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asteroid dynamical families are groups of asteroids in orbital element space ( gradie , chapman & williams 1979 , gradie , chapman & tedesco 1989 , valsecchi _ et al .
this clustering was first discovered by hirayama ( 1918 , for a review see binzel 1993 ) , who also proposed that families may be the remnants of parent bodies that broke into fragments .
about half of all known asteroids are believed to belong to families ; recent work ( zappal _ et al .
_ 1995 , hereafter z95 ) , applying a hierarchical clustering method to a sample of 12,487 asteroids , finds over 30 families .
the contrast between families and the background is especially strong in the space spanned by the so - called _ proper _ orbital elements .
these elements are nearly invariants of motion and are thus well suited for discovering objects with common dynamical history ( valsecchi _ et al .
_ 1989 , milani & kneevi 1992 , hereafter mk92 ) .
the current asteroid motion is described by _ osculating _
orbital elements which vary with time due to perturbations caused by planets , and are less suitable for studying dynamical families .
asteroid clustering is much weaker in the space spanned by directly observed osculating elements than in the space spanned by derived proper elements .
figure 1 compares the osculating ( top panel , bowell 2001 ) and proper ( bottom panel , mk92 ) orbital inclination vs. orbital eccentricity distributions of 1,720 asteroids from the outer region of the main asteroid belt ( proper semi - major axis larger than 2.84 au ) .
this region contains all three major asteroid families : eos , koronis and themis , with approximate ( @xmath3 ) of ( 3.0 , 0.18 , 0.08 ) , ( 2.9 , 0.03 , 0.05 ) and ( 3.15,0.02 , 0.15 ) , respectively . here
@xmath4 is proper semi - major axis , @xmath5 is the sine of the orbital inclination angle , and @xmath6 is eccentricity .
the proper elements are derived from the osculating elements by an approximate perturbation method ( mk92 ) , and it is possible that the overdensities evident in the bottom panel are at least partially created by that algorithm ( valsecchi _ et al .
_ 1989 , bendjoya 1993 ) . a firm proof that families are real therefore requires their confirmation by a method that is _ not _ based on dynamical considerations , for example , that dynamically selected groups have distinctive colors . while there is observational evidence that at least the most populous asteroid families have characteristic colors ( degewij , gradie & zellner 1978 , chapman 1989 ) , even the most recent studies of the colors of asteroid families include fewer than 50 objects per family ( florczak _ et al .
_ 1998 , doressoundiram _ et al .
_ 1998 , florczak _ et al .
_ 1999 ) . the large number ( about 10,000 ) of color measurements for catalogued asteroids ( bowell 2001 ) recently made available by the sloan digital sky survey ( sdss , york _
et al . _ 2000 ) allows a detailed investigation of this question .
the sdss is a digital photometric and spectroscopic survey which will cover one quarter of the celestial sphere in the north galactic cap and produce a smaller but much deeper multi - epoch survey in the southern galactic hemisphere ( stoughton _ et al .
the survey sky coverage will result in photometric measurements ( smith _ et al .
_ 2002 , hogg _
2002 ) for about 50 million stars and a similar number of galaxies , and spectra for about 1 million galaxies and 100,000 quasars .
although primarily designed for observations of extragalactic objects , the sdss is significantly contributing to studies of solar system objects , because asteroids in the imaging survey must be explicitly recognized to avoid contamination of the quasar samples selected for spectroscopic observations ( lupton _ et al .
_ 2001 ) . the sdss will increase the number of asteroids with accurate five - color photometry ( fukugita _ et al .
_ 1996 , gunn _ et al .
_ 1998 ) by more than two orders of magnitude ( to about 100,000 ) , and to a limit more than five magnitudes fainter than previous multi - color surveys ( ivezi _ et al .
_ 2001 , hereafter i01 ) .
most of the asteroids observed by the sdss are new detections , because the sdss finds moving objects to a fainter limit ( @xmath7 ) than the completeness limit of currently available asteroid catalogs ( @xmath8 ) .
however , sdss observations , which are obtained with a baseline of only 5 minutes ( lupton _ et al .
_ 2001 , i01 ) , are insufficient to determine accurate orbits , and we consider only objects that have previously determined orbital parameters .
the details of the matching procedure and a preliminary sample are described by juri _
_ 2002 ( hereafter j02 ) .
here we extend their analysis to a significantly larger sample , and introduce a new method for visualizing the distribution of asteroids in a multi - dimensional space spanned by orbital parameters and colors .
the currently available sdss moving object list ( ivezi _ et al .
_ 2002 , hereafter sdssmoc ) includes over 58,000 observations ; 10,592 are detections of unique objects listed in the catalog of known asteroids ( bowell 2001 ) , and 2,010 detections are multiple observations of the same objects . for a subset of 6,612 objects from this list ,
the proper orbital elements are also available ( mk92 ) and are analyzed here .
these samples are about an order of magnitude larger than used in previous studies of the colors of asteroids , and also benefit from the wide wavelength range spanned by sdss filters band extends to the near - infrared range and allows efficient recognition of vesta type asteroids ( binzel & xu 1995 ) . ]
( gunn _ et al .
_ 1998 ) .
sdss colors can distinguish asteroids of at least three different color types ( i01 , j02 ) . using four of the five sdss bands ,
we construct the color - color diagram shown in figure 2 .
the horizontal axis color . ] is and the vertical axis is @xmath9 , where @xmath10 , @xmath11 , and @xmath9 are the asteroid colors measured by sdss ( accurate to about 0.03 mag ) .
each dot represents one asteroid , and is color - coded according to its position in this diagram ( note that these colors do not correspond directly to asteroid colors as would be seen by the human eye ) . as discussed by i01 ,
the asteroid distribution in this diagram is highly bimodal , with over 90% of objects found in one of the two clumps that are dominated by rocky s type asteroids ( @xmath12 ) , and carbonaceous c type asteroids ( @xmath13 ) .
most of the remaining objects have @xmath14 color similar to s type asteroids , and distinctively blue @xmath9 colors .
they are dominated by vesta type asteroids ( binzel & xu 1995 , j02 ) .
figures 3 and 4 show two two - dimensional projections of the asteroid distribution in the space spanned by proper semi - major axis , eccentricity , and the sine of the orbital inclination angle , with the points color - coded as in figure 2 .
the vertical bands where practically no asteroids are found ( at @xmath4 of 2.065 , 2.501 , 2.825 and 3.278 au ) are the 4:1 , 3:1 , 5:2 , and 2:1 mean motion resonances with jupiter ( the latter three are the kirkwood gaps ) .
figure  5 is analogous to the bottom panel in figure  1 .
a striking feature of figures 3 , 4 and 5 is the color homogeneity and distinctiveness displayed by asteroid families .
each of the three major hirayama families , eos , koronis and themis , and also the vesta family at ( @xmath3 ) of ( 2.35 , 0.12 , 0.09 ) , has a characteristic color .
this strong color segregation provides firm support for the reality of asteroid dynamical families .
the correlation between the asteroid colors and their heliocentric distance has been recognized since the earliest development of asteroid taxonomies ( chapman , morrison & zellner 1975 , gradie & tedesco 1982 , zellner , tholen & tedesco 1985 , gradie , chapman & tedesco 1989 ) .
our analysis indicates that this mean correlation ( see e.g. figure 23 in i01 ) is mostly a reflection of the distinctive colors of asteroid families and their heliocentric distribution .
when only orbital elements are considered , families often partially overlap each other ( z95 ) , and additional independent information is needed to improve their definitions . with such a massive , accurate and public database as that discussed here ( sdssmoc ) , it will be possible to improve the classification of asteroid families by simultaneously using both the orbital elements and colors .
for example , the sdss colors show that the asteroids with ( @xmath15 ) about ( 2.65 , 0.20 ) are distinctively blue ( figure 3 ) , proving that they do not belong to the family with ( @xmath15 ) about ( 2.60 , 0.23 ) , but instead are a family in their own right .
while this and several similar examples were already recognized as clusters in the orbital parameter space ( z95 ) , this work provides a dramatic independent confirmation .
figures 3 , 4 and 5 suggest that the asteroid population is dominated by families : even objects that do not belong to the most populous families , and thus are interpreted as background in dynamical studies , seem to show color clustering . using the definitions of families based on dynamical analysis ( z95 ) , and aided by sdss colors ,
we estimate that at least 90% of asteroids are associated with families .    proper orbital elements ( mk92 ) are not available for asteroids with large semi - major axis and orbital inclination .
in order to examine the color distribution for objects with large semi - major axis , such as trojan asteroids ( @xmath16 ) and for objects with large inclination , such as asteroids from the hungaria family ( @xmath17 ) , we use osculating orbital elements .
figure 6 shows the distribution of all the 10,592 known asteroids observed by the sdss in the space spanned by osculating semi - major axis and the sine of the orbital inclination angle , with the points color - coded as in figure 2 .
it is remarkable that various families can still be easily recognized due to sdss color information .
this figure vividly demonstrates that the asteroid population is dominated by objects that belong to numerous asteroid families .
we are grateful to e. bowell for making his astorb file publicly available , and to a. milani , z. kneevi and their collaborators for generating and distributing proper orbital elements .
we thank princeton university for generous financial support of this research , and m. strauss and d. schneider for helpful comments .
the sloan digital sky survey ( sdss ) is a joint project of the university of chicago , fermilab , the institute for advanced study , the japan participation group , the johns hopkins university , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new mexico state university , princeton university , the united states naval observatory , and the university of washington .
apache point observatory , site of the sdss telescopes , is operated by the astrophysical research consortium ( arc ) .
funding for the project has been provided by the alfred p. sloan foundation , the sdss member institutions , the national aeronautics and space administration , the national science foundation , the u.s .
department of energy , the japanese monbukagakusho , and the max planck society .
the sdss web site is http://www.sdss.org/.                                                lupton , r.h .
_ 2001 , in _ astronomical data analysis software and systems x _ , asp conference proceedings , vol.238 , p. 269 . edited by f. r. harnden , jr . , francis a. primini , and harry e. payne .
san francisco : astronomical society of the pacific , issn : 1080 - 7926
we discuss optical colors of 10,592 asteroids with known orbits selected from a sample of 58,000 moving objects observed by the sloan digital sky survey ( sdss ) . 
 this is more than ten times larger sample that includes both orbital parameters and multi - band photometric measurements than previously available . 
 we confirm that asteroid dynamical families , defined as clusters in orbital parameter space , also strongly segregate in color space . 
 in particular , we demonstrate that the three major asteroid families ( eos , koronis , and themis ) , together with the vesta family , represent four main asteroid color types . 
 their distinctive optical colors indicate that the variations in chemical composition within a family are much smaller than the compositional differences between families , and strongly support earlier suggestions that asteroids belonging to a particular family have a common origin . 
 we estimate that over 90% of asteroids belong to families .    
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