Data Set Information
DATA_SET_TERSE_DESCRIPTION Asteroid dynamical families calculated by David Nesvorny using the Heirarchical Clustering Method. This is the version of February 2015.
Data Set Overview                                                           
    This asteroid dynamical family analysis has been carried out by David     
    Nesvorny (Nesvorny et al. 2015) using his Hierarchical Clustering Method  
    (HCM) code, with synthetic proper elements for 384,337 numbered asteroids.
    This analysis includes both low and high-inclination orbits.              
    The HCM code applies the HCM method of Zappala et al. (1990, 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. See Nesvorny et al. (2015) for a general discussion of
    the family identification methods and specific description of this data   
    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 a  
    (2015) 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   
    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. (2015) for additional       
    information.  In summary, each family is treated individually, taking into
    account local resonances, radiation forces, etc. and this requires        
    significant human effort.                                                 
    got to here.                                                              
    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% 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 541 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 2015)    
    includes 122 families. The increase relative to the previous family lists 
    is due to the increase in number of cataloged proper elements.            
    Data Products                                                             
    Files listing the members for each of 119 families from synthetic proper  
    elements in this analysis are in the directory data/families.  Note that  
    three of the 122 families listed in the families list are not represented 
    by files listing their members for the following reasons:                 
     - 007 James Bond:  James Bond is not an asteroid.  (Asteroid 9007 James  
    Bond is a member of the Vesta family.)                                    
     - 503:  This family has no members in the current analysis.              
     - 640 P/2012 F5 (Gibbs):  This family was derived by another researcher  
    and is not included here.  See Nesvorny et al. (2015).                    
    The filenames are the concatenation of the family number and name.  The   
    file gives a listing of the 122 families with their      
    family number (FIN), family name, the distance cutoff used, and the number
    of members.  The family name is the name of the largest asteroid in the   
    family.  The family number is assigned as follows:                        
      - less than 100 include Hungarias, Hildas, and Jupiter                  
      - in the 400s include inner main belt families with                     
                 2.0 > a > 2.5 AU and i < 17.5,                               
      - in the 500's include central belt families with                       
                 2.5 < a < 2.82 AU and i < 17.5,                              
      - in the 600s include outer main belt families with                     
                 2.82 < a < 3.7 AU and i < 17,                                
      - in the 700s include inner main belt families with                     
                 2.0 < a < 2.5 AU and i > 17,                                 
      - in the 800s include central main belt families with                   
                 2.5 < a < 2.82 AU and i > 17.5,                              
      - in the 900s include outer main belt families with                     
                 2.82 < a < 3.5 AU and i > 17.5.'                             
    Ancillary Data                                                            
    The document directory includes the Nesvorny HCM code and the input file  
    of proper elements which were used to generate this family analysis.  The 
    code and input file 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_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.                             
    numb_syn.asc (numb.syn) - The Knezevic and Milani synthetic proper        
    elements for numbered asteroids, used as input to hcluster_syn.c.         
    Running the code:                                                         
    On a Linux platform, code hcluster_syn.c can be compiled by typing: 'gcc  
    hcluster_syn.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_syn 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 45 for the Koronis       
    family, for which 45 m/s is adequate).                                    
    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.  Version 3.0, archived in 2015, contains 122 families     
    based on synthetic proper elements, including high-inclination families.  
    Families based on analytic elements are not provided in this version      
    because the catalogs of analytic and synthetic elements are now almost the
    same size, and the synthetic elements are more precise.                   
    The HCM analysis software has not been modified from one version to the   
    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.     
    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, 
    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.             
    Nesvorny, D., Broz, M., Carruba, V., 2015. Identification and Dynamical   
    Properties of Asteroid Families. In Asteroids IV (P. Michel, F. DeMeo,    
    W.F. Bottke, R. Binzel, Eds.).  Univ. of Arizona Press, Tucson, also      
    available on astro-ph.                                                    
    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 2015-11-19T00:00:00.000Z
START_TIME 1965-01-01T12:00:00.000Z
STOP_TIME 3000-01-01T12:00:00.000Z
MISSION_START_DATE 1965-01-01T12:00:00.000Z
MISSION_STOP_DATE 2015-01-01T12:00:00.000Z
NODE_NAME Small Bodies
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
    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 V3.0. EAR-A-VARGBDET-5-NESVORNYFAM-V3.0. NASA Planetary Data System, 2015.
ABSTRACT_TEXT This data set contains asteroid dynamical family memberships for 122 families calculated from synthetic proper elements, including high-inclination families. These families were calculated by David Nesvorny (Nesvorny et al. 2015) using his code based on the Hierarchical Clustering Method (HCM) described in Zappala et al. (1990, 1994). The input synthetic proper elements for 384,337 numbered asteroids were calculated by Knezevic and Milani.