Data Set Information
DATA_SET_NAME NESVORNY HCM ASTEROID FAMILIES V2.0
DATA_SET_ID EAR-A-VARGBDET-5-NESVORNYFAM-V2.0
NSSDC_DATA_SET_ID
DATA_SET_TERSE_DESCRIPTION
DATA_SET_DESCRIPTION Data Set Overview : This asteroid dynamical family analysis has been carried out by David Nesvorny using his Hierarchical Clustering Method (HCM) code, with analytic proper elements for 401,488 asteroids and synthetic proper elements for 302,212 asteroids. This analysis includes both low and high-inclination orbits. The HCM code applies the HCM method of Zappala et al. (1990, 1994). The input proper elements files were calculated by Milani and Knezevic using a semianalytical method described in Milani and Kenzevic (1994). The synthetic proper elements were computed by Zoran Knezevic following the method described in Knezevic et al. (2002). The distance cutoffs have been selected by Nesvorny individually for each family based on a trial and error method using visualization software. In three cases, namely Vesta/Flora, Massalia/Nysa-Polana, Eunomia/Adeona, artificial cuts in proper element space were used to prevent HCM from hopping between two different families. Overview of the Method : The asteroid belt has collisionally evolved since its formation (see, e.g., Davis et al. 2002). Possibly its most striking feature is the presence of asteroid families that represent remnants of large, collisionally disrupted asteroids (Hirayama 1918). Asteroid families can be identified as clusters of asteroid positions in the space of proper elements: the proper semimajor axis (a_P), proper eccentricity (e_P), and proper inclination (i_P) (Milani and Knezevic 1994, Knezevic et al. 2002). These orbital elements describe the size, shape and tilt of orbits. Proper orbital elements, being more constant over time than the osculating orbital elements, provide a dynamical criterion of whether or not a group of bodies has a common ancestor. To identify an asteroid family, we use a numerical code that automatically detects a cluster of asteroid positions in 3-dimensional (3D) space of proper elements. We briefly describe the code below. See Nesvorny et al. (2005, 2006) for a more thorough description. The code implements the so-called Hierarchical Clustering Method (hereafter HCM) originally proposed and pioneered in studies of the asteroid families by Zappala et al. 1990, 1994). The HCM requires that members of the identified cluster of asteroid positions in the proper elements space be separated by less than a selected distance (the so-called 'cutoff'). The procedure starts with an individual asteroid position in the space of proper elements and identifies bodies in its neighborhood with mutual distances less than a threshold limit (d_cutoff). Following Zappala et al. (1990, 1994), we define the distance in a_P, e_P, i_P space by d : n a_P sqrt{C_a (da_P/a_P)^2 + C_e (de_P)^2 + C_i (dsin i_P)^2}, where n a_P is the heliocentric velocity of an asteroid on a circular orbit having the semimajor axis a_P, da_P : abs[a_P^(1) - a_P^(2)], de_P : abs[e_P^(1) - e_P^(2)], and d sin i_P : abs[sin i_P^(1) - sin i_P^(2)]. The upper indexes (1) and (2) denote the two bodies in consideration. C_a, C_e, and C_i are weighting factors; we adopt C_a : 5/4, C_e : 2 and C_i : 2 (Zappala et al. 1994). Other choices of C_a, C_e, and C_i yield similar results. Once bodies with d < d_cutoff are identified, each of them is used as a starting point of the algorithm and new bodies are searched in its neighborhood. The procedure is then iterated until no new bodies can be found. The final result of the HCM method is a cluster of asteroids that can be connected by a chain in proper elements space with segments shorter than d_cutoff. In other words, any member of the cluster will have, by definition, at least one neighbor with distance d < d_cutoff. Also, asteroids that were not classified as members cannot be connected to any member by a segment shorter than d_cutoff. Note that spectroscopic interlopers are not removed from the resulting family lists. Selection of the Cutoff : The cutoff distance d_cutoff is a free parameter. With small d_cutoff the algorithm identifies tight clusters in proper element space. With large d_cutoff the algorithm detects larger and more loosely connected clusters. For the main belt, the appropriate values of d_cutoff are between 1 and 200 m/s. To avoid an a priori choice of d_cutoff, we developed software that runs HCM starting with each individual asteroid and loops over 200 values of d_cutoff between 1 and 200 m/s with a 1 m/s step. The result of this algorithm can be conveniently visualized in a 'stalactite diagram' (see Nesvorny et al. 2005). The stalactite diagram is useful when we want to systematically classify the asteroid families identified by HCM. With modern data (proper asteroid catalog 2005 or newer), more than fifty families can be found (see below). We also developed software that allows us to visualize, in 3D, the overall distribution of asteroid proper elements and highlight families found by HCM. The software can also 'subtract' a cluster (or any number of clusters) from the distribution and show background. This is helpful because it allows us to check on the 3D distribution of each family, see if it ends at or steps over specific resonances, and give us a general idea about the appropriate range of d_cutoff values in each case. By subtracting all identified families from the overall distribution, we can also verify that no meaningful concentrations were left behind. To select appropriate d_cutoff for each cluster, insights into the dynamics of the main-belt asteroids are required. Nesvorny et al. (2005) illustrated this for the Koronis family by discussing the number of members of the cluster linked to (158) Koronis changes with d_cutoff. With small d_cutoff values, the algorithm accumulates members of a very tightly clustered group -- the product of the collisional breakup of a Koronis family member about 5.8 My ago (Karin cluster, Nesvorny et al. 2002). With d_cutoff about 20 m/s, the HCM starts to agglomerate the central part of the Koronis family. With even larger d_cutoff, the algorithm steps over the secular resonance that separates central and large semimajor axis parts of the Koronis family (this particular shape resulted from long-term dynamics driven by radiation forces, Bottke et al. 2001). Finally, with very large d_cutoff, the algorithm starts to select other structures in the outer main belt that have unrelated origins. Therefore, according to these considerations, d_cutoff : 10 m/s is the best choice for the Karin cluster and d_cutoff : 50 m/s is best for the Koronis family (note that these specific values are based on the 2008 update of proper element catalog and may change as the catalogs grow). For other families, we choose d_cutoff using similar criteria that are not explained here in detail. See Nesvorny et al. (2005, 2006) for additional information. In summary, each family is treated individually, taking into account local resonances, radiation forces, etc. and this requires significant human effort. Why is 'distance' a velocity? ----------------------------- The 'distance' referred to by the distance cutoff is the distance in proper elements phase space, which is related to the relative velocity of the fragments as they were ejected from the sphere of influence of the parent body. Thus this 'distance' has units of velocity. Robustness and Completeness of the Resulting Families : To determine the statistical significance of each family we generated mock distributions of proper elements and applied the HCM to them. For example, to demonstrate a greater than 99.9% statistical significance of the Karin cluster, we generated 1000 mock orbital distributions corresponding to the Koronis family determined at d_cutoff : 50 m/s , and applied the HCM algorithm to these data. With d_cutoff : 10 m/s, we were unable to find a cluster containing more than a few dozen members, yet the Karin family contains 493 members with this d_cutoff. We are thus confident that the Karin cluster and other families to which we applied the same technique are statistically robust. For a discussion of the statistical significance of asteroid families with only a few known members (e.g. Datura, Lucascavin, Emilkowalski), see Nesvorny et al. (2006) and Nesvorny and Vokrouhlicky (2006) In these cases, the true membership was established based on past orbital histories of asteroids. As a byproduct of these numerical integrations, it was determined that these families formed less than 1 My ago. To determine whether our algorithm produced a reasonably complete list of asteroid families, we searched for residual clusters in the background asteroid population using proper elements and Sloan Digital Sky Survey (SDSS; Ivezic et al. 2001) colors simultaneously. This method is based on an assumption that each individual family represents a reasonably homogeneous distribution of colors that may be different from that of asteroids in the local background. We define the distance in a_P, e_P, i_P, PC_1, PC_2 space, where PC_1 and PC_2 are the principal SDSS-color components (see Nesvorny et al. 2005 for a definition), by d_2 : sqrt{d^2 + C_PC [(dPC_1)^2 + (dPC_2)^2]} , where d is the distance in a_P, e_P, i_P sub-space defined in the above equation, dPC_1 : abs[PC_1^(1) - PC_1^(2)] and dPC_2 : abs[PC_2^(1) - PC_2^(2)]. The indexes (1) and (2) denote the two bodies in consideration. C_PC is a factor that weights the relative importance of colors in our generalized HCM search. With d in m/s, we typically used C_PC : 10^6 and varied this factor in the 10^4 - 10^8 range to test the dependence of results. We found no statistically robust concentrations in the extended proper element/color space that could help us to identify new families. This result shows that our list of dynamical families based on the proper element data is reasonably complete. The current catalog (as of 2012) includes 64 analytic families while version 1.0 had 55 and Nesvorny et al. (2005) list 41. This increase is due to the increase in number of cataloged proper elements (100,000 in 2005, about 300,000 in 2010, and over 400,000 in 2012), which allowed us to identify new cases. Data Products : Files listing the members for each of the 64 families from analytic proper elements and 79 families from synthetic proper elements in this analysis are in the directory data/families. The filenames are the concatenation of the family number and name. The file anafamilieslist.tab gives a listing of the 64 analytic families with their family number, family name, the distance cutoff used, and the number of members, while the file synfamilies.tab gives the same information for the 79 synthetic families. The family name is the name of the largest asteroid in the family. The family numbers from analytic proper elements are 1XX for inner belt (2-2.5 AU), 2XX for central belt (2.5-2.82 AU) and 3XX for outer belt (2.82-3.6 AU), and those from synthetic proper elements are 4XX for inner belt (2-2.5 AU), 5XX for central belt (2.5-2.82 AU) and 6XX for outer belt (2.82-3.6 AU). The XX code for analytic and synthetic families is the same, so, for example, 101 and 401 are the families numbers for the Vesta family in the analytic and synthetic analyses respectively. In addition, the high-inclination families, identified from the synthetic proper elements, with I > 17 deg have family numbers 7XX (inner), 8XX (central) and 9XX (outer). These high-inclination families were not included in version 1.0 of this data set. The number XX increases with the designation number of the asteroid after which the family is named (e.g., 101 is the Vesta family named after (4) Vesta, listed on on the 1st line of 101_vesta.tab; 102 is the Flora family named after (8) Flora). Families with very few members, typically 3 to 6, are highlighted by using XX > 50 (e.g., 151 is the Datura family with 6 members). Ancillary Data : The document directory includes the Nesvorny HCM code and the two input files of proper elements which were used to generate this family analysis. The code and input files have been renamed to conform to PDS document filenaming requirements. In the list below, the original filename is given in parentheses. These files are provided as documentation of the algorithms and input data used for generating the family memberships. hcluster_c.asc (hcluster.c) - The Nesvorny HCM code for analytic proper elements (compile with nrutil.c and nrutil.h). hcluster_syn_c.asc (hcluster_syn.c) - The Nesvorny HCM code for synthetic proper elements (compile with nrutil.c and nrutil.h). nrutil_c.asc (nrutil.c) - memory allocation functions used by hcluster.c and hcluster_syn.c. nrutil_h.asc (nrutil.h) - header of nrutil.c. allnum_pro.asc (allnum.pro) - The M&K analytic proper elements for numbered asteroids, used as input to hcluster.c. ufitobs_pro.asc (ufitobs.pro) - The M&K analytic proper elements for unnumbered asteroids, used as input to hcluster.c. numb_syn.asc (numb.syn) - The Knesevic synthetic proper elements for numbered asteroids, used as input to hcluster_syn.c. Running the code: On a Linux platform, code hcluster.c can be compiled by typing: 'gcc hcluster.c -o hcluster -lm'. This works on Opteron 2360 workstation running Fedora core. On other platforms, known compilation issues may arise with memory allocation routines. On input, hcluster requests the designation number of an asteroid whose proper elements serve as a starting point of the HCM algorithm (e.g., type 158 for the Koronis family, where 158 stands for asteroid (158) Koronis). The second and last input is the cutoff distance in m/s (e.g., enter 50 for the Koronis family, for which 50 m/s is adequate). The procedure is similar for hcluster_syn.c. Modification History : Version 1.0 of this data set, archived in 2010, contained 55 families from the analytic proper elements of Milani and Knezevic. Version 2.0, archived in 2012, contains a new HCM analysis of an expanded set of analytic proper elements of M&K resulting in 64 families, plus an HCM analysis based on synthetic proper elements of Knezevic et al. resulting in 79 families. References : Bottke, W.F., D. Vokrouhlicky, M. Broz, D. Nesvorny, and A. Morbidelli 2001. Dynamical Spreading of Asteroid Families via the Yarkovsky Effect. Science 294, 1693-1696. Davis, D.R., D.D. Durda, F. Marzari, A. Campo Bagatin, and R. Gil-Hutton 2002. Collisional Evolution of Small-Body Populations. In Asteroids III (W.F. Bottke, A. Cellino, P. Paolicchi, and R. Binzel, Eds.). Univ. of Arizona Press, Tucson, pp. 545-558. Hirayama, K. 1918. Groups of asteroids probably of common origin. Astron. J. 31, 185-188. Ivezic, Z., and 32 colleagues 2001. Solar System Objects Observed in the Sloan Digital Sky Survey Commissioning Data. Astron. J. 122, 2749-2784. Knezevic, Z., A. Lemaitre, and A. Milani 2002. The Determination of Asteroid Proper Elements. In Asteroids III (W.F. Bottke, A. Cellino, P. Paolicchi, and R. Binzel, Eds.). Univ. of Arizona Press, Tucson, pp. 603-612. Milani, A., and Z. Knezevic, Asteroid Proper Elements and the Dynamical Structure of the Asteroid Belt, Icarus 107, 219-254, 1994. Nesvorny, D., W.F. Bottke, L. Dones, and H.F. Levison 2002. The recent breakup of an asteroid in the main-belt region. Nature 417, 720-771. Nesvorny, D., R. Jedicke, R.J. Whiteley, Z. Ivezic, 2005. Evidence for asteroid space weathering from the Sloan Digital Sky Survey. Icarus 173, 132-152. Nesvorny, D. and D. Vokrouhlicky, 2006. New Candidates for Recent Asteroid Breakups. The Astronomical Journal 132, 1950-1958. Nesvorny, D., Vokrouhlicky, D., Bottke, W. F., 2006b. The Breakup of a Main-Belt Asteroid 450 Thousand Years Ago. Science 312, 1490. Zappala, V., A. Cellino, P. Farinella, Z. Knezevic, Asteroid Families, I. Identification by hierarchical clustering and reliability assessment, Astronomical Journal, 100, 2030-2046, 1990. Zappala, V., A. Cellino, P. Farinella, and A. Milani, 1994. Asteroid families. II: Extension to unnumbered multiopposition asteroids. The Astronomical Journal 107, 772-801.
DATA_SET_RELEASE_DATE 2012-05-30T00:00:00.000Z
START_TIME 1965-01-01T12:00:00.000Z
STOP_TIME N/A (ongoing)
MISSION_NAME SUPPORT ARCHIVES
MISSION_START_DATE 2004-03-22T12:00:00.000Z
MISSION_STOP_DATE N/A (ongoing)
TARGET_NAME ASTEROID
TARGET_TYPE ASTEROID
INSTRUMENT_HOST_ID VARGBTEL
INSTRUMENT_NAME VARIOUS GROUND-BASED DETECTORS
INSTRUMENT_ID VARGBDET
INSTRUMENT_TYPE UNKNOWN
NODE_NAME Small Bodies
ARCHIVE_STATUS LOCALLY_ARCHIVED
CONFIDENCE_LEVEL_NOTE Confidence Level Overview : Individual distance cutoffs have been selected subjectively for each family with the intent of separating family members from background objects. Family membership will vary with selection of different distance cutoffs. The original review of V1.0 of this data set on June 7, 2010 found that the documentation of the method was insufficient. After extensive improvements to the data set description, a follow-up external peer review with was held on November 8, 2010. The follow-up review found that the data set documentation is now sufficient to enable a data user to understand and use the data and to understand the method by which the family memberships were determined.
CITATION_DESCRIPTION Nesvorny, D., Nesvorny HCM Asteroid Families V2.0. EAR-A-VARGBDET-5-NESVORNYFAM-V2.0. NASA Planetary Data System, 2012.
ABSTRACT_TEXT This data set contains asteroid dynamical family memberships for 64 families calculated from analytic proper elements, and 79 families calculated from synthetic proper elements, including high-inclination families. These families were calculated by David Nesvorny using his code based on the Hierarchical Clustering Method (HCM) described in Zappala et al. (1990, 1994). The input analytic proper elements for 401,408 numbered and unnumbered asteroids were calculated by Milani and Knezevic. The input synthetic proper elements for 302,212 numbered asteroids were calculated by Knezevic.
PRODUCER_FULL_NAME CAROL NEESE
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