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0 Lunar and Planetary Institute Provided by the NASA Astrophysics Data System STATISTICAL CLASSIFICATION of ASTEROIDS

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0 Lunar and Planetary Institute Provided by the NASA Astrophysics Data System STATISTICAL CLASSIFICATION of ASTEROIDS STATISTICAL CLASSIFICATION OF ASTEROIDS FROM SURFACE PROPERTIES R. J. Pike, U. S. Geological Survey, Menlo Park, California 94025 The asteroids pose a unique puzzle within the larger problem of Solar System genesis and evolution (see ref. 1 for a recent summary). Until mater- ial from the asteroids is examined first-hand their time and mode of origin can only be interpreted from orbital configurations, chemical composition suggested by remotely- sensed information, and meteoritic analogs (2,3). Among the many new data on asteroids are measurements of surface properties (includ- ing luminosity, size, and color) obtained from narrow-band spectrophotometry in the visible and near-infrared wavelengths, infrared radiometry, and polarimetry as a function of solar phase angle (4,5,6,7). In an important interpretive synthesis (8), values of up to 13 descriptive variables were compiled for 110 asteroids and classification of these bodies by inferred mineralogic composition attempted. Most of the 110 asteroids were classified into either Type C ("carbona- ceousrT)or Type S ("siliceous") bodies (8), largely on the basis of distinc- tively bimodal distributions of five descriptive variables. However, the C and S categories overlap for each variable, and no simple criterion gives a clear-cut dichotomous grouping. Graphical analysis of this type is always helpful in taxonomy, but the resulting groups inherently risk misclassif'ying some asteroids in the sample (or oversimplifying the breakdown) because only two variable can be examined conveniently at a time. Graphical methods also will become increasingly unwieldy as more asteroids are observed and more variables are measured. Therefore, multivariate techniques, which are not re- stricted by the dimensional limitations of graphs, are used here to compare a small sample of asteroids mutually with respect to most of the measurements of surface characteristics available to (.8). In this example, asteroids are grouped together only if they share in several, but not necessarily all, of the discriminating attributes. The statistical approach (9) demonstrated here was applied previously to crater landforms (10). Eight of the asteroid surface properties tabulated by (8) are retained for this exercise (diameter and distance from the Sun are omitted): B-V, a standard UBV color index from photometry; Pmin, depth of the polarization- phase curve at small phase angles; -log pv, geometric albedo (both radiometric and polarimetric values) ; R/B, spectrophotometric reflectivity at 0.7wrn / that at 0.$m; BEND, curvature between reflectance in red and drop in albedo to- wards shorter wavelengths; IR, reflectance at 1.05~- reflectance at y0.73 m; and DEPTH, depth of absorption band near 0.95pm. These measurements are available for only 22 of the ll0 asteroids originally studied. Although small, the resulting subsample is sufficiently large and diverse to illustrate the multivariate approach to classification of asteroids. Analysis of the 22x8 matrix by principal components (11,10) shows that 94% of the information in the matrix can be expressed by only four components a able 1). More than half the total variance is accounted for by just the first component (P-l),which includes mainly (as indicated by high scores: correlations of each raw variable with each component) B-V, Pmin, -log pv (pol. ), R/B, and to a lesser extent -log pv (rad. ) and DEPTH. Because these six variables also are those by which C and S classes were defined graph; ically (8), the dominant descriptive aspect present in the data is the 0 Lunar and Planetary Institute Provided by the NASA Astrophysics Data System STATISTICAL CLASSIFICATION OF ASTEROIDS R. J. Pike clear-cut separation of these two major types of asteroids. Thus P-1 will strongly prefigure any groups of asteroids based on principal components (Figs. 1,2). P-2 (18% of variance) comprises principally BEND, but also the radiometric albedo (-log pv); P-3 (12%) consists largely of IR; P-4 (8%) has a moderately high score on DEPTH. The last three components, which are much less important than P-1, play a commensurately subordinate role in generating Figs. 1 and 2. Results of the principal-components analysis may be displayed simply by plotting a second set of scores, correlations of each asteroid with each component, either by one component at a time or by two at once. In one such graph (Fig. l),all five asteroids' classified as Type C (8) group far -- if loosely -- from the 16 S-Type bodies and 4 Vesta. The "unclassified" 4 Vesta has more affinity for S-asteroids, but lies apart from them, mainly on the basis of P-2 scores. Although both 8 Flora and 63 Ausonia group apart some- what from the main cluster of S-bodies, only 63 Ausonia is classified (8) as a "peculiar" type S. Also 887 Alinda falls away from this cluster; it too has not been classified as a specie1 subtype. The Type-C body 14 Lutetia is classified (8) as a "peculiarf1 subtype, but on Fig. 1 it seems to be less of an outlier than 13 Fortuna, which has no special designation. All-in-all, Fig1 suggests that themis basis for further subdividing and C and S categories of asteroids. The outcome of a principal-components analysis also may be displayed by a formal cluster analysis (9,10,12 ), a hierarchical grouping technique that uses all the scores (~ig.2), not just those for the first one or two components (F. 1). To assure that the less significant principal components do not disproportionately influence the clustering procedure, scores of asteroids on components are weighted (multiplied by) the percentage of total variance accounted for by each component a able 1). The result of such a procedure (~ig.2) for the sample asteroid data shows again the highly dichotomous clustering that supports the basic classification (8). Moreover, the atypical 63 Ausonia (s-type) and 21 Lutetia (c-type) bodies join their respective clusters at higher values of the distance f'unction, an indication that the grouping procedure correctly recognizes their peculiarities. This also is true for 8 Flora (s), 887 Alinda (s), and 19 Portuna (c), the three less typical asteroids indentified in Fig. 1. Although the unclassified 4 Vesta groups with the 16 type S asteroids, it joined the cluster last -- clear indication that it differs significantly from all bodies in that group. Fig. 2 also suggests that the two main asteroid types could safely be sub- divided f'urther. This demonstration indicates only one of several ways that multivariate methods could prove helpful in studying the rapidly-growing body of data on the asteroids. The statistical outcome described only briefly here for a small sample of asteroids could be interpreted further, in terms of probable chemical and mineralogic composition from analogies with meteoritic materials and laboratory mixtures (3,8), as well as in terms of orhital parameters and size of the bodies. Other asteroids and descriptive variables that have be.- come available since the canpilation used here (8) could be added to the analysis to obtain more detailed and sophisticated classifications (3). 0 Lunar and Planetary Institute Provided by the NASA Astrophysics Data System STATISTICAL CLASSIFICATION OF ASTEROIDS R. J. Pike References : (1) DELSM, A.H. (ed. ) , 1977, Interrelated Origin of Comets Asteroids and Meteorites; (2) MATSON, D.L., et al., 1976, Proc. Lunar Sci. Conf. 7th, p. 3603-3627; (3) GAl?FEY, M. J. and McCORD, T.B., 19'77, Proc. Lunar Sci. Conf. 8th, p. ll3-,143; (4) VEVERKA, J., 1973, Icarus, 19, p. .U4-117; (5) MORRISON, D., 1974, Astrophys. J., 194, p. 203--6) ZELLNER, B., fi al Astron. J., p. ll00-1U0; McCORD, T.B. and CHAPMAN, C.R., -* 9 1974, 79, (7) 1975, Astrophys. J., 195 & 197, p. 553-562 & 781-790; (8) CHAPMAN, C.R., --*,et al -Icarus, 25, p. 104-130; (9) SNEATH, P.H.A. and SOKAL, R.R., 1973, Numerical Taxonomy; (10) PIKE, R. J., 1974, E.P.S.L., 22, p. 245-255; (u) -HAFMAN, H.H., 1967, Modern Factor ~nal~sis;(12)~~~~~,J.M., 1970, Kans. ,Geol. Surv. Contr. 46. -- Tabh I. PRl?fCIP&Cm VariaUe P-1 P-2 p-3 PJ, !J B-V 4.883 0.378 -0.032 0.143 Pmin 0.951 0.101 0.029 -0.122 2 -log pr (pol.) 0.761 0.536 0.097 -0.125 -10s (nd.1 0.98 0.232 0.~9-0.009 R/B -0.902 0.276 -0.045 0.205 BEND -0.270 0.737 -0.517 -0.281 8 Dt -0.305 0.469 O.Q2 -0.057 DEPTH 0.663 0.3ll -0.106 0.658 0 $ variance 56.77 17.89 ll.88 7.59 Fig. 1. Grouping of 22 asteroids byg ~.ightsurface properties on P-1 and P-2 ($55 total variance). IJarnes and 0 0.6 t,y-pes in Pig, 2. Type S (left) and SCORE ('.EIQ1TElJ) ON :dT PRINCIPAL COEIWNENT C (riEht) are clearly separated, and some subty-pes mipht be dis- / tinguished on ttis basis, COEFFICIEHF OF DISTANCE FUNCl'ION 0 0.05 0.10 0.15 I I I I 1 I 9 mis 433 Ems Figure 2, Grouping of 22 este-ofis ?ycluster 40 Harmonia 532 Herculina analysis on four i~eirtlt,edpriacipal 9 Jum co~ponents,Tj~e S and C bodies very 6 He& 17 Thetis well separated. .\ty-pica1 asteroids 7 Iris 15 Eunomis e.g, 63 ~us0ni.a)join clusters I&e, 39 Laetitia at low affinity (hi&[ distance- 11 Parthenope 5 Astraea function coefficient ), sueznst ing 69 Julia d valid subtypes, 887 XlMa Q Flora S 61 4usonia S pec. 4 'Iesta U 1 Ceres C 2 Pallas C 511 Davida C 19 Fortuna c 21Lutetia Cpc.
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