin deliminators: [0.06824 0.09066667 0.1127619 0.13485714 0.15695238 0.17904762 0.20114286 0.2232381 0.24533333 0.26742857 0.28952381 0.31161905 0.33371429 0.35580952 0.37790476 0.4 ] A17 (H - Ks) Index of H (1.65 휇푚) and K (2.15 휇푚) band magnitudes from the VISTA survey (Sutherland et al. 2015), in the MOVIS database A14 (i - z) (Popescu et al. 2016). Index of I (762.5 nm) and Z (913.4 nm) band magnitudes taken Units: magnitude from the SDSS (Fukugita et al. 1996). Reference: Popescu et al.(2018) L4 Bin Number: 8 Units: magnitude 2 Reference: Szabo et al.(2007) L4 푅 value: 0.9991 L4 Bin Number: 15 L4 Bin deliminators: [-0.33295512 -0.2505985 -0.1688955 L4 푅2 value: 0.9614 -0.0871925 -0.0054895 0.0762135 0.1579165 0.2396195 L4 Bin deliminators: [-0.55087 -0.492 -0.434 -0.376 -0.318 -0.26 0.3213225 ] L5 Bin Number: 14 -0.202 -0.144 -0.086 -0.028 0.03 0.088 0.146 0.204 0.262 0.32 ] 2 L5 Bin Number: 15 L5 푅 value: 0.9906 L5 푅2 value: 0.9656 L5 Bin deliminators: [-0.1558507 -0.05802146 0.03845707 L5 Bin deliminators: [-0.37082 -0.31533333 -0.26066667 -0.206 0.13493561 0.23141414 0.32789268 0.42437121 0.52084975 -0.15133333 -0.09666667 -0.042 0.01266667 0.06733333 0.122 0.61732829 0.71380682 0.81028536 0.90676389 1.00324243 0.17666667 0.23133333 0.286 0.34066667 0.39533333 0.45 ] 1.09972096 1.1961995 ]

A15 (Y - J) A18 tax푐 Index of Y (1.02 휇푚) and J (1.25 휇푚) band magnitudes from the Canonical taxonomic designation, based on the (DeMeo et al. 2009). VISTA survey (Sutherland et al. 2015), in the MOVIS database Note: any ’P-type’ have been modernised into the X-types. Refer- (Popescu et al. 2016). ence used is in tax푟푒 푓 . Units: magnitude Reference: Popescu et al.(2018) A19 tax L4 Bin Number: 15 푟푒 푓 2 L4 푅 value: 0.9875 Source of canonical taxonomic classification (tax푐) Tholen1989: L4 Bin deliminators: [0.02060934 0.0655506 0.1098277 0.1541048 Tholen(1989); Bendjoya2004: Bendjoya et al.(2004); For-

MNRAS 000,1–26 (2020) 26 T. R. Holt et al.

Table B1. Ulysses clan- 퐷: Diameter of the object. From NASA-JPL HORI- ZONS Solar System Dynamics Database https://ssd.jpl.nasa.gov/ (Giorgini et al. 1996). Where not available, generated from H magnitude and mean geometric albedo (0.075).; Δ푉푟푒 푓 : dispersal velocity calculated from inverse Gauss equations, see Section 2.3, to the reference object; Δ푉푐푒푛푡.: as Δ푉푟푒 푓 , with calculations to the fictitious cluster center; 퐹푒푠푐: Fraction e of clones that escape the Jovian Trojan population in (Holt et al. 2020a)

full_name 퐷 Δ푉푟푒 푓 Δ푉푐푒푛푡. 퐹푒푠푐 km 푚푠−1 푚푠−1

4834 Thoas (1989 AM2) 72.33 9.83 23.99 2.20E-01 5254 Ulysses (1986 VG1) 76.15 0.00 17.81 - 5264 Telephus (1991 KC) 68.47 34.09 16.83 - 11396 (1998 XZ77) 37.11 33.67 14.19 - 13782 (1998 UM18) 24.97 13.89 28.86 8.90E-01 16099 (1999 VQ24) 36.77 28.36 11.69 - 20424 (1998 VF30) 45.80 17.92 3.48 - 20716 (1999 XG91) 26.37 11.34 9.36 - 21595 (1998 WJ5) 35.18 12.63 6.26 - 21599 (1998 WA15) 28.31 48.31 28.04 - 23958 (1998 VD30) 46.00 18.02 5.02 - 24501 (2001 AN37) 24.54 17.78 1.21 - 63195 (2000 YN120) 24.69 35.93 18.19 - 111819 (2002 DD1) 19.34 17.35 9.23 3.30E-01 252173 (2001 DL10) 15.45 40.86 20.81 - 310027 (2010 AH95) 11.10 36.22 16.84 - 355768 (2008 RY57) 11.72 10.25 10.38 - nasier2004 (Fornasier et al. 2004); Lazzaro2004: Lazzaro et al. (2004); Fornasier2007: Fornasier et al.(2007); H2012: Hasselmann et al.(2012).

APPENDIX B: INDIVIDUAL SUPERCLANS, CLANS AND SUBCLANS The figures here (Figs B1-B12) show each of the separate super- clans, along with the L4 unassociated clans (Fig. B1) and unassoci- ated L5 clans (Fig. B9). These are additionally available individually from the PDS. We include table B1 as an example of those included in the data archive, available from the PDS. In this dataset, the dispersal veloc- ity calculated from inverse Gauss equations, see Section 2.3, to the reference object (Δ푉푟푒 푓 .) and to a fictitious cluster center (Δ푉푐푒푛푡.) are given for each superclan, clan and subclan independently, for the subset of Jovian Trojans used in this analysis.

This paper has been typeset from a TEX/LATEX file prepared by the author.

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 27

24537 (2001 CB35)

11 18063 (1999 XW211) 114710 (2003 GX7) 11 0.98030.9803 D (T1989) 11 911 Agamemnon (1919 FD) 11 D (H2012, 54) 11 32498 (2000 XX37) 3596 Meriones (1985 VO) 0.98030.9803 429970 (2013 AQ54) 0.98030.9803 15440 (1998 WX4) 41340 (1999 YO14) 0.98030.9803 24244 (1999 XY101) 0.7628 0.76280.7628 11 5027 Androgeos (1988 BX1) 0.7628 11 0.96080.9608 D (H2012, 81) 85807 (1998 WR10) 63294 (2001 DQ90) 0.94130.9413 0.9798 312787 (2010 VA114) 162822 (2001 BD49) D (H2012, 61) 0.92180.9218 0.9057 36279 (2000 BQ5) D (H2012, 71) 0.97990.9799 37301 (2001 CA39) 15398 (1997 UZ23) 0.98 0.97990.9799 51378 (2001 AT33) D (H2012, 79) 0.98030.9803 161024 (2002 FM7) 55563 (2002 AW34) (a) 1998WR10 clan. (b) Agamemnon clan.

160135 (2000 YB131) 111 13362 (1998 UQ16) D (H2012, 71) 190268 (2007 XU3) 254679 (2005 LU50) 0.94220.94220.9422 0.96220.96220.9622 111 0.98130.98130.9813 5123 (1989 BL) 5028 Halaesus (1988 BY1) D (H2012, 72) 13387 Irus (1998 YW6) 0.94220.94220.9422 0.98040.9804 38617 (2000 AY161) 111 37297 (2001 BQ77) 0.98040.98040.9804 63210 (2001 AH13) 0.88630.88630.8863 20428 (1998 WG20) 0.88630.8863 13475 Orestes (1973 SX) 111 0.97980.97980.9798 X (H2012, 78) 0.92440.92440.9244 12974 Halitherses (1973 SB2) 23119 (2000 AP33) 0.8310.8310.831 111 5436 Eumelos (1990 DK) 11 11 11 13183 (1996 TW) 89858 (2002 CK96) 111 0.98090.98090.9809 11 13366 (1998 US24) 0.99980.9998 39369 (2002 CE13) 0.99980.99980.9998 9712 Nauplius (1973 SO1) 0.9599 111 11 58473 (1996 RN7) 90337 (2003 FQ97) 111 111 11 111 9807 (1997 SJ4) 257405 (2009 SG330) 65134 (2002 CH96) (c) Halaeusus clan. (d) Halitherses clan.

2759 Idomeneus (1980 GC) D (H2012, 96) 0.9216 24536 (2001 CN33) 0.92160.9216 0.9216 111 0.97980.9798 0.9798 4063 Euforbo (1989 CG2) D (B2004) 0.92160.9216 0.92160.9216 37299 (2001 CN21) 0.9216 111 24505 (2001 BZ) 15663 Periphas (4168 T-2) 111 D (H2012, 53) 0.97980.9798 22054 (2000 AP21) 11 0.97980.9798 0.9798 11 111 4833 Meges (1989 AL2) 111 3793 Leonteus (1985 TE3) D (B2004)

326125 (2011 YY61) 22014 (1999 XQ96) (e) Idomeneus clan. (f) Periphas clan.

356893 (2011 XL3) 11 1 280072 (2002 CL218) 11 1 226027 (2002 EK127) 11 1 9799 (1996 RJ)

11 65257 (2002 FU36) 1 11 2146 Stentor (1976 UQ) 1 0.97990.97990.9799 0.97990.9799 3709 Polypoites (1985 TL3)D (B2004) 11 83983 (2002 GE39) 111 1 18062 (1999 XY187) D (H2012, 78) 11 111 11 7641 (1986 TT6) D (HCL2012, 92) 4035 (1986 WD) 1 111 D (B2004) 264154 (2009 VA107) 88225 (2001 BN27) (g) Polypoites clan. (h) Stentor clan.

13782 (1998 UM18) 0.96940.9694 (2011 YQ4) 42146 (2001 BN42) 0.96940.9694 0.96940.9694 4834 Thoas (1989 AM2) 11 D (B2004) 0.96940.9694 11 20716 (1999 XG91) 11 4501 Eurypylos (1989 CJ3) 21595 (1998 WJ5) 0.96940.9694 0.97950.9795 21900 Orus (1999 VQ10) L D 355768 (2008 RY57) 0.96940.9694 0.96940.9694 5254 Ulysses (1986 VG1) D (B2004) 353201 (2009 SP246) 0.96940.9694 0.96940.9694 11 5264 Telephus (1991 KC) D (H2012, 99) 0.93990.93990.9399 111819 (2002 DD1) 0.93990.9399 2456 Palamedes (1966 BA1) 0.9694 20424 (1998 VF30) D (H2012, 86) 0.98940.9894 0.93990.9399 0.98940.9894 0.93990.9399 11 14268 (2000 AK156) 23958 (1998 VD30) 11 0.98940.9894 24501 (2001 AN37) 0.98940.9894 0.99980.99980.9998 24531 (2001 CE21) 63195 (2000 YN120) 0.99980.9998 0.98940.9894 310027 (2010 AH95) 24341 (2000 AJ87) 0.98940.9894 C (F2007) 0.98940.9894 0.96930.9693 11396 (1998 XZ77) D (H2012, 95) 0.98030.9803 0.98940.9894 16099 (1999 VQ24) 11 9817 Thersander (6540 P-L) 0.97970.9797 21599 (1998 WA15) D (H2012, 97) 53477 (2000 AA54) 252173 (2001 DL10) (i) Thersander clan. (j) Ulysses clan. Figure B1. Consensus trees of L4 Trojans that are not associated with any superclan. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen(1989); B2004: Bendjoya et al. (2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012). L indicates objects to be visited by the Lucy spacecraft (Levison et al. 2017). Red highlights are members of the 1996 RJ collisional family.

MNRAS 000,1–26 (2020) 28 T. R. Holt et al.

0.97970.9797

83975 (2002 AD184) 11 11 21284 Pandion (1996 TC51) 11 24486 (2000 YR102) 11 63265 (2001 CP12) D (H2012, 53) 13385 (1998 XO79) 0.99870.9987 168364 (1996 TZ19) 0.95010.9501 0.99870.9987 0.99870.9987 5283 Pyrrhus (1989 BW) Neg (B2004) 0.99870.9987 0.99870.9987 24519 (2001 CH) 0.99870.9987 0.99870.9987 38610 (2000 AU45) Epeios Clan 0.99870.9987 65111 (2002 CG40) 0.99870.9987 0.99870.9987 312638 (2010 AP111) 0.94960.9496 0.99880.9988 0.99880.9988 12921 (1998 WZ5) X (F2007) 0.99890.9989 2148 Epeios (1976 UW) 0.99970.9997 37710 (1996 RD12) 3564 Talthybius (1985 TC1) D (H2012, 91) 89829 (2002 BQ29) 0.95090.9509 588 Achilles (1906 TG) D (T1989) 55571 (2002 CP82) 0.97070.9707 0.99960.9996 0.95090.9509 116954 (2004 HS1) 0.97070.9707 160534 (1996 TA58) 0.97110.9711 0.97110.9711 38619 (2000 AW183) Achilles Clan 0.97110.9711 5259 Epeigeus (1989 BB1) D (H2012, 77) 0.95090.9509 0.97110.9711 0.95090.9509 0.97110.9711 33822 (2000 AA231) 0.97110.9711 3794 Sthenelos (1985 TF3) 0.97110.9711 23075 (1999 XV83) 24312 (1999 YO22) 0.97990.9799 89844 (2002 CP64) 0.97990.9799 36267 (1999 XB211) 25895 (2000 XN9) 0.97990.9799 11 11 15527 (1999 YY2) 11 1991 EL Clan 0.97990.9799 23480 (1991 EL) 162861 (2001 DY103) 0.97990.9799 0.97990.9799 166148 (2002 EU14) 0.97990.9799 0.97990.9799 11395 (1998 XN77) 0.97990.9799 42187 (2001 CS32)

Figure B2. Consensus tree of the L4 Greater Achilles superclan, including Epeios, achilles and 1991 EL clans. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen (1989); B2004: Bendjoya et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012).

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 29

13060 (1991 EJ) 0.95070.9507 3540 Protesilaos (1973 UF5) 0.97070.9707 202752 (2007 PX30) 0.95070.9507 23624 (1996 UX3) 0.93110.9311 0.980.98 20720 (1999 XP101) 60383 (2000 AR184) D (H2012, 71) 0.93110.9311 22056 (2000 AU31) 1 41268 (1999 XO64) 0.97070.9707 23968 (1998 XA13) 0.9707 12972 Eumaios (1973 SF1) 0.97070.9707 24534 (2001 CX27) 0.97070.9707 63290 (2001 DS87) 0.9701 11668 Balios (1997 VV1) 83978 (2002 CC202) 0.97010.9701 0.94030.9403 15521 (1999 XH133) 233925 (2009 UL2) 0.97070.9707 0.90130.9013 13182 (1996 SO8) Eurymedon 0.99980.9998 0.99980.9998 4057 Demophon (1985 TQ) 11 0.93190.9319 5012 Eurymedon (9507 P-L) 0.93190.9319 1 C (H2012, 61) Clan 15529 (2000 AA80) 168033 (2005 JJ143) 0.97090.9709 0.97090.9709 659 Nestor (1908 CS) XC (T1989) 0.97930.9793 0.97930.9793 22203 Prothoenor (6020 P-L) 0.9590.959 0.9590.959 15033 (1998 VY29) 0.97930.9793 0.97930.9793 22059 (2000 AD75) Nestor Clan 0.959 0.97890.9789 4060 Deipylos (1987 YT1) D (B2004) 23152 (2000 CS8)

Figure B3. Consensus tree of the L4 Greater Nestor superclan, including Eurymedon and Nestor clans. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen(1989); B2004: Bendjoya et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012).

MNRAS 000,1–26 (2020) 30 T. R. Holt et al.

100619 (1997 TK14) 4086 Podalirius (1985 VK2) 11 11 9857 (1991 EN) Ajax 11 1404 Ajax (1936 QW) 0.929 11 23135 (2000 AN146) Subclan 0.929 0.97940.9794 0.929 0.97940.9794 7119 Hiera (1989 AV2) 11 11 9431 (1996 PS1) Hiera 11 24403 (2000 AX193) 11 Ajax 0.97940.9794 11 0.97940.9794 25911 (2001 BC76) Subclan 316158 (2009 UW26) Clan 0.97940.9794 0.9570.957 0.97940.9794 207749 (2007 RC286) 2002 CQ 0.97940.9794 134 42367 (2002 CQ134) 0.97940.9794 55578 (2002 GK105) Subclan 42554 (1996 RJ28) 55568 (2002 CU15) 11 0.97740.9774 316550 (2010 XE81) 12917 (1998 TG16) D (F2007) 0.97740.9774 0.9010.901 5258 (1989 AU1) DX (B2004) 0.97740.9774 0.9010.901 11 111932 (2002 GG33) Anius 11 8060 Anius (1973 SD1) 0.99960.9996 Subclan 0.97740.9774 18060 (1999 XJ156) X (F2007) 39793 (1997 SZ23) 0.98050.9805 Eurybates 137879 (2000 AJ114) 0.90070.9007 312457 (2008 QH42) Clan 0.90090.9009 315208 (2007 RS22) 0.97810.9781 3548 Eurybates (1973 SO) Eurybates 0.97810.9781 0.99980.9998 L C (F2007) 39285 (2001 BP75) 0.98030.9803 C (F2007) 24380 (2000 AA160) Subclan 11 C (F2007) 28958 (2001 CQ42) C (F2007)

Figure B4. Consensus tree ofthe L4 Greater Ajax superclan, including Ajax and Eurybates clans. This is a duplicate of Fig.4, and is included here for completeness. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen(1989); B2004: Bendjoya et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012).. L indicates objects to be visited by the Lucy spacecraft (Levison et al. 2017). Green highlights are members of the Eurybates collisional family.

MNRAS 000,1–26 (2020) Astrocladistics of the Trojans 31

38606 (1999 YC13)

0.97920.9792 173086 Nireus (2007 RS8) 200023 (2007 OU6) 0.97060.9706 0.95930.95930.97060.9706 1868 Thersites (2008 P-L) DX (B2004) 0.97080.9708 D (H2012, 64) 11 4946 Askalaphus (1988 BW1) 0.99950.9995 0.99950.9995 266869 (2009 UZ151) D (H2012, 87) Thersites 11 2797 Teucer (1981 LK) 0.95930.9593 11 264155 (2009 VJ109) 11 Clan 20995 (1985 VY) D (H2012, 71) 11 11 8317 Eurysaces (4523 P-L) 37298 (2001 BU80) 624 Hektor (1907 XM) D (T1989) 11 129602 (1997 WA12) 0.87910.8791 22035 (1999 XR170) 0.99870.9987 0.99870.9987 11 24275 (1999 XW167) 42230 (2001 DE108) 11 163702 (2003 FR72) 11 11 11429 Demodokus (4655 P-L) 11 11 6090 (1989 DJ) D (B2004) 11 11 4489 (1988 AK) D (H2012, 93) 11 11 6545 (1986 TR6) D (F2007) 11 11 2920 Automedon (1981 JR) 11 Hektor 11 41379 (2000 AS105) 11 11 3801 Thrasymedes (1985 VS) 11 11 1583 Antilochus (1950 SA) D (T1989) Clan 11 11 12916 Eteoneus (1998 TL15) 11 XD (B2004) 11 5285 Krethon (1989 EO11) 224020 (2005 JL160)

Figure B5. Consensus tree of the L4 Greater Hektor superclan, including Thersites and Hektor clans. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen(1989); B2004: Bendjoya et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012).. Orange highlights are members of the Hektor collisional family.

MNRAS 000,1–26 (2020) 32 T. R. Holt et al.

65209 (2002 DB17) 0.97820.9782 31835 (2000 BK16) D (H2012, 61) 0.97860.9786 3391 Sinon (1977 DD3) 0.97880.9788 107004 (2000 YC112) 38607 (2000 AN6) 0.9790.979 0.9790.979 15094 Polymele (1999 WB2) L P 5041 Theotes (1973 SW1) 0.99980.9998 21271 (1996 RF33) X (H2012, 93) 0.99980.9998 19725 (1999 WT4) 0.99980.9998 13383 (1998 XS31) 0.99980.9998 0.99980.9998 11 0.99980.9998 24233 (1999 XD94) X (H2012, 66) 63291 (2001 DU87) 0.99980.9998 0.97990.9799 0.99980.9998 0.97990.9799 24420 (2000 BU22) 0.97990.9799 C (F2007) 111805 (2002 CZ256) 0.95130.9513 0.95130.9513 0.99980.9998 23144 (2000 AY182) 11 24426 (2000 CR12) 16152 (1999 YN12) 0.97970.9797 11 63202 (2000 YR131) 0.97970.9797 23963 (1998 WY8) X (H2012, 56) 0.97970.9797 11 166285 (2002 GY127) 0.97970.9797 65232 (2002 EO87) 19913 Aigyptios (1973 SU1) 0.97990.9799 0.97970.9797 1869 Philoctetes (4596 P-L) Philoctetes 0.99980.9998 24539 (2001 DP5) 0.99980.9998 0.97960.9796 42403 Andraimon (6844 P-L) 0.97960.9796 0.97960.9796 Clan 63286 (2001 DZ68) 0.97980.9798 0.97980.9798 8241 Agrius (1973 SE1) 0.97960.9796 11 0.97960.9796 9590 (1991 DK1) D (H2012, 73) 13184 Augeias (1996 TS49) Andraimon 11 42168 (2001 CT13) 11 11 63259 (2001 BS81) 11 11 38574 (1999 WS4) Subclan 11 39692 (1996 RB32) 23285 (2000 YH119) D (H2012, 93) 24357 (2000 AC115) 11 0.95970.9597 24506 (2001 BS15) 0.92370.9237 8125 Tyndareus (5493 T-2) 12658 Peiraios (1973 SL) 0.94280.9428 0.97980.9798 0.94280.9428 57920 (2002 EL153) 10664 Phemios (5187 T-2) 0.97110.9711 11 14235 (1999 XA187) D (H2012, 68) 161017 (2002 EP106) 0.95090.9509 C (H2012, 55) 35673 (1998 VQ15) 5209 (1989 CW1) 0.97980.9798 0.87710.8771 18263 Anchialos (5167 T-2) 0.94270.9427 11351 Leucus (1997 TS25) L D (F2007) 0.98090.9809 11 83977 (2002 CE89) 11 4543 Phoinix (1989 CQ1) 11 43706 Iphiklos (1416 T-2) 11 21601 (1998 XO89) 11 1437 Diomedes (1937 PB) DX (T1989) 11 11 11 11397 (1998 XX93) Diomedes 11 11 15539 (2000 CN3) 11 11 53436 (1999 VB154) 11 Clan 65228 (2002 EH58) 7214 Anticlus (1973 SM1) 11 23939 (1998 TV33) 0.98090.9809 0.98090.9809 23123 (2000 AU57) 11 14707 (2000 CC20) D (H2012, 70) 11 13062 Podarkes (1991 HN) D (F2007) 11 21593 (1998 VL27) 11 15651 Tlepolemos (9612 P-L) 11 13331 (1998 SU52) 0.980.98 107804 (2001 FV58) 13694 (1997 WW7) 11 11 11 9694 Lycomedes (6581 P-L) 11 Lycomedes 0.98010.9801 39287 (2001 CD14) 103508 (2000 BV1) 11 111785 (2002 CQ186) Clan 13230 (1997 VG1) 11 11 23126 (2000 AK95) Amphiaraos 11 22049 (1999 XW257) 11 11 17874 (1998 YM3) 11 Subclan 11 10247 Amphiaraos (6629 P-L) 11 103989 (2000 DC94)

Figure B6. Consensus tree of the L4 Greater Diomedes superclan, including Philoctetes, Diomedes, and Lycomedes clans. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen(1989); B2004: Bendjoya et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012).. L indicates objects to be visited by the Lucy spacecraft (Levison et al. 2017). Green highlights are members of the Eurybates collisional family.

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7543 Prylis (1973 SY) 0.960.96 0.960.96 65000 (2002 AV63) 0.960.96 1749 Telamon (1949 SB) D (H2012, 97) 0.960.96 11 5244 Amphilochos (1973 SQ1) Telamon Clan 0.86460.8646 11 21370 (1997 TB28) 39264 (2000 YQ139)

0.9030.903 12714 Alkimos (1991 GX1) 4007 Euryalos (1973 SR) 11 0.9030.903 136557 Neleus (5214 T-2) 162811 (2001 AG51) 0.88410.8841 163155 (2002 CL130) 11 11 7152 Euneus (1973 SH1) X (B2004) 0.88410.8841 11 11 4138 Kalchas (1973 SM) X (B2004) Kalchas 11 89924 (2002 ED51) 11 22008 (1999 XM71) Clan 0.86640.8664 11 24508 (2001 BL26) 11252 Laertes (1973 SA2) 0.93590.9359 13379 (1998 WX9) 0.97730.9773 38052 (1998 XA7) 0.8390.839 39278 (2001 BK9) 0.88410.8841 24225 (1999 XV80)

0.88410.8841 38600 (1999 XR213) 5023 Agapenor (1985 TG3) X (H2012, 65) 0.8650.865 0.99980.9998 243484 (2009 TA23) 0.90290.9029 0.90290.9029 89871 (2002 CU143) Theoklymenos 24498 (2001 AC25) 0.92270.9227 Clan 10989 Dolios (1973 SL1) 0.92270.92270.52680.5268 0.92270.9227 20144 (1996 RA33) 0.99870.9987 5652 Amphimachus (1992 HS3) 0.98080.9808 0.92270.9227 0.98080.9808 0.92270.9227 65583 Theoklymenos (4646 T-2) 24390 (2000 AD177) D (F2007) 0.96910.9691 3063 Makhaon (1983 PV) D (L2004) 11 Makhaon 204911 (2008 QE5) 0.99990.9999 16974 (1998 WR21) 11 Subclan 17351 Pheidippos (1973 SV)

Figure B7. Consensus tree of the L4 Greater Telamon superclan, including Telamon, Kalchas, and Theoklymenos clans. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen(1989); B2004: Bendjoya et al.(2004); L2004: Lazzaro et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012).

MNRAS 000,1–26 (2020) 34 T. R. Holt et al.

38614 (2000 AA113) 0.97010.9701 13463 Antiphos (5159 T-2) X (F2007) 0.97010.9701 15535 (2000 AT177) D (F2007) 0.97010.9701 24485 (2000 YL102) X (H2012, 64) 0.9701 54678 (2000 YW47) 0.94980.9498 11 24530 (2001 CP18) 65224 (2002 EJ44) 0.94980.9498 22404 (1995 ME4) 0.94980.9498 128383 (2004 JW52) 0.97010.9701 22055 (2000 AS25) 0.97010.9701 79444 (1997 UM26) 23382 Epistrophos (4536 T-2)D (H2012, 65) 1 0.97970.9797 1 312643 (2010 BZ111) Epistrophos 11 11 38621 (2000 AG201) 11 D (H2012, 53) 0.97970.9797 11 39293 (2001 DQ10) Clan 360103 (2013 CW) 58479 (1996 RJ29) 0.97970.9797 161027 (2002 FM38) 0.97970.9797 23706 (1997 SY32) 0.9797 1647 Menelaus (1957 MK) 0.95990.9599 1143 Odysseus (1930 BH) D (T1989) 0.95990.9599 14690 (2000 AR25) 0.9799 24882 (1996 RK30) X (H2012, 73) 0.97990.9799 42179 (2001 CP25) Odysseus 0.97970.9797 0.97950.9795 9713 Oceax (1973 SP1) 161020 (2002 EK158) 0.95960.9596 0.95960.9596 11 13372 (1998 VU6) Clan 22009 (1999 XK77) 0.97990.9799 63272 (2001 CC49) C (H2012, 62) 0.97990.9799 0.97990.9799 21372 (1997 TM28) 36271 (2000 AV19) 1 11 22052 (2000 AQ14) 0.97990.9799 161044 (2002 GG181) 63292 (2001 DQ89) 11 11 5025 (1986 TS6) 63257 (2001 BJ79)

Figure B8. Consensus tree of the L4 Greater Odysseus superclan, including Epistrophos and Odysseus clans. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen(1989); B2004: Bendjoya et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012)..

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16070 (1999 RB101) D (H2012, 69) 0.93910.9391 76820 (2000 RW105) 32435 (2000 RZ96) 0.97940.9794 0.93910.9391 0.97940.9794 0.97940.9794 30506 (2000 RO85) 301760 (2010 JP42) 0.93910.9391 58008 (2002 TW240) D (H2012, 58) 76824 (2000 SA89) 129145 (2005 CE) 0.97880.9788 0.97880.9788 5648 (1990 VU1) 0.95930.9593 0.97880.9788 XD (B2004) 0.97880.9788 51935 (2001 QK134) 1990 VU 0.97880.9788 1 11 0.97880.9788 118815 (2000 SM108) 11 22808 (1999 RU12) 0.97880.9788 11 0.91890.9189 18228 Hyperenor (3163 T-1) 11 0.91890.9189 11 11 5907 (1989 TU5) Subclan 29196 (1990 YY) 55457 (2001 TH133) 187476 (2006 BB213) 11 0.93950.9395 73677 (1988 SA3) 0.95940.9594 15977 (1998 MA11) D (F2004) Idaios 0.98030.9803 24459 (2000 RF103) 11 77891 (2001 SM232) 0.98030.9803 30705 Idaios (3365 T-3) 11 0.98030.9803 D (H2012, 69) Subclan 0.98030.9803 128299 (2003 YL61) 11 47969 (2000 TG64) D (H2012, 58) 56962 (2000 SW65) 99943 (2005 AS2) (a) 1990VU1 clan. (b) 1999RU12 clan.

32794 (1989 UE5) DX (F2007) 0.9794 155332 (2006 BA157) 32499 (2000 YS11) D (H2012, 89) 0.9794 0.96120.9612 0.9794 0.96120.9612 88775 (2001 SY76) 11663 (1997 GO24) DX (F2007) 1 0.9735 11552 Boucolion (1993 BD4) D (H2012, 66) 76812 (2000 QQ84) 1 0.97350.9735 36425 (2000 PM5) 24451 (2000 QS104) 1 0.97350.9735 32811 Apisaon (1990 TP12) X (H2012, 59) 0.97350.9735 0.97350.9735 1173 Anchises (1930 UB) X (T1989) 0.97350.9735 1 11273 (1988 RN11) 51962 (2001 QH267) 0.97350.9735 1 11089 (1994 CS8) X (F2004) 1 18493 Demoleon (1996 HV9) DX (F2007) 11 1 161646 (2006 BL56) 122733 (2000 SK47) D (H2012, 58) (c) Anchises clan. (d) Apisaon clan.

23549 Epicles (1994 ES6) D (F2007) 153708 (2001 UK76) 62714 (2000 TB43) 0.9304 1 0.9304 291327 (2006 BQ194) 0.9999 51354 (2000 RX25) 0.9999 4805 Asteropaios (1990 VH7) 0.9999 178268 (2008 AH32) 0.9126 1 11554 Asios (1993 BZ12) 0.9126 1 0.9999 X (H2012, 93) 4828 Misenus (1988 RV) 284882 (2009 FY59) 0.9999 97893 (2000 QV65) 0.9999 124696 (2001 SC137) 0.9999 Erichthonios 0.892 0.9588 0.9999 9430 Erichthonios (1996 HU10) 4792 Lykaon (1988 RK1) D (B2004) 0.9999 D (F2004) 0.8994 Lykaon 11488 (1988 RM11) XD/D (F2007, H2012, 51) 0.8994 39474 (1978 VC7) 0.9999 0.9999 0.9803 30498 (2000 QK100) Subclan 106001 (2000 SR283) 0.9516 1 D (H2012, 52) 32482 (2000 ST354) X (H2012, 72) 284443 (2007 EE51) Subclan 1 17442 (1989 UO5) 158231 (2001 SJ256) 1 1 29314 Eurydamas (1994 CR18) X (H2012, 66) 0.8942 30704 Phegeus (3250 T-3) 0.8942 1 32397 (2000 QL214) 156125 (2001 SH347) 0.952 1 54582 (2000 QU179) 1988 RS 1 414468 (2009 KM14) 0.952 10 1 Dolan 0.952 5257 (1988 RS10) 1 7815 Dolon (1987 QN) 1 0.952 1 24472 (2000 SY317) 153758 (2001 UQ214) 1 0.9998 1 55060 (2001 QM73) 1 Subclan 0.9997 11487 (1988 RG10) Subclan 1 0.9997 1 55419 (2001 TF19) 185485 (2007 EL68) 248550 (2005 XS92) (e) Asteropaios clan. (f) Dolon clan.

34298 (2000 QH159) D (H2012, 54) 0.9784 0.9996 4707 Khryses (1988 PY) C (F2007) 47967 (2000 SL298) 0.97840.9784 D (F2007, H2012) 17418 (1988 RT12) 0.9788 0.9788 110359 (2001 SA318) 0.97880.9788 0.97880.9788 31037 Mydon (1996 HZ25) 1 1 12126 (1999 RM11) 45822 (2000 QQ116) (g) Khryses clan. Figure B9. Consensus trees of L5 Trojan clans that are not associated with any superclan. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen(1989); B2004: Bendjoya et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012).. L indicates objects to be visited by the Lucy spacecraft (Levison et al. 2017). Brown highlights are members of the Ennomos collisional family.

MNRAS 000,1–26 (2020) 36 T. R. Holt et al.

1

0.9792 884 Priamus (1917 CQ) D (T1989) 124985 (2001 TK131) 0.8377 4832 Palinurus (1988 TU1) D (H2012, 80) 0.8566 2241 Alcathous (1979 WM) D (T1989) 0.8566 1873 Agenor (1971 FH) 0.8566 1 23987 (1999 NB63) 343161 (2009 KH3) 0.8319 0.8319 63955 (2001 SP65) D (H2012, 54) 0.8566 73795 (1995 FH8) 0.8566 11509 Thersilochos (1990 VL6) 6997 Laomedon (3104 T-3) 0.8566 D (H2012, 55) 0.8566 617 Patroclus (1906 VY) L X (T1989) 5119 (1988 RA1) 0.8322 6002 (1988 RO) 155337 (2006 KH89) 0.9735 0.9735 295336 (2008 HY8) 0.8566 1 0.9534 1 106060 (2000 SS316) 125159 (2001 UV93) 0.9525 11887 Echemmon (1990 TV12) 34642 (2000 WN2) 0.95340.9332 0.8569 0.9332 32437 (2000 RR97) 0.98 1 30505 (2000 RW82) D (H2012, 59) 369886 (2012 RM6) 0.9802 2895 Memnon (1981 AE1) C (B2004) Memnon 0.9802 0.9802 3317 Paris (1984 KF) D (B2004) 0.907 1 1 62426 (2000 SX186) 80119 (1999 RY138) D (H2012, 65) Subclan Memnon Clan 0.9732 11275 (1988 SL3) 0.801 37519 Amphios (3040 T-3) 0.9727 0.9727 1 32475 (2000 SD234) 32501 (2000 YV135) 0.9997 105808 (2000 SZ135) D (H2012, 68) 0.9997 Amphios 0.9997 131447 (2001 QZ113) 31806 (1999 NE11) 1 1 19844 (2000 ST317) 24449 (2000 QL63) Subclan 76837 (2000 SL316) 0.9732 0.9732 122460 (2000 QB146) 0.9732 1 31342 (1998 MU31) 76826 (2000 SW131) 0.7955 19020 (2000 SC6) D (H2012, 343996 (2011 QK3) 343896 (2011 JK8) 74) 0.9065 30504 (2000 RS80) 0.8568 0.9458 4722 Agelaos (4271 T-3) 52273 (1988 RQ10) 0.972 D (H2012, 70) 32339 (2000 QA88) 1 D (H2012, 80) 0.9723 1 0.9735 16667 (1993 XM1) D (H2012, 88) 0.8198 0.947 51345 (2000 QH137) 55678 Lampos (3291 T-1) D (H2012, 79) 1 Lampos 0.9999 1 1 156237 (2001 UH146) 156250 (2001 UM198) 51994 (2001 TJ58) 0.9801 D (H2012, Subclan 1971 FV Clan 0.9801 284433 (2007 DU52) 1 0.9592 0.9592 155789 (2000 TD9) 0.9594 56) 0.9594 3708 (1974 FV1) 0.8385 0.9798 0.8385 0.9798 110380 (2001 SO343) 1974FV 0.9598 1 0.9598 122391 (2000 QZ75) 1 1 32356 (2000 QM124) 99328 (2001 UY123) D Subclan 157741 (2006 BE202) 0.9248 0.92480.947 23463 (1989 TX11) (F2007) 0.905 154990 (2005 AA66) 0.9779 51359 (2000 SC17) D (F2007) 57714 (2001 UY124) 1989 TX11 Clan 4348 Poulydamas (1988 RU) 0.9996 X (B2004) 0.9996 30806 (1989 UP5) 0.9996 0.9996 17423 (1988 SK2) 0.9996 2674 Pandarus (1982 BC3) Pandarus 0.8313 0.8886 1 D (T1989) 158333 (2001 WW25) 157471 (2005 AX71) 0.889 160164 (2001 TW252) Subclan 0.889 0.9609185906 (2000 SF94) 283519 (2001 TP47) 0.889 0.889 0.9732 56976 (2000 SS161) D (H2012, 58) Phereclos Clan 125059 (2001 TB233) 0.952 Phereclos 0.7649 0.952 54646 (2000 SS291) 0.9793 0.9793 0.9996 2357 Phereclos (1981 AC) D (T1989) 0.9591 110832 (2001 UA58) Subclan 156294 (2001 WU66) 0.9592 1 30499 (2000 QE169) D (H2012, 55) 55460 (2001 TW148) 127534 (2002 WR17) 119528 (2001 US179) 0.8681 0.9719 0.9719 52511 (1996 GH12) 0.8681 58084 Hiketaon (1197 T-3) 38257 (1999 RC13) 0.8945 56968 (2000 SA92) D (F2007) 24452 (2000 QU167) 0.8692 0.9592 D (F2007) 105896 (2000 SG187) 0.8692 99311 (2001 SQ282) 18037 (1999 NA38) 1 0.9747 1 18278 Drymas (4035 T-3) 1 1 5511 Cloanthus (1988 TH1) D (F2007) 0.9747 122581 (2000 RJ24) 17365 (1978 VF11) 17420 (1988 RL13) 0.9747 0.9741 1 11869 (1989 TS2) D (H2012, 56) 0.9747 120454 (1988 SJ2) 18268 Dardanos (2140 T-3) D (F2004) 0.8621 51350 (2000 QU176) 0.8621 62692 (2000 TE24) 105746 (2000 SP92) 0.9494 0.9494 30708 Echepolos (4101 T-3) 51365 (2000 TA42) 1 1 76867 (2000 YM5) 1 122592 (2000 RE29) 1 129153 (2005 EL140) 1 1 1 1 1 1208 Troilus (1931 YA) FCU (T1989) 1 299491 (2006 BY198) 1 17172 (1999 NZ41) Triolus 1 1 1 117447 (2005 AX46) 1 Troilus Clan 1 1 29977 (1999 NH11) Subclan 1 32480 (2000 SG348) 32464 (2000 SB132) 1 1988 RY 1 22180 (2000 YZ) 11 30791 (1988 RY11) 19018 (2000 RL100) Subclan 1 1 9023 Mnesthus (1988 RG1) 17415 (1988 RO10) 1 17171 (1999 NB38) 1 0.9141 2363 Cebriones (1977 TJ3) D (T1989) 4709 Ennomos (1988 TU2) 1 24470 (2000 SJ310) 53419 (1999 PJ4) 0.9141 0.9279 0.999 32496 (2000 WX182) 51910 (2001 QQ60) 0.9735 Cebriones Clan 1 5120 Bitias (1988 TZ1) 16956 (1998 MQ11) 0.9798 54656 (2000 SX362) 1 1 51969 (2001 QZ292) 1 Bitias 1 32440 (2000 RC100) 1 1 29603 (1998 MO44) 129135 (2005 AD21) Subclan

Figure B10. Consensus trees of the L5 Greater Patroclus superclan, including Memnon, 1971 FV1, 1989 TX11, Phereclos, Trollus and Cebriones clans. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen(1989); B2004: Bendjoya et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012).. L indicates objects to be visited by the Lucy spacecraft (Levison et al. 2017). Brown and Purple highlights are members of the Ennomos and 2001 UV209 collisional families respectively.

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0.8095116134 (2003 WZ142) 0.935 319282 (2006 BY73) 15502 (1999 NV27) 0.9794 D (F2004) 0.9794 184988 (2006 FF12) 0.9794 0.9794 17419 (1988 RH13) C (H2012, 62) 1988 RH Clan 0.8884 68519 (2001 VW15) 13 0.9787 2207 Antenor (1977 QH1) D (T1989) 125106 (2001 UR39) 0.5379 4708 Polydoros (1988 RT) D (H2012, 74) 0.5379 127532 (2002 WH9) 0.9997 1 7352 (1994 CO) D/X (B2004, F2004) 0.9547 1 98153 (2000 SY68) 1 0.9732 18940 (2000 QV49) D (F2004) 31820 (1999 RT186) D (F2007) 1994 CO Clan 0.9547 24448 (2000 QE42) D (H2012, 64) 1 150876 (2001 SA220) 1 1 30807 (1989 UQ5) 1 D (H2012, 62) 1 110859 (2001 UW79) 0.9546 179902 (2002 VO4) 1989 UQ Clan 4754 Panthoos (5010 T-3) 5 64270 (2001 TA197) 51346 (2000 QX158) D (H2012, 59) 0.9546 105720 (2000 SR79) 1 0.9596 1 1 98037 (2000 RE20) 1 36922 (2000 SN209) Hippokoon 1 0.9594 0.9546 0.9594 1 30698 Hippokoon (2299 T-3)D (F2007, H2012) 106091 (2000 SZ361) 32370 (2000 QY151) Subclan 0.9596 154992 (2005 CV68) 0.9594 77902 (2001 TY141) 0.9596 54653 (2000 SB350) Sarpedon 0.9394 0.9546 47963 (2000 SO56) 0.9394 2223 Sarpedon (1977 TL3) DU/D (T1989, B2004, F2004) Sarpedon 0.9598 84709 (2002 VW120) D (F2004) Clan 0.9598 0.95980.9799 18054 (1999 SW7) D (H2012, 74) Subclan 0.9598 54655 (2000 SQ362) 0.92 370105 (2001 TA132) 491611 (2012 TX51) 17414 (1988 RN10) 0.9544 2893 Peiroos (1975 QD) D (T1989) 36624 (2000 QA157) 1 0.954 34746 (2001 QE91) 1 1 1867 Deiphobus (1971 EA) 247967 (2003 YD149) 0.9744 114208 (2002 VH107) D (H2012, 59) 24458 (2000 RP100) 1 Helicaon 0.954 1 155786 (2000 SD358) 1 48764 (1997 JJ10) 1 1 30942 Helicaon (1994 CX13)D (H2012, 59) 0.9542 47962 (2000 RU69) Subclan 53418 (1999 PY3) 76857 (2000 WE132) 0.9795 Aneas Clan 0.9544 24446 (2000 PR25) 0.9544 1 D (H2012, 59) Iphidamas 1 4791 Iphidamas (1988 PB1) 1 1 29976 (1999 NE9) D (H2012, 81) 0.9544 105803 (2000 SH132) 25347 (1999 RQ116) Subclan 0.9747 D (B2004) 0.9747 1172 Aneas (1930 UA) D (T1989) 0.9744 129147 (2005 CY70) 117389 (2004 YD23) 0.9997 Aneas 0.9997 4867 Polites (1989 SZ) 0.9997 12444 Prothoon (1996 GE19) 0.9997 0.9997 12929 (1999 TZ1) 18046 (1999 RN116) Subclan

Figure B11. Consensus trees of the L5 Greater Aneas superclan, including 1988 RH13, 1994 CO, 1989 UQ5, Sarpedon and Aneas clans. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen(1989); B2004: Bendjoya et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al. (2012).. Brown highlights are members of the Ennomos collisional family.

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65590 Archeptolemos (1305 T-3) 282198 (2001 UM166) 0.9647 12052 Aretaon (1997 JB16) 5130 Ilioneus (1989 SC7) D (F2004) 1 109549 (2001 QM257) 0.9735 0.9732 125045 (2001 TK211) 17416 (1988 RR10) D (F2004) 0.9732 1 1 133853 (2003 YQ133) 1 153141 (2000 SP203) 0.9735 1 P (F2004) 1988 RR 0.9732 1 34785 (2001 RG87) 10 0.9732 114345 (2002 XN72) 1 5476 (1989 TO11) 0.9732 47957 (2000 QN116) Subclan 0.9732 34521 (2000 SA191) 0.9732 25883 (2000 RD88) 0.9732 3451 Mentor (1984 HA1) 0.9735 0.9732 1 X (H2012, 96) Mentor Clan 1 289501 (2005 EJ133) 5637 Gyas (1988 RF1) 1 99334 (2001 VC92) Mentor 1 1 68444 (2001 RH142) 1 133862 (2004 BR38) 1 1 12242 Koon (1988 QY) Subclan 48438 (1989 WJ2) 57013 (2000 TD39) 1 1 4715 (1989 TS1) 25344 (1999 RN72) D (B2004) 0.947 55267 (2001 RP132) 31819 (1999 RS150) 1 24453 (2000 QG173) 0.9735 1 1 184983 (2006 CS19) 1 246114 (2007 GR70) 0.9795 0.9735 0.9795 47959 (2000 QP168) 161664 (2006 DM16) 0.9795 1 1 1872 Helenos (1971 FG) 0.9795 283173 (2009 HZ62) 4829 Sergestus (1988 RM1) 1 XD (F2004) Helenos Clan 0.9735 1 47955 (2000 QZ73) 1 1 31814 (1999 RW70) 161916 (2007 EO34) 152297 (2005 TH49) 106160 (2000 TG61) 1 1 117385 (2004 YN20) Ophelestes 0.9735 1 52767 Ophelestes (1998 MW41) 1 1 23694 (1997 KZ3) D (F2007) 32430 (2000 RQ83) D (F2004) Subclan 0.9735 1 216409 (2008 GM84) 1 98143 (2000 SS60) 1 1 51340 (2000 QJ12) 122962 (2000 SG215) 32420 (2000 RS40) 0.9735 1 1 24444 (2000 OP32) 99309 (2001 SH264) 64326 (2001 UX46) 0.9592 0.9735 1 1871 Astyanax (1971 FF) D (F2004) 0.9796 76804 (2000 QE) D (F2007) Astyanax 153500 (2001 RN122) 1 1 17492 Hippasos (1991 XG1) 0.9735 98362 (2000 SA363) Subclan 1 31344 (1998 OM12) Astyanax Clan 77906 (2001 TU162) 0.9735 32615 (2001 QU277) D (F2004) 0.9735 106143 (2000 TU44) 0.9735 1 51958 (2001 QJ256) 187456 (2005 XK5) 0.9735 18137 (2000 OU30) D (F2004) 99306 (2001 SC101) 1 0.9735 24454 (2000 QF198) CX (H2012, 57) 0.9798 0.9395 151883 (2003 WQ25) Acamas 0.9395 16560 Daitor (1991 VZ5) CX (H2012, 0.9735 0.9998 1 2594 Acamas (1978 TB) 48604 (1995 CV) 77) Subclan 48249 (2001 SY345) D (F2004) 0.9735 77860 (2001 RQ133) 0.9735 34835 (2001 SZ249) 0.9735 9030 (1989 UX5) D (F2007) 0.9735 111198 (2001 WX20) 1989 UX5 0.9735 0.9735 131635 (2001 XW71) 0.9735 51351 (2000 QO218) 0.9509 0.9774 54596 (2000 QD225) Subclan 182522 (2001 SZ337)

Figure B12. Consensus trees of the L5 Greater Astyanax superclan, including Mentor, Helenos, and Astyanax clans. Numbers indicate fraction of 10000 trees where branch is present. Letters associate objects with Bus-Demeo taxonomy (Bus 2002; DeMeo et al. 2009), classified by associated reference T1989: Tholen (1989); B2004: Bendjoya et al.(2004); F2007: Fornasier et al.(2007); H2012, with associated confidence rating: Hasselmann et al.(2012).. Brown highlights are members of the Ennomos collisional family.

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