Taxonomy of Asteroid Families Among the Jupiter Trojans: Comparison Between Spectroscopic Data and the Sloan Digital Sky Survey Colors

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ninto ention c l,and ple, spectra S 2013 ESO Sky l to p eL4 he hese pro- in s sur- ter- 34 si- he w c - 2 F. Roig et al.: Taxonomy of Trojan asteroid families that are members of the main asteroid families in L4 and L5. Surface mineralogy base on NIR spectra has been analyzed by Emery & Brown (2003), and recently by Yang & Jewitt (2007) who addressed the presence of water ice on the Trojan surfaces. A very complete analysis of the properties of Jupiter Trojans observed by the Sloan Digital Sky Survey (SDSS) has been devel- oped by Szabó et al. (2007), who addressed an interesting correlation between colors and orbital inclinations. All these studies indicate that Jupiter Trojans seems to be a quite homogeneous population in terms of taxonomy and surface mineralogy. In spite of these works, the amount of spectroscopic data of Jupiter Trojans presently available is still small to allow a statistical analysis of the taxonomic properties of these bodies. Moreover, since spectra come from different sources they do not constitute a homogeneous data sample. In this paper, we analyze the taxonomy of Jupiter Trojans using data contained in the 3rd release of the SDSS Moving Objects Catalog (MOC3), and compare the results to the available spectroscopic data, with particular emphasis on Trojan asteroid families. The SDSS-MOC3 colors have proved to be a very use- ful tool to characterize the taxonomy of Main Belt asteroids, as recently addressed by Roig & Gil-Hutton (2006), Binzel et al. (2006, 2007), Duffard & Roig (2007), Roig et al. (2007), Gil-Hutton & Brunini (2007), and Hammergren et al. (2007). The paper is organized as follows: Section 2 introduces the two Figure 1. Distribution of 40863 observations selected from the data samples used in this study and compares their internal ac- SDSS-MOC3 (gray dots) in the space of first and second princi- curacy. Section 3 is devoted to the global analysis of the color pal components. The black dots correspond to 371 observations and taxonomy distributions of the data samples. Section 4 con- of known Jupiter Trojans, but those surrounded by a circle have centrates on the particular analysis of selected asteroid families. been discarded (see text). Finally, Section 5 contains the conclusions.

fluxes as: 2. Selection of the data samples PC1 = 0.886Fu + 0.416Fg − 0.175Fi + 0.099Fz − 0.849 In this work, we will analyze two different data sets containing = . . + . + . . information on Trojan asteroids taxonomy. They are described PC2 −0 049Fu − 0 003Fg 0 284Fi 0 957Fz − 1 261 in the following. The use of principal components allows an easy interpretation of the observations in a bidimensional space. Observations with 2.1. The Sloan sample PC1 & 0 correspond to featureless spectra (e.g. C-, X- and D- type asteroids), while those with PC1 . 0 correspond to featured The first data set is constituted by observations from the SDSS- spectra that show a broad absorption band longwards of 7000 Å MOC3 and their selection required some care. The SDSS-MOC3 (e.g. S- and V-type asteroids). The value of PC2 is related to the includes photometric measurements of more than 204000 mov- overall slope of the spectrum, the larger the PC2 the higher the ff ing objects, of which only 67637 observations have been e ec- slope. For featureless spectra, PC2 gives an idea of how reddish tively linked to 43424 unique known asteroids. The observations is the spectrum; for featured spectra, it gives an idea of the band consist of calibrated magnitudes in the u, g, r, i, z system of fil- depth (see Roig & Gil-Hutton 2006). ters, centered at 3540, 4770, 6230, 7630 and 9130 Å, respec- Within these 40 863 observations, we identified 371 tively, and with bandwidths ∼ 100 Å (Fukugita et al. 1996). We observations corresponding to 257 different Trojan aster- adopted here a procedure similar to that of Roig & Gil-Hutton oids listed in the database of Trojan proper elements (2006). First, we used the solar colors provided by Ivezic´ et al. maintained by the PETrA Project (Beaugé&Roig 2001; (2001) to compute the reflectance fluxes Fν in the five bands, http://staff.on.br/froig/petra). Their distribution in normalized to 1 at the r band. Then, we discarded the observa- the space of principal components is also shown in Fig. 1 (black tions with error > 10% in any of the Fg, Fr,Fi and Fz fluxes. dots). Most of these observations of Trojan asteroids have val- Observations showing anomalous values of the fluxes, like Fu > ues of PC1 & 0 compatible with featureless spectra, and values 1.0, Fg > 1.3, Fi > 1.5, Fz > 1.7, and Fg < 0.6 were also dis- of PC2 & 0 indicating that they have moderate to high spec- carded. Note that the error in Fu has not been constrained, which tral slopes. There are, however, some observations (circled dots allows to get a final data set with more than twice the amount of in Fig. 1) that either depart significantly from the overall distri- observations than if we restrict this error to be less than 10%. As bution of other Trojan observations, or they clearly fall within we will explain later, this error is not critical for our study. the region of featured spectra occupied by the S-type asteroids We ended up with a sample of 40863 observations corre- (PC1 . 0.05 and PC2 . 0.2). Direct inspection of the re- sponding to 28910 unique known asteroids. The distribution of flectance fluxes indicates that these observations are not com- these observationsin the space of principal componentsis shown patible with featureless spectra or they show anomalous fluctu- in Fig. 1 (gray dots), where the first and second principal com- ations, therefore we discarded them as well. The final sample ponents, PC1 and PC2, have been computed from the reflectance contains 349 observations corresponding to 250 unique known F. Roig et al.: Taxonomy of Trojan asteroid families 3

Trojan asteroids. Hereafter we will refer to this sample as the Sloan sample. The Sloan sample includes 200 observations of asteroids in the L4 swarm and 149 observationsof the L5 swarm. About 40% of these observations correspond to asteroid family members. It is worth mentioning that the main goal of our selection method is that it provides a sample of good quality observations from the SDSS-MOC3 that can be easily linked to family and to background (i.e. non family) asteroids. Our approach is different from that introduced by Szabó et al. 2007, who applied a kine- matic criterion to select candidate Trojan asteroids within the SDSS-MOC3. These authors got a much larger sample of 1,187 observations, but these observations cannot be separated in those corresponding to family and to non family asteroids. Each observation in our Sloan sample has been characterized −1 by its equivalent spectral slope S , in Å . The slope was computed from a least-squares fit to a straight line passing through the fluxes Fg, Fr, Fi and Fz. This fit takes into account the individual errors of the fluxes to estimate the slope and its error ∆S . Hereafter, we will refer to this set of 349 slopes as the Sloan slopes. Note that the flux Fu has not been used to compute the spectral slope. The reason for this it twofold: (i) we know, from spectroscopic observations, that the reflectance flux in the u band usually drops off and significantly deviates from the linear trend Figure 2. Distribution of the parameter ǫ (see text) for the of the spectrum; (ii) we intend to compare the Sloan sample to a Sloan sample (gray histogram) and for the Spectroscopic sam- sample of spectroscopic data, described below, where most spec- ple (hatched histogram). Each histogram has been normalized tra do not cover the wavelengths . 5000 Å. Since Fu does not such that its area is 1. contribute effectively to determine the slope, there is no harm in keeping its error unconstrained as we did. Table 1 providesthe list of all the know Trojan asteroids con- to account for uncertainties in the sample related to use of data tained in our Sloan sample. This table also gives the estimated obtained by different surveys. It is worth noting that the slopes spectral slope, S , with its correspondig error, ∆S , and the num- computed here are not compatible with other published slopes ber of observations, Nobs, in the sample. For Nobs ≥ 2, the slope (e.g. Jewitt & Luu 1990, Fornasier et al. 2007) due to different given in this table is the weighted mean of the individual Sloan 2 normalization wavelengths –usually 5500 Å– and also due to slopes, with the weights defined as 1/ (∆S ) . different wavelenghts intervals used to fit the data. In fact, our slopes may be up to 20% smaller than those published in the 2.2. The Spectroscopic sample literature. Hereafter, we will refer to our set of 91 slopes as the Spectroscopic slopes, to distinguish them from the Sloan slopes. The second data set analyzed here is a collection of 91 spec- Table 2 providesthe list of all the know Trojan asteroids con- tra corresponding to 74 individual Trojan asteroids published tained in our Spectroscopic sample. For asteroids with Nobs ≥ 2, in the literature. All the spectra are defined in the visible the slope shown in this table has been computed as the weighted wavelength range and have been obtained by different ob- mean of the individual Spectroscopic slopes. It is worth recalling servational surveys, in particular: 3 spectra come from the that in Table 1 an asteroid with Nobs ≥ 2 had all its observations SMASS1 survey (Xu et al. 1995), 2 spectra from the SMASS2 made by the same survey, i.e. the SDSS, while in Table 2 an survey(Bus& Binzel 2002), 33 spectra from Bendjoya et al. asteroid with Nobs ≥ 2 had its observations made by different (2004), 25 spectra from Fornasier et al. (2004), 13 spectra from spectroscopic surveys. the S3OS2 survey (Lazzaro et al. 2004), and 15 spectra from Dotto et al. (2006). Hereafter we will refer to this data set as the Spectroscopic sample. This sample includes 52 spectra of aster- 2.3. Accuracy of the samples oids in the L4 swarm and 39 spectra of the L5 swarm. About 40% of these spectra correspond to asteroid family members. The Sloan sample is ∼ 4 times larger than the Spectroscopic To determine the spectral slope, each spectrum in the sam- sample, which in terms of statistics does not appear to be a significant improvement. However, the Sloan sample is expected to ple was first rebinned by applying a 20 Å running box average. be more homogeneous than the Spectroscopic sample because, The rebinned spectrum was then normalized to 1 at 6230 Å to in the former case, the observations come from the same survey, make it comparable to the Sloan fluxes. Finally, the slope of the while in the latter they came from different surveys. Moreover, normalized spectrum was computed from a least-squares fit to a the spectroscopic surveys have been usually dedicated either straight line in the interval 5000-9200 Å. This wavelength inter- to observe family members only (e.g. Fornasier et al. 2004, val is similar to the one adopted to compute the Sloan slopes, and Dotto et al. 2006, Fornasieret al. 2007) or to observe back- it is well covered by most spectra in our sample except for a few ground asteroids only (e.g. Lazzaro et al. 2004, Bendjoya et al. cases for which the fit had to be done over a smaller available 2004). But the Sloan sample includes both family members and range. Following the same approach as Fornasier et al. (2007), background asteroids observed by the same survey. The Sloan the error in the slope was estimated by adding an “ad-hoc” er- sample is also expected to include a significant amount of very −1 ror of ±5 × 10−6 Å to the standard error of the fit. The idea is small Trojans that spectroscopic surveys normally do not ob- 4 F. Roig et al.: Taxonomy of Trojan asteroid families serve. Although the SDSS photometry is not as precise as spec- The D-type observations dominate over the P-type in the ap- 2 1 troscopy, this is not crucial in the case of the Trojan asteroids proximate proportion 3 : 3 , but the Sloan sample shows a larger because they all show featureless spectra that are properly char- abundance of P-type relative to D-type than the Spectroscopic acterized by the average spectral slope. sample. The bimodality observed in Fig. 3a has also been In order to verify the reliability of the Sloan and the reported by Szabó et al. (2007) analyzing SDSS-MOC3 col- Spectroscopic samples, we performed the following test. For ors1. The Sloan slopes appear more tightly clustered than the each asteroid with Nobs ≥ 2 in Table 1 we computed the pa- Spectroscopic slopes, which might be related to the less homo- rameter geneity of the Spectroscopic sample. Nevertheless, the Sloan |S − S | slopes appear well correlated to the Spectroscopic slopes, as ǫ = 1 2 ∆S + ∆S shown in Fig. 3b for the few observations corresponding to as- 1 2 teroids included in both samples. ff where S i are the spectral slopes of two di erent observations To analyze the distribution of spectral slopes of the asteroid ǫ < of that asteroid. A value of 1 indicates that this two ob- families, we first proceeded to identify the different families in ff servations are self-consistent, since their di erences are within each Trojan swarm. We used the catalog of 1702 Trojan asteroids the individual errors. We can apply the same procedure to each with known resonant proper elements maintained by the PETrA ≥ asteroid with Nobs 2 in Table 2, and compare the results. Project (Beaugé & Roig 2001) and applied to this catalog the ǫ In Fig. 2, we show the distribution of values for the Sloan Hierarchical Clustering Method (HCM, Zappalà et al. (1995)). and Spectroscopic samples. The Sloan sample shows a good The mutual distance between any pair of asteroids in the proper self-consistency among the observations of each asteroid with elements space was computed according to the metric Nobs ≥ 2. Since in most cases the individual errors are ∼ 10%, this result supports the idea of a quite homogeneous sample. 1/2 1 δa 2 On the other hand, a significant fraction of the Spectroscopic d = + 2 (δe)2 + 2 (δ sin I)2 sample shows differences among the observations of each as- 4 a !   0  teroid with N ≥ 2 that are beyond their errors. This may be   obs   explained by different observational conditions, different instru- (Milani 1993), where δa, δe and δ sin I are the differences in mental setup and different reduction processes among the differ- proper semi-major axis, proper eccentricity and proper sinus of ent surveys. The inconsistency could be minimized by increasing inclination, respectively, between the given pair of asteroids, and the “ad-hoc” error introduced to estimate the slope error, but this a0 = 5.2026 AU is the average proper semi-major axis of the “ad-hoc” error is already of ∼ 10%. Therefore, the result shown Trojan population. Those bodies for which d ≤ dcut were clus- in Fig. 2 supports the idea that the Spectroscopic sample is less tered together to form the families. The cutoff value dcut was homogeneous than the Sloan sample, as expected. chosen to be 110 ms−1 for the L4 swarm and 120 ms−1 for the L5 swarm, which are comparable to the corresponding quasi- random level of each swarm2. We have verified that values of 3. Global distribution of spectral slopes −1 dcut within ±10 ms around the above values produce practi- In this section we analyze the distribution of spectral slopes of cally the same results. Clusters with less than 8 members in the the whole population of known Trojan asteroids included in our L4 swarm and with less than 6 members in the L5 swarm were data samples, with particular attention to the asteroid families. considered statistical fluctuations and were disregarded. For a First, we compare the Sloan and the Spectroscopic samples, and detailed explanation on the definition of dcut and the application then we discuss each sample separately. of the HCM to the Trojan case refer to Beaugé & Roig (2001). The distribution of the detected families in the space of proper eccentricity and inclination is shown in Fig. 4. 3.1. Comparisons between the samples In Fig. 5, we show the slope distribution of family mem- In Fig. 3 a we show the distribution of Sloan slopes (349 obser- bers (panel a) compared to the background asteroids (panel b). vations) compared to the distribution of Spectroscopic slopes (91 The gray histograms correspond to the Sloan sample, while observations). Both distributions show a clear bimodality, that is the hatched histograms correspond to the Spectroscopic sample. more evident in the Sloan sample. This bimodality is related to Except for a few background asteroids with very small and even the presence of two different taxonomic types among the Jupiter negative slopes (these latter observed by Bendjoya et al. (2004)), Trojans: (i) the D-type, with spectral slopes S & 7.5 × 10−5 the distribution of Sloan slopes of background asteroids is com- −1 parable to the distribution of Spectroscopic slopes, both showing Å , that correspond to redder surfaces, and (ii) the P-type, with a clear abundance of D-type asteroids. The situation is quite dif- −5 −1 slopes 1.5 . S . 7.5×10 Å , that correspond to less reddish ferent for the family members, since the Sloan sample shows a colors. There is also a small amount of observations compatible clear bimodality that is not observed in the Spectroscopic sam- −1 with the C-type taxonomy, with slopes S . 1.5 × 10−5 Å , that ple. It is worth noting that the Sloan sample contains about correspond to more neutral colors. The limiting slopes between 3 times more observations of family members and goes much −1 the taxonomic classes are estimated within a ±0.7×10−5 Å in- deeper in absolute magnitude than the Spectroscopic sample. terval of tolerance, which is the approximate bin size in Fig. 3. It This result may indicate that family members contribute with is worth stressing that these limiting slopes are totally arbitrary. a significant amount of the P-type asteroids found among the Moreover, they are not compatible with the values adopted by Trojan swarms. It also indicates that families appear to be bluer the usual taxonomies, where the separation between the P- and than the background. −5 −1 D-types occurs at S ∼ 5.5 × 10 Å . Nevertheless, our choice 1 ∗ Indeed, the principal color tc introduced by these authors is strongly is based on the natural separation of the slopes induced by the correlated to both the second principal component PC2 and the spectral bimodality in their distribution and it is valid as far as no min- slope S . eralogical constraint is known to define the P and D taxonomic 2 The quasi-random level is the maximum level of statistical signifi- types. cance of the HCM. F. Roig et al.: Taxonomy of Trojan asteroid families 5

Figure3. (a) Distribution of spectral slopes from the Sloan sample (349 observations, gray histogram) and from the Spectroscopic sample (91 observations, hatched histogram). Each histogram has been normalized such that its area is 1. Both distributions show a bimodality related to the presence of two taxonomic types: P-type (smaller slopes) and D-type (larger slopes). (b) Comparison between the Spectroscopic slopes and the Sloan slopes from observations of asteroids included in both samples

Figure 4. Left panel. Asteroid families (big dots) identified in the L4 swarm, projected in the space of proper eccentricity and inclination. Background asteroids are represented by small dots. The cutoff level is 110 m s−1. Right panel. The same but for the L5 swarm. The cutoff level is 120 m s−1.

3.2. Global analysis of the Sloan sample shows the distribution of Sloan slopes of family members in the L4 swarm (gray histogram) and in the L5 swarm (outlined histogram). The diﬀerence between the swarms is notorious. While It is well known that asteroid families do not appear equally dis- in L4 the Sloan slopes show a predominance of P-type asteroids tributed among the L4 and L5 swarms. While the families in L4 among the families, the L5 families appear dominated by D-type are more conspicuous and tend to form large clusters, the fami- asteroids. The families in L5 are signiﬁcantly redder than those lies in L5 are smaller and tighter. The total number of families is in L4. On the otherhand,the slope distribution of backgroundas- also larger in L4 than in L5. Thus, it is interesting to analyze the distribution of Sloan slopes separately in each swarm. Figure 6a 6 F. Roig et al.: Taxonomy of Trojan asteroid families

Figure5. (a) Distribution of spectral slopes of observations corresponding to family members. The gray histogram correspond to the Sloan slopes and the hatched histogram to the Spectroscopic slopes. (b) The same but for the observations corresponding to background asteroids. Each histogram has been normalized such that its area is 1. teroids, shown in Fig. 6b, is almost the same in the two swarms, the background that it is strongly correlated. This correlation with a significant peak of D-type asteroids. appears to be the same in both swarms, as Szabó et al. (2007) The behavior observed in Fig. 6a,b may explain the differ- conjectured. ent color distributions between the L4 and L5 swarms reported by Szabó et al. (2007) from the analysis of SDSS-MOC3 col- We must note that the separation in low and high inclina- ors. These authors pointed out that the amount of redder aster- tion populations proposed by Szabó et al. (2007) partially works oids (higher slopes), relative to the bluer ones (smaller slopes), to explain the different color distributions between L4 and L5 is much larger in the L5 swarm than in the L4 swarm. The situ- because the family members are not uniformly distributed in ation is clearly illustrated in Fig. 6c. They explained this differ- terms of proper inclination. In fact, the families in the L4 swarm ence on the basis of an observational selection effect that causes are mostly concentrated at low inclinations while the families in to detect more asteroids with high orbital inclination, relative to L5 spread over a wider range of proper inclinations, as we can those with low orbital inclination, in the L5 swarm compared to see in Fig. 4. If we consider only the high inclination asteroids the L4 swarm. Since there is a clear correlation between color (sin I & 0.2), then the L4 swarm is dominated by background and orbital inclination, such that the bluer bodies have low incli- asteroids (Fig. 4) which are predominantly red (Fig. 7b). The L5 nations while the redder ones are predominantly found at high swarm has a larger proportion of asteroid families at high incli- inclinations, and since this correlation appears to be the same nations (Fig. 4), but these are also predominantly red (Fig. 6a) in both swarms, Szabó et al. (2007) conclude that it is natural as the background. Thus, both swarms show the same color dis- to find a large fraction of redder bodies in the L5 swarm. The tribution at large inclinations. On the other hand, if we consider authors tried to overcome the observational selection effect by the low inclination asteroids (sin I . 0.2), the asteroid families separating their observations in those corresponding to high in- significantly contribute to the slope distribution. While the back- clination asteroids (> 10◦) and those corresponding to low in- ground tends to be bluer (Fig. 7b), the families cover a wider clination bodies (< 10◦), and showing that, with this separation, range of colors (Fig. 6a) and this tends to disguise the differ- the differences between L4 and L5 almost disappear. ences in slope distribution between the swarms. This is precisely We believe, however, that a separation in terms of asteroid the result found by Szabó et al. (2007). families and background asteroids, instead of orbital inclinations, provides a much better explanation, since it is clear from Another interesting result concerns the correlation between Fig. 6 that the swarms differ in their color distributions due to the spectral slope and absolute magnitude (or size). Figure 8 is anal- presence of the asteroid families. The advantage of this scenario ogous to Fig. 7, but in terms of absolute magnitude instead of is that it has a physical basis and does not require to invoke any orbital inclination. If we eliminate the few large bodies (H . 9) strange observational bias. It is also interesting to analyze the from the sample then the families (Fig. 8a) do not show any ap- color-inclination correlation in terms of asteroid families. In Fig. parent correlation, but the background asteroids (Fig. 8b) shows 7 we show the distribution of asteroid family members (panel a) a weak correlation since bodies in the range 9 . H . 11 are and background asteroids (panel b) in the plane of spectral slope predominantly red. Note that, if we consider together the fami- vs. orbital inclination. Dots and crosses represent the L4 and L5 lies and the background, the slope-size correlation is disguised observations, respectively. The family members do not show any and this is probably the reason why Szabó et al. (2007) did not apparent correlation between color and inclination, contrary to detected this correlation in their analysis. F. Roig et al.: Taxonomy of Trojan asteroid families 7

Figure6. (a) Distribution of the Sloan slopes of family members only. The gray histogram correspond to the L4 swarm and the outlined histogram to the L5 swarm. (b) Same as (a) but for the background asteroids only. (c) Same as (a) but for both family members and background asteroids together. Each histogram has been normalized such that its area is 1.

The results of Figs. 7b and 8b led to concludethat largeback- but our Spectroscopic sample includes about the same amount ground asteroids in both Trojan swarms tend to be redder and of family members in both swarms. tend to be located at large orbital inclinations. Besides, neither the correlation between slope and inclination, nor the one between slope and size are observed in the Spectroscopic sample. This may be due to the smaller number 3.3. Global analysis of the Spectroscopic sample of objects contained in the sample and to its less homogeneity. It is interesting to note that the background of the Spectroscopic The behavior observed in Fig. 6 is not reproduced among the sample includes some large P-type asteroids and also some high- Spectroscopic sample. This is probably due to the fact that inclination P-type asteroids that are not observed in the Sloan our Spectroscopic sample is deﬁcient in observations of family sample. members in the L4 swarm. In fact, the actual population in the An analysis of a much larger data set of spectroscopic L4 swarm is at least ∼ 1.6 times larger than in the L5 swarm, data has been performed by Fornasier et al. (2007). Their sam- 8 F. Roig et al.: Taxonomy of Trojan asteroid families

Figure7. (a) Distribution of the Sloan slopes of family members as a function of proper inclination. Dots correspond to the L4 swarm and crosses to the L5 swarm. (b) Same as (a) but for the background asteroids. Note the significant lack of high-inclination background asteroids with small slopes (P-types). ple includes the same observations that we include in our ier to breakup than D-type asteroids. Recall that this is just an Spectroscopic sample plus other spectroscopic observations assumption and there is no evidence, neither observational nor from Jewitt & Luu (1990), Fitzsimmons et al. (1994) and from theoretical, to support it. Therefore, large P-type asteroids will themselves, totalizing 142 different Trojan asteroids. They found tend to fragment in smaller bodies while large D-type aster- a situation very similar to the one observed in Fig. 6c, indicat- oids will tend to remain intact, causing a loss of large P-type ing that the L4 swarm has a larger fraction of P-type asteroids, asteroids as suggested in Fig. 8b. In addition, fragments from relative to D-type, compared to the L5 swarm. Fornasier et al. P-type asteroids may acquire larger ejection velocities after a (2007) did not find any slope-size correlation, although they de- breakup than fragments from D-type asteroids. Since the islands tected that the distribution of spectral slopes is narrower at large of stability around L4 and L5 shrink at large inclinations (e.g. sizes. In fact, from figure 9 of their paper, it is possible to infer Marzari et al. 2003, Schwarz et al. 2004), many of these P-type a slight predominance of D-type asteroids among the large as- fragments might be ejected beyond the stability limits of the teroids (50 . D . 120 km). This situation would be similar to swarms causing the lack of high-inclination P-type asteroids ob- the one obtained in the range (9 . H . 11) by overlapping the served in Fig. 7b. The predominance of P-type asteroids among two panels in Fig. 8. An analysis of the slope-size relation using the L4 families is in line with this scenario but, on the other hand, the data in Fornasier et al. (2007) and separating asteroid fami- the predominance of D-type asteroids among the L5 families is lies from background asteroids might help to check whether the against it. result shown in Fig. 8 correspond to a real correlation or is just Another scenario involves the idea that the P and D classes an artifact of our Sloan sample. represent the same mineralogy but modified by some aging process, like the space weathering. Let us assume that the space 3.4. Discussion weathering produces a reddening of the surfaces, so D-type asteroids have older surfaces than P-type asteroids. The surfaces The fact that only the background asteroid show correlations may be renewed either by disruptive collisions, that expose the between spectral slope, absolute magnitude and orbital inclina- “fresh” interior of the parent body, or by resurfacing collisions. tion, and that the correlations are similar in both the L4 and L5 We could expect that both collisional phenomena are more fre- swarms, may put important constraints to the origin and evo- quent at low inclinations than at high inclinations, and more fre- lution of Jupiter Trojans. No dynamical mechanism among the quent among the small bodies than among the large ones. Thus, Trojans is known to favor the evolution of asteroids according high inclination and large asteroids would be, on average, older 3 to their size or to their surface physical properties . Therefore, (i.e. redder) than low inclination and small ones, in agreement these correlations may have a primordial origin. Alternatively, with Figs. 7b and 8b. This scenario would also imply that fami- the correlations may be the by-product of collisional evolution. lies in L5 are, on average, older than those in L4. We speculate here about two possible scenarios. One scenario involves the idea that the P and D classes are The above scenarios have several limitations because none related to different mineralogies and, consequently, to different of them are well constrained. The mineralogy associated to material strengths. Let us assume that P-type asteroids are eas- the P- and D-types is totally unknown. In fact, some authors claim that D-type asteroids would be more fragile than P-types 3 The Yarkovsky effect, that depends on size and surface properties, (Dahlgren et al. 1997). The actual effect of space weathering on also depends on the Sun distance and it is negligible at 5 AU. spectrally featureless surfaces and the time scale to produce a F. Roig et al.: Taxonomy of Trojan asteroid families 9

Figure8. (a) Distribution of Sloan slopes of family members as a function of absolute magnitude. Dots correspond to the L4 swarm and crosses to the L5 swarm. (b) Same as (a) but for the background asteroids. Note the significant lack of large background asteroids with small slopes (P-types). significant change in the spectral slope are also unknown. Some 4.1. Families in the L4 swarm authors propose that the space weathering would tend to neu- tralize the colors of initially red surfaces (Moroz et al. 2004), so 4.1.1. The Menelaus clan 4 P-type asteroids would have older surfaces than D-types . The Several families in the L4 swarm merge together at high values rate of collisional events that can produce disruption or resur- −1 of the cutoff (dcut > 125 ms ) to form a big clan of families, facing depending on diameter and orbital inclination is poorly similar to the Flora clan in the inner asteroid Main Belt. This clan constrained. Last, but not least, it may happen that what we ob- gets its name after the main member, asteroid (1647) Menelaus. serve is the product a complex combination of all these effects. The structure of the Menelaus clan is shown in Fig. 9 (left) in the form of a dendogram (Zappalà et al. 1995). Each stalactite in the dendogram represents a different family within the clan, and it is easy to see how the families are better resolved as we 4. Distribution of spectral slopes for selected go to lower values of the cutoff. The word “clan" invokes some asteroid families kind of common origin, but the fact that several families forma clan does not necessarily imply that they all come from the same In the previous section we discussed the global distribution of ancestor. The taxonomic analysis of the clan members may help spectral slopes among Trojan asteroid families and background to better understand this problem. asteroids. In this section we analyze some particular families, As seen in Fig. 9, the more robust family of the clan is selected in view of their interest and the number of its members the Menelaus family itself, which counts more than 100 mem- contained in both the Sloan and the Spectroscopic samples. For bers at the quasi random level (∼ 104 ms−1) and represents the this analysis we did not consider all the observations available largest family in the L4 swarm. The small families of Telamon, in the samples. Instead, we used the slopes listed in Tables 1 and Melanthios and Podarkes separate from the Menelaus family at 2 (i.e. for asteroids with more than one observation we consider lower cutoffs but they soon disappear. On the other hand, the the average slope of the observations). Eurybates family appears as a very robust cluster that survives down to very small cutoffs. Indeed, the Eurybates family forms a 4 An interesting idea is that the space weathering may have two very tight cluster within the Menelaus family, as shown in Fig. 9 phases: an initial phase in which it produces a reddening of the surfaces (right). From the solely analysis of Fig. 9 it is difficult to decide up to a saturation level, and a second phase in which it produces the whether the Eurybates family is a sub-cluster of the Menelaus opposite effect, leading to more neutral color surfaces, together with family,i.e. a family formedby the secondarybreakupof a former a reduction of the overall albedo. Within this scenario, P-type aster- Menelaus family member, or the Eurybates and Menelaus fami- oids could have either too young (high albedo) or too old (low albedo) lies are two different families that simply overlap in the space of surfaces, while D-types would have mid-age surfaces. D-type asteroids proper elements. would also be, on average, more numerous because an asteroid would spend most of its life showing a reddish surface, unless a collision mod- The taxonomy of these two families has been analyzed by ifies it. This might be causing the overall abundance of D-type asteroids Dotto et al. (2006 - hereafter D06) and by Fornasier et al. (2007 among the Trojans. The knowledege of the albedo values for a large - hereafter F07), who obtained spectra of 3 members of the amount of Jupiter Trojans might help to better contrain this scenario. Menelaus family and 17 members of the Eurybatesfamily. These Unfortunately, up to now very few Trojans have known albedos authors found that the Menelaus family is mostly a D-type fam- 10 F. Roig et al.: Taxonomy of Trojan asteroid families

Figure 9. Left panel. Dendogram of the Menelaus clan, indicating the main families identified. The dashed horizontal line is the cutoff used in this study. Right panel. Distribution in the space of proper elements of the Menelaus family (gray circles) as detected −1 −1 at dcut = 110 ms , and of the Eurybates family (black circles) as detected at dcut = 70ms . The size of each circle is proportional to the asteroid size. ily, but the Eurybates family is dominated by C-type asteroids. A the other hand, the 1986 TS6 family has been observed by D065 slightly different result is obtained from the analysis of our data and F07. The available data, including the Sloan slopes, indicate samples. that this family has two well separated components, one P-type and one D-type, regardless of bodies size. Note, however, that Figures 10a,b show the spectral slopes of the Menelaus and these two components cannot be resolved in terms of proper el- Eurybates families as a function of the absolute magnitude. At ements, i.e. the P- and D-type members are mixed in the same large sizes (H < 11, that correspond to ∼ 40 km), the Menelaus cluster even for the smallest possible cutoffs. The largest aster- family shows a slight predominance of D-type asteroids –(1749) oid in the family, (5025) 1986 TS6, shows significantly different −1 Telamon, (5258) 1989 AU1 and (13362) 1998 UQ16– compared values of Sloan slope (5 × 10−5 Å ) and Spectroscopic slope to one P-type asteroid –(5244)Amphilochos–, and another aster- −1 (15 × 10−5 Å ), but the latter has been computed from a very oid –(1647) Menelaus– that appears to be a P-type but could be noisy spectrum of Bendjoya et al. (2004) so its anomalous large classified as D-type if we account for its error and recall that the − value should be considered with care. . × −5 1 limiting slope of 7 5 10 Å between the P- and D-types has The above results points to the idea that not only the − −1 a ±0.7 × 10 5 Å uncertainty (actually, D06 classified this as- Menelaus clan as a whole, but also the individual families are teroid as D-type). On the other hand, at the small sizes (H > 11) quite heterogeneous in terms of taxonomic classes, including the family is clearly dominated by P-type asteroids. from the reddest D-type asteroids to the neutral-color C-type ones. Note also that the spectral slopes do not show any par- The results for the Eurybates family (Fig. 10b) are more ticular trend with size. in line with the findings of F07, although we do not detect a predominance of C-type asteroids due to the small amount of observations in the Sloan sample. Three asteroids –(9818) 4.1.2. Other families Eurymachos, (18060) 1999 XJ166 and (24426) 2000 CR12– are P-type and one asteroid –(43212) 2000 AL113– is C-type. Figure 11 shows the distributions of spectral slopes in terms of These four asteroids got the same taxonomic classification by absolute magnitude of two families that are not members of the F07. There is also one asteroid –(65225) 2002 EK44– that ap- Menelaus clan: 1986 WD and Laertes. The 1986 WD family pears to be a P-type but due to its error can be classified as C- has been studied by D06 and F07 who found a wide range of type, in agreement with F07. The last body –2002 AE166– is a slopes, from the D- to the C-type. The Sloan slopes tend to con- C-type asteroid and was not observed by F07. firm these findings. This family is small (∼ 15-20 members) and at cutoff values slightly smaller than the quasi random level it looses half of its members. The family is no longer identified at Figures 10c,d show the spectral slopes of other members −1 of the Menelaus clan: the Epeios and 1986 TS6 families. The cutoffs smaller than 95 ms . Therefore, the diversity of taxo- Epeios family has not been previously observed by any spectroscopic survey, so the Sloan slopes shown here provide the first 5 These authors refer to it as the Makhaon family due to the large taxonomic information about this family, which appears consti- cutoff used, but it is clear from Fig. 9 that Makhaon is a different family. tuted mostly by P-type asteroids, especially at the large sizes. On This has been correctly addressed by F07. F. Roig et al.: Taxonomy of Trojan asteroid families 11

Figure 10. Distribution of Sloan slopes against absolute magnitude for four families of the Menelaus clan. Full circles correspond to Sloan slopes. Triangles correspond to Spectroscopic slopes. The vertical dot- ted lines deﬁne the slope transition, within −1 ±0.7 × 10−5 Å , between the diﬀerent taxonomic classes indicate above the plots.

Figure 11. Same as Fig. 10 but for two families in the L4 swarm. nomic classes may be related to a significant contamination of Unfortunately, this family is located at a very small inclination interlopers. (sin I ∼ 0.08), and it cannot be distinguished from the background also dominated by P-type asteroids. The identification of The case of the Laertes family is somehow different. This the Laertes family as a real P-type family relies more in the ac- family is also small (∼ 15-20 members) but it survives down curacy of the HCM than in the distribution of its spectral slopes. to cutoff 80 ms−1 loosing only 40% of its members. All the members are small bodies (H > 11), including (11252) Laertes. Other interesting cases are the high inclination families in The few members contained in the Sloan sample (the family has the L4 swarm. There are only three of these families, with never been observed spectroscopically) show a quite homoge- sin I > 0.25: Hektor, Teucer and Sinon. The distribution of the neous distribution of spectral slopes, all belonging to the P-type. respective spectral slopes are shown in Fig. 12. Hektor and Sinon 12 F. Roig et al.: Taxonomy of Trojan asteroid families

Figure 12. Same as Fig. 10 but for three high-inclination families in the L4 swarm. families have not been observed by previous spectroscopic sur- The Agelaos and 1999 RV165 families are somehow differ- veys, and the Sloan slopes provide the first clues about their tax- ent from the other families of the Anchises clan. None of them onomic composition. The slopes in Fig. 12 point to a predomi- survive down to small cutoffs and they appear less homogeneous nance of D-type asteroids, making these families indistinguish- in terms of taxonomy. Their distribution in proper elements is −1 able from the background. shown in Fig. 13. At dcut > 135 ms , the Agelaos family in- corporates asteroid (1173) Anchises and becomes the Anchises family. At the same cutoff, the 1999 RV165 family becomes 4.2. Families in the L5 swarm the Antenor family after incorporating asteroid (2207) Antenor. −1 4.2.1. The Anchises clan These two families merge together at dcut > 145 ms . The 1999 RV165 family has only one member in the Sloan The L5 swarm has its own clan of families, although it is some- sample classified as P-type, so we cannot say too much about how different from the Menelaus clan in L4. The Anchises clan, it. The Agelaos family has two members observed in the Sloan named after asteroid (1173) Anchises, is quite tight and con- sample, one P- and one D-type, but this family has also been −1 stituted by only five families identified at dcut = 120 ms : observed by F07 who identified it as the Anchises family. Panthoos, Polydoros, Sergestus, Agelaos and 1999 RV165. All Analyzing the slopes provided by these authors together with the −1 these families merge in the clan at dcut = 150 ms . The taxo- Sloan slopes, we conclude that 3 members are P-type –(1173), nomic analysis of this clan indicates that it is populated by both (23549),(24452)–and 3 membersare D-type –(47967),(52511), P- and D-type asteroids covering a wide range of spectral slopes. 2001 SB173–. It is worth noting that the Sloan slope of (24452) But at variance with the Menelaus clan, the individual families is compatible with the slope published by F07. of the Anchises clan appear to be more homogeneous in terms of taxonomy. The Panthoos family appear to be a P-type family (Fig. 14a) 4.2.2. Other families and it is well distinguishable from the background, dominated by D-type asteroids. This is a quite robust family that remains Figure 15 shows the distributions of spectral slopes in terms of isolated over a wide range of cutoff values,from90 to 140ms−1. absolute magnitude of four L5 families: Aneas, Phereclos, 1988 RG10 and Asios. Its distribution in the space of proper elements for dcut = 130 m s−1 is shown in Fig. 13. It is worth noting that F07 studied this The Aneas family has been studied by (Fornasier et al. 2004 family and found that it is a D-type family. However, due to an - hereafter F04) and by F07, who treated it as the Sarpedon fam- incorrect choice of the cutoff level, all the 8 asteroids that they ily. This family is actually formed from the merging of two fami- used to perform their classification are not actual members of the lies: Sarpedon and 1988 RN10. The Sarpedon family is resolved −1 Panthoos family but of the Sergestus family. These two families at dcut < 130 ms , and the 1988 RN10 family is resolved at −1 < −1 = merge together at dcut > 140 ms . dcut 140 ms . Both families are identified down to dcut 90 −1 The Polydoros family is another example of a quite robust m s . In Fig. 15a we show the spectral slopes of the whole family that is detected down to cutoff 90 ms−1. This family Aneas family (i.e. Aneas + Sarpedon + 1988 RN10). The val- merges with the Sergestus family for d ≥ 130 ms−1 to form ues indicate that this is a quite homogeneous D-type family, in cut 6 the single Polydoros family shown in Fig. 13. The distribution agreement with F07 . The only two P-type members shown in −1 of spectral slopes of the Polydoros (+Sergestus) family, shown Fig. 15a abandon the family at dcut < 115 ms , so they are in Fig. 14b, indicates that this is a quite homogeneous D-type probably interlopers. So far, this family is one of the most ho- family. Interestingly, the spectral slope of (4829) Sergestus mea- mogeneous families in terms of taxonomy already detected, to- sured by F07 indicates that this asteroid is likely to be a P-type, gether with the Eurybates family in L4. so it may be an interloper. Recall, however, that the Polydoros and Sergestus families are taxonomically indistinguishable from 6 Two members of the Sarpedon family observed by F07 –(48252) the background and this makes difficult the discussion about in- and (84709)–, that are not included in our Spectroscopic sample, are terlopers. also classified as D-type. F. Roig et al.: Taxonomy of Trojan asteroid families 13

The 1988RG10 and the Asios families, shown in Figs. 15b,c, have not been observed before by spectroscopic surveys. The distribution of Sloan slopes indicates that the 1988 RG10 family would be a quite homogeneous D-type family. For the Asios family the results are inconclusive. The last family to be discussed here is the Phereclosfamilyshown in Fig. 15d. Ithas been analyzed by F04 and F07 and their results point to a quite homogeneous D-type family. The only observation contained in the Sloan sample correspond to asteroid (18940), already observed by F04, and its Sloan slope is compatible with its Spectroscopic slope.

4.3. Discussion While the individual families in L5 appear to be taxonomically homogeneous, the individual families in L4 show a wide range of spectral slopes and a mixture of the C-, P- and D-types. There are, at least, two possibilities to explain the presence of diﬀerent taxonomic classes within a single family:

– The family contains several interlopers, i.e. background asteroids that overlap with the family in proper elements. The amount of interlopers is significant because the presently observed family members are so sparse that we need to use ff Figure 13. Distribution in the space of proper elements of the large cuto values to detect the family. Therefore, only the −1 families detected at small cutoffs, like the Eurybates family, Anchises clan as detected at dcut = 130ms . It is constituted by can be considered, for the time being, as the less contami- five families: Panthoos, Polydoros, Sergestus, Agelaos and 1999 RV165. (1173) Anchises is incorporated to the Agelaos family nated by interlopers. Actually, the analysis of the Eurybates −1 family made by F07 indicates that it would be the most ho- at dcut > 135 ms . The size of each circle is proportional to the mogeneous family of the Menelaus clan in terms of taxon- asteroid size. omy. Note that the contamination by background interlopers would not introduce significant inhomogeneities in the tax- Karin family inside the Koronis family (Nesvorný et al. 2002), onomy of L5 families, even if these families were not well the Baptistina family inside the Flora clan (Bottke et al. 2007), defined, because most of these families are taxonomically and the Veritas family (Nesvorný et al. 2003). Within this hy- indistinguishable from the background (in other words, the pothesis, the color distribution of the Eurybates/Menelaus fam- L5 families are dominated by D-type asteroids and the L5 ilies may be explained if we assume that the space weathering background too). causes a reddening of the surfaces with age. Then, we may spec- – We may invoke some aging process on the surfaces of ulate that the membersof the Eurybatesfamily are the fresh frag- the asteroids, like the space weathering, that originates the ments from the interior of a former member of the Menelaus wide range of slopes observed within a single family. In family. The remaining members of the Menelaus family would this case we must presume that the surfaces of the mem- have much older surfaces thus being much redder. An analysis of bers of the family do not have the same age. In fact, many the family ages based on purely dynamical/collisional arguments small members in the family may have been formed by sec- is mandatory to better address this issue. ondary collisions, thus showing younger surfaces. Also, the small members, having a larger collision probability, may be more frequently affected by collisional resurfacing pro- 5. Conclusions cesses. Unfortunately, the space weathering is not well con- We have analyzed the distribution of spectral slopes and colors strained in the case of the Trojan asteroids, and we cannot of Trojan asteroids using a sample of data fromthe SDSS-MOC3 say whether it produces a reddening of the spectra with age, together with a collection of spectra obtained from several sur- or viceversa (Moroz et al. 2004), or both. The lack of a clear veys. Our analysis has been focused on the Trojan asteroid fami- correlation between spectral slope and size among the Trojan lies. We have studied the global properties of the sample as well families, together with the still small amount of asteroids as the properties of some individual families. Our results can be with known spectral slope and the poorly constrained col- summarized as follows: lisional evolution of Trojan families, prevents to perform a reliable analysis of any aging process. Moreover, the appar- – The analysis of photometric data from the SDSS-MOC3 pro- ent taxonomical homogeneity of the L5 families seems to duces reliable results that are comparable with those ob- play against the surface aging scenario. tained from the analysis of spectroscopic data. – The distribution of spectral slopes among the Trojan aster- Nevertheless, the case of the Eurybates/Menelaus families con- oids shows a clear bimodality. About 2/3 of the Trojan popu- stitutes an interesting paradigm of the possible effect of space lation is constituted by reddish objects that may be classified weathering on the surfaces of Trojan asteroids. The compact- as D-type asteroids. The remaining bodies show less reddish ness of the Eurybates family, compared to the Menelaus family, colors compatible with the P-type, and only a small fraction may be interpreted as a rough measure of youthfulness. There (less than 10%) is constituted of bodies with neutral colors are many examples in the Main Belt that support this idea: the compatible with the C-type. 14 F. Roig et al.: Taxonomy of Trojan asteroid families

Figure 14. Distribution of Sloan slopes against absolute magnitude for three families of the Anchises clan: (a) Panthoos, (b) Polydoros and Sergestus. Full circles correspond to Sloan slopes. Triangles correspond to Spectroscopic slopes. The vertical dot- ted lines deﬁne the slope transition, within −1 ±0.7 × 10−5 Å , between the diﬀerent taxonomic classes indicate above the plots.

Figure 15. Same as Fig. 14 but for four different families in the L5 swarm.

– The members of asteroid families show a bimodal distribu- These differences can be attributed to the presence of aster- tion with a very slight predominance of D-type asteroids. oid families. The background, on the contrary, is significantly dominated – The background asteroids show the same spectral slope dis- by D-type asteroids. tributions in both swarms, with a significant fraction (∼ – The L4 and L5 swarms show significantly different distri- 80%) of D-type asteroids. The families in L4 are dominated butions of spectral slopes. The distribution in L4 is bimodal by P- and C-type asteroids, while the families in L5 are dom- with a slight predominanceof D-type asteroids. The distribu- inated by D-type asteroids. tion in L5 is unimodal with a clear peak of D-type asteroids. – The background asteroids show correlations between spectral slope and orbital inclination and between spectral slope F. Roig et al.: Taxonomy of Trojan asteroid families 15

and size. D-type asteroids dominate among the high inclination bodies and also among the large bodies. Low inclination bodies are slightly dominated by P-type asteroids. These correlations are most probably the result of the background collisional evolution, either by fragmentation or by collisional resurfacing. Similar correlations are not observed among the family members. – Individual families in the L5 swarm are taxonomically homogeneous, but in the L4 swarm show a mixture of taxonomic types. This may be attributed to the presence of interlopers or to a surface aging eﬀect. – Any taxonomic analysis of individual families must be ac- companied by a detailed analysis of the families structure as a function of the cutoﬀ level of detection. An estimation of the family ages is also mandatory to complement these analysis.

Acknowledgements. We wish to thank Sonia Fornasier, Elisabetta Dotto, Phillipe Bendjoya and Alberto Cellino who kindly allowed us to use their spectroscopic data. Fruitful discussions with Jorge Carvano are also highly appreci- ated. This work has been supported by CNPq (Brazil) and SECYT (Argentina).

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F. 1985, Icarus, 61, 355 16 F. Roig et al.: Taxonomy of Trojan asteroid families level of ff band. For asteroids with r Family milies were defined at a cuto obs N ] 1 5203 277 4 94 Asios 4 11 4 305 1988RN10 384 1988RL13 2 Polydoros 9209 1 98 2 09 1 84 3 83 1 68 168 1 95 Polydoros 1 56 4 1 55 1 3788 1 172 Sarpedon 1988RN10 1 94 297 Phereclos 1 9106 198 1 13 Agelaos 298 2 01 Sarpedon 180 1 11 2000QE169 2 37 1 89 196 2 99 1988RG10 110 7 33 Panthoos 1 91 1 32 1 4 1988RN10 98 400 1988RN10 2 − ...... 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 Å 5 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − 10 19 81 38 26 39 11 28 97 71 03 76 93 27 66 18 32 25 31 27 16 19 72 56 50 34 31 16 02 51 84 58 18 32 67 08 83 11 24 52 06 19 ...... × [ S reflectance fluxes, normalized to 1 at the z , i , r , g No. Name 18701872 Glaukos2674 Helenos3451 Pandarus3708 Mentor4792 1974FV1 8 4827 Lykaon 5 5257 Dares 9 5638 1988RS10 3 6997 Deikoon 9 Laomedon 10 12 8 10 7 L5 swarm 1155411869 Asios16560 1989TS216667 1991VZ517414 1993XM1 1988RN10 9 5 17420 2 9 1988RL13 10 18137 2000OU30 7 9 11273 1988RN11 5 1741617419 1988RR10 1988RH1318046 1999RN116 12 18940 3 2000QV49 10 1984424018 2000ST31724452 1999RU134 6 24454 2000QU167 12 25347 2000QF19829314 1999RQ116 5 30499 1994CR18 5 30505 2000QE169 3 30705 2000RW82 8 30708 Idaios 4 10 31814 Echepolos32339 11 1999RW7032482 2000QA8832499 2000ST354 8 32811 11 2000YS11 9 34298 Apisaon 9 38257 2000QH159 5 47969 1999RC13 9 2000TG64 8 4 4 9 19020 2000SC6 9 tions. Family membership is indicated in the last column. Fa was computed by a linear fit to the S Family obs N ctral slope ] 1 6674 1 56 1 92 2 57 1 1 Hektor 87 1986WD 1 38 1 Kalchas 04 1 7914 1 1 73 1986WD 1 Eurybates 97 104 Menelaus 2 72 1 7201 2 3 96 2 1998XZ77 75 2 Menelaus 9382 1 03 3 66 380 1 68 Teucer 188 1 78 Teucer 2 45 1 87 1 1 1986WD 1986TS6 66 16671 1998XZ77 1 1 11 Menelaus 83 1 1 9901 1 173 Eurybates 111 Epeios 11445 Menelaus 2 98 1 1 Epeios 22 1 Demophon − ...... 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 Å 5 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − 10 21 39 90 68 54 38 23 04 77 33 07 91 82 06 76 79 88 69 53 82 32 83 26 49 31 39 70 18 98 94 57 92 96 98 83 50 21 15 27 04 05 ...... × [ S for the L5 swarm. 1 − 1), the table gives the average weighted slope of the observa > obs No. Name N 50285259 Halaesus5264 Epeigeus5284 Telephus6545 Orsilocus 1986TR6 9 11 10 9590 9 1991DK1 10 7 5027 Androgeos 11 72148241 Antielus Agrius9818 Eurymachos 4 3 5 1749 Telamon 8 22602759 Neoptolemus2797 Idomeneus3564 Teucer 10 3793 Talthybius4489 Leonteus 9 4946 1988AK5012 Askalaphus 8 9 5023 Eurymedon5025 Agapenor 6 10 1986TS6 9 4 4 5 10247 Amphiaraos 6 11396 1998XZ7713362 1998UQ1613475 9 14235 Orestes15536 1999XA187 9 15663 2000AG19116152 Periphas18060 9 1999YN12 3 18062 9 1999XJ15619725 1999XY18720424 1999WT4 9 4 20995 1998VF30 4 10 21370 1985VY21599 1997TB28 5 22049 1998WA15 10 22052 1999XW257 10 22404 2000AQ14 8 1995ME4 8 5 6 4 L4 swarm 13331 1998SU5213387 Irus 4 7 for the L4 swarm and 120 m s Known Trojan asteroids included in our Sloan sample. The spe 1 − Table 1. 110 m s two or more observations ( F. Roig et al.: Taxonomy of Trojan asteroid families 17 Family obs N ] 1 8774 1 11 1 07 1 22 1 41 1 13 2 10 1 16 1 302 Agelaos 48 Panthoos 2 122 1999RV165 19327 2000SA191 4 32 1 23 1 65 1 29 229 1 16 Asios 1 49 2 17 1 54 1 1 4348 1 44 2 16 156 1 45 Deiphobus 4 44 1 07 193 117 2000RO85 2 10 Sergestus 2 94 1 88 156 193 1988RL13 249 1988RG10 1 1988RG10 1 1988RG10 2000SA191 16 129 1988RG10 05 1 117 Asios 1 Panthoos − ...... 0 0 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 2 1 1 1 1 1 1 Å 5 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − 10 41 89 85 33 64 38 40 86 78 26 06 64 53 87 35 31 84 58 59 70 87 45 60 80 37 37 01 06 08 25 81 12 92 89 02 07 86 16 98 14 19 31 85 ...... × [ S 1988SJ22000QZ752000RE292000SG187 12 2000SK47 10 2000SM250 11 2000SP92 5 2000SR79 11 9 2000SZ1352000TU44 10 2001QM257 8 2001RN122 9 2001SA220 8 8 2001SC101 10 2001SC137 13 2001SD30 9 9 9 No. Name L5 swarm 4824951345 2001SY34551346 2000QH13751364 2000QX15851935 2000SU333 9 51994 2001QK134 9 52273 2001TJ58 8 52511 1988RQ10 6 10 52767 1996GH12 1998MW4155457 9 11 55460 2001TH133 11 2001TW148 7 57013 8 6 2000TD395800858084 2002TW24062201 Hiketaon 9 63955 2000SW5464270 7 2001SP6565590 2001TA19773795 Archeptolemos 9 8 76820 1995FH8 11 76824 2000RW105 6 9 76837 2000SA8977891 2000SL316 8 2001SM232 8 6 10 6 54596 2000QD2255567856976 Lampos 2 2000SS16157626 2001TE165 10 5 3 Family obs N ] 1 6214 1 2 4388 2 2 15 1986WD 2 20 2 29 1 31 1 34 119 Hektor 2 18 1 17 129 Makhaon 1 31 1 7981 1 1 Epeios 32 Epeios 53 108 1 99 Menelaus 198 102 Kalchas 146 Epeios 1 16 1986WD 1 120 Eurybates 25 1998XZ77 1 106 1999XM78 299 Epeios 1 48 1 39 1 0500 1 1 Sinon 1986TS6 21 1 7231 1 198 Laertes 26 1986WD 1 189 Kalchas 19787 Eurybates 1 198 1986WD 1 37 115 1986TS6 1 − ...... 0 1 1 0 2 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 Å 5 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − 10 81 61 80 70 03 65 10 25 64 00 49 56 53 42 75 89 58 82 46 21 52 64 71 58 54 29 29 86 89 87 32 85 89 87 13 28 19 12 74 24 70 05 04 ...... × [ S No. Name 2312323144 2000AU5723285 2000AY18223382 2000YH11923706 Epistrophos 7 23939 5 1997SY32 10 23963 1998TV3324225 1998WY8 8 24233 1999XV80 6 1999XD94 5 24426 2 24485 2000CR12 4 2000YL102 4 24508 5 2001BL26 4 2488231835 1996RK3032498 2000BK16 5 33822 2000XX3735272 2000AA231 4 36259 10 1996RH1036279 10 1999XM7438052 9 2000BQ538606 11 1998XA738614 1999YC13 9 38617 2000AA113 10 2000AY161 2 11 5 3 3861938621 2000AW18339264 2000AG20139287 2000YQ139 8 39293 2001CD1441268 5 2001DQ10 11 42168 1999XO6442179 2001CT13 3 42403 2001CP25 9 43212 10 Andraimon43706 2000AL113 3 51378 Iphiklos 4 53477 2001AT33 6 55568 2000AA54 1 55571 2002CU15 2002CP82 5 9 6 12 4 L4 swarm 23075 1999XV83 11 24403 2000AX19324498 11 24505 2001AC25 2001BZ24539 2001DP5 3 11 8 continued. Table 1. 18 F. Roig et al.: Taxonomy of Trojan asteroid families Family obs N ] 1 6812 2 56 1 66 167 1 24 2000SY317 2 82 2 1 Bitias 1988RG10 − ...... 1 1 1 1 1 1 1 Å 5 ± ± ± ± ± ± ± − 10 98 70 83 07 74 83 61 ...... × [ S 2001TK1312001TO1082001VB522001WX20 8 2001XV105 9 2002VH107 10 2003WQ25 5 8 8 10 No. Name L5 swarm Family obs N ] 1 80 1 20 1 1986TS6 31 1 55 3 06 2 34 1 Menelaus 35 1 39 255 Epeios 42 1 74 1 1 1875 1 1 31 Makhaon 3 23 1 14 1 55 138 Sinon 1 3514 447 1 1998XZ77 1 1998XZ77 Laertes 3228 1 198 Menelaus 13274 1999XM78 1 2 Euryalos Demophon 31 1 Laertes 5232 1 31 1 29 1 1 70 Menelaus 07 2 1 26 Hektor 01 143 1 Sinon 13171 Eurybates 2 25 133 1 57 Sinon 1 1 07 Menelaus 1 37 2 1999XM78 − ...... 0 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 Å 5 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − 10 42 28 55 97 88 26 27 92 43 27 57 45 93 72 72 20 98 41 30 39 20 85 41 24 74 44 80 71 15 96 99 47 45 94 38 56 77 14 78 17 81 84 47 ...... × [ S 1995QC61996TA581997WA121999XJ55 4 2000AG90 10 2000AJ114 8 2000AL8 11 11 2000BV1 10 2000YB1312000YC112 11 2000YS109 10 4 2001AG51 7 2001BD49 4 5 11 No. Name 5847358479 1996RN760383 1996RJ2963202 2000AR18463210 2000YR131 4 63257 2001AH13 10 6 63259 2001BJ79 4 2001BS81 11 4 5 L4 swarm 57920 2002EL153 8 6326563272 2001CP1263286 2001CC4963291 2001DZ6863292 2001DU87 10 63294 2001DQ89 7 65000 2001DQ90 7 65134 2002AV63 5 65194 2002CH96 3 65209 11 2002CV26465224 2002DB17 8 65225 2002EJ44 2 10 65583 2002EK4479444 Theoklymenos 9 80302 1997UM26 5 83975 1999XC64 7 2 83977 2002AD18483983 2002CE89 5 88225 2002GE39 8 89829 5 2001BN2789871 2002BQ29 5 89924 2002CU143 8 13 2002ED51 5 10 9 continued. Table 1. F. Roig et al.: Taxonomy of Trojan asteroid families 19 Family obs N ] 1 − Å 5 − 10 × [ S No. Name L5 swarm Family obs N ] 1 73 2 8652 2 1 Epeios 6761 2 277 Hektor 1 66 2 4227 1 1 Menelaus 41 1 11 1 Euryalos 31 1 3669 151 117 Eurybates 210 Epeios 191 1998US24 1 53 Laertes 1 2 Laertes 25 Menelaus 135 Euryalos 1 5469 1 64 2 70 1 1 Epeios 6829 159 154 Demophon 1 Menelaus 1 45 Hektor 76 1 15 1 1 Menelaus − ...... 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 Å 5 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − 10 01 87 96 77 43 10 29 12 05 87 42 42 95 64 49 26 79 37 26 50 16 99 52 84 32 75 01 83 95 60 69 35 ...... × [ S 2001BS162001DL102001DO932001FV58 10 2002AE166 9 12 2002CH1092002CL109 12 2002CL130 0 6 2002CN1302002CQ186 6 2002CZ256 6 9 2002DD1 6 2002DW152002DX12 2 2002EK51 10 2002EP106 9 2002ES83 8 2002ET136 12 2002EU14 3 2002EX5 10 2002FL37 8 2002FM7 6 2002GG33 2 2002GO150 5 2003FJ64 12 13 2003FR72 1 2003GU352003GX7 7 2004HS1 5 2004JO43 7 2004KJ4 11 5214T-2 7 4 7 7 No. Name L4 swarm continued. Table 1. 20 F. Roig et al.: Taxonomy of Trojan asteroid families erent ff Family e rebinned spectra normalized to 1 at 6240 Å. obs N for the L5 swarm. 1 ] − 1 22 2 Sarpedon 5735 1 2 Cloanthus 62 1 Phereclos 6056 2 1 Aneas 7057 2 1 53 1 5959 1 1 Polydoros 59 1 Sarpedon 57 1 Sarpedon 54 1 Phereclos 54 157 Sarpedon 1 Phereclos 61 157 Sergestus 1 72 1 53 1 52 2 1994CO 5555 157 160 Anchises 159 Aneas 1 1998MA11 156 Sarpedon 59 Polydoros 256 1 Sarpedon 159 Phereclos Sergestus 165 Sarpedon 15960 Sergestus 1 1 − ...... 3 0 2 0 1 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 Å 5 erent observations of the same asteroid come from di ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − ff 10 31 27 46 34 61 98 19 02 78 45 94 40 12 67 08 36 68 34 59 60 46 96 83 50 05 26 56 89 02 50 29 58 60 ...... × 1 [ − S tions. We recall that di for the L4 swarm and 120 m s 1 − No. Name 11721871 Aneas2223 Astyanax Sarpedon3317 5 9 11 3451 Paris Mentor4348 Poulydamas 7 1 4 55115648 Cloanthus 1990VU1 13 9430 10 Erichthonios 10 23572895 Phereclos Memnon 3708 8 1974FV147154792 1989TS15130 Lykaon 8 Ilioneus 14 6998 13 7352 Tithonus 9 1994CO 9 6 L5 swarm 1108915502 1994CS815977 1999NV2717416 1998MA1118137 1988RR10 3 9 18268 2000OU30 7 18493 Dardanos 9 18940 1996HV9 7 23694 2000QV49 12 24467 1997KZ325347 2000SS165 4 5 30698 1999RQ11632430 Hippokoon 10 7 32615 2000RQ83 8 34785 2001QU277 7 48249 2001RG87 6 2001SY345 8 2 9 level of 110 m s ff was computed by a linear fit, in the interval 5000–9200 Å, of th Family S obs N ] 1 61 2 54 1 63 1 59 1 53 1 Menelaus 65 1 Kalchas 14 2 52 154 Makhaon 1 Teucer 61 1 Euneus 57 1 1986TS6 56 2 1986TS6 64 1 76 2 1986TS6 91 2 1986WD 62 1 Menelaus 62 2 54 2 56 1 64 1 46 2 53 1 Menelaus 71 1 1986TS6 05 2 55 2 54 1 3955 2 54 1 1 53 1 5253 1 159 Menelaus 1 53 166 1986WD 1 60 1 54 155 1986TS6 1 5654 1 1 1986TS6 1986TS6 56 1 1986WD − ...... spectral slope 1 0 0 0 0 0 4 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 1 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Å 5 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − 10 77 01 07 34 19 92 42 08 19 90 54 36 68 62 53 12 33 67 61 09 75 58 75 94 28 55 89 80 30 76 99 48 53 15 66 78 05 59 70 74 10 ...... × 6 [ Families were defined at a cuto − S 1), the table gives the average weighted slope of the observa > obs N No. Name 911 Agamemnon 9 588 Achilles 2 1647 Menelaus 6 40684138 Menestheus Kalchas 10 4834 Thoas 6 11 1143 Odysseus2920 11 3063 Automedon Makhaon3793 10 Leonteus 8 7 7152 Euneus 5 40354060 1986WD Deipylos 12 1 5244 Amphilochos 2 5283 Pyrrhus 1749 Telamon3709 10 Polypoites4063 11 Euforbo44894833 1988AK Meges 8 8 10 6090 1989DJ 12 48354836 1989BQ4902 Medon5025 Thessandrus5126 1986TS6 Achaemenides 5 8 5254 8 5258 Ulysses 0 15 5264 1989AU1 Telephus5285 Krethon 9 7 6545 11 1986TR67641 1986TT6 6 9 4 1868 Thersites 8 L4 swarm 1291712921 1998TG1613463 1998WZ515094 Antiphos15535 11 1999WB220738 2000AT177 4 24390 1999XG191 2000AD177 4 10 2 9 9 11351 1997TS25 9 Trojan asteroids included in our Spectroscopic sample. The Table 2. For asteroids with more than one observation ( surveys. Family membership is indicated in the last column.