Description of the Nesvorny HCM Asteroid Families Bundle bundle V2.0 ==================================================================== Bundle Generation Date: 2024-12-02 Peer Review: 2024_Asteroid_Review Discipline node: Small Bodies Node ===================================================================== This asteroid dynamical family analysis has been carried out by David Nesvorny and colleagues (Nesvorny, Roig, Vokrouhlicky, Broz 2024) using the Hierarchical Clustering Method (HCM) code, with synthetic proper elements for 1.25 million asteroids. This analysis includes both low and high-inclination orbits. This package also includes the analysis and family identification from the previous version. The synthetic proper elements were computed for all (non-resonant) main belt asteroids using methods similar to those described in Knezevic et al. (2002). The HCM code applies the HCM method of Zappala et al. (1990, 1994). The distance cutoffs have been selected by Nesvorny individually for each family based on a trial and error method using visualization software. See Nesvorny et al. (2024) for a general discussion of the family identification methods and specific description of this data set. The family identifications are based on observations up to February 9, 2024. Any objects discovered after that date are not included and have not been assigned a family. Proper Elements =============== The orbital elements of main belt asteroids were downloaded from the MPC catalog on February 9, 2024. We selected asteroid orbits with the semimajor axis a>1.6 au, perihelion distance q>1.3 au (to avoid near-Earth asteroids), aphelion distance Q<5 au (to avoid unstable Jupiter-crossing orbits), and $a<3.8$ au (to avoid Hildas in the 3:2 resonance with Jupiter). A different strategy must be employed to compute the proper elements for Hildas (Broz et al. 2011). This represents 1,261,151 orbits in total. For comparison, Version 3.0 catalog (from 2015) included 384,336 orbits. We do not distinguish between the numbered and unnumbered (single- or multi-opposition) bodies, but the information about the quality of the osculating orbits (the number of oppositions) is propagated to the final catalog. The osculating orbits are given with respect to the J2000 ecliptic reference system and, for the vast majority of cases, at the JD 2460200.5 epoch (a small number of orbits given at different epochs are ignored). The planetary orbits (Mercury to Neptune) were obtained for the same epoch from the DE 441 Ephemerides. These ephemerides are calculated by JPL. We used the center of mass -- planet plus its satellites -- and the total mass of each system. The gravitational effects of Ceres and other massive asteroids were ignored. The reference system was rotated to the invariant plane of planets (as defined by the total angular momentum of planetary orbits). The orbital integrations were performed with the Swift integrator (Levison and Duncan 1994) We used a short time step (1.1 days) and integrated all orbits backward in time for 10 Myr. The symplectic corrector was applied to compensate for high-frequency noise terms (Wisdom 2006). We adopted the general relativistic correction from Quinn et al. (1991). The integrations were split over 12,620 Ivy-bridge cores on the NASA's Pleiades Supercomputer and ran for 60 wall-clock hours. The orbital elements were saved in double precision every 600 years for the total of 16,666 outputs per orbit. This allowed us to resolve frequencies as high as 1000 arcsec/yr. The binary output files represent 1.3 Tb of data in total. We did not apply any low-pass filter on output, because our tests showed that the use of filter did not have an appreciable effect on the final product. The Frequency Modified Fourier Transform (FMFT; Sidlichovsky and Nesvorny 1996) was applied to obtain a Fourier decomposition of each signal. We used the complex variable x(t) + iota y(t) with x=e cos(varpi) and y=e sin(varpi) for the proper eccentricity, and x=sin(i) cos(Omega) and y=sin(i) sin(Omega) for the proper inclination, where varpi and Omega are the perihelion and nodal longitudes. FMFT was first applied to the planetary orbits to obtain the planetary frequencies g_j and s_j, governing the perihelion and nodal evolution of planetary orbits, respectively. The forced terms with these frequencies were identified in the Fourier decomposition of each asteroid orbit and subtracted from asteroid's x(t) + iota y(t). We experimented with different techniques to extract the amplitude of the proper terms from the remaining signal. The most reliable method consists in computing the mean of sqrt{x(t)^2+y(t)^2}, with the forced terms removed, over a relatively long interval (5 Myr). This defines the proper elements e_P and sin i_P. The proper semimajor axis a_P was computed as the mean value of the osculating semimajor axis over the same time interval. The uncertainties of a_P, e_P and sin i_P were obtained as the RMS of the proper elements computed from different intervals within the 10-Myr integration time span. Asteroid Families ================= 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 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. 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, 2024) for additional information. The range of cutoff velocities used here is 7 to 200 m/s. The 153 new families reported here reflect the increased number of asteroids in proper element catalogs. As the number of identified families roughly doubled when the catalog tripled in size, we anticipate that a similar trend will hold in the future. For example, the Rubin observatory is expected to discover ~5 million main belt asteroids. This should lead to the identification of at least ~500 new (small and recently formed) families. In previous versions, the individual family files included information about the C parameter defined in Section 4 in Nesvorny et al. (2015). The parameter C was obtained by fitting an envelope to the V shape of each family in the semimajor axis and absolute magnitude. The C parameter can be used to estimate an approximate age of each family (see Equation 1 in Nesvorny et al. 2015) and identify large interlopers. We do not include the C parameter in the present distribution. Including it will require additional analysis and detailed characterization of individual families. This is left for future work (Broz et al., in preparation). 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. Data Products ============= Files listing the members for each of 153 new families are in the directory data/families_2024 as .csv files. The families from the previous version are included as .tab files in data/families_2015. The filenames are the concatenation of the family number and name. The file document/list_of_new_families_2024.txt gives a listing of the 153 new families with their family name, the distance cutoff used, and the number of members. The family name is the name of the reference -often the brightest- asteroid in the family. The file data/familylist.tab gives the listing for the families from the previous version. The families are separated into inner, middle, pristine, outer, and high-i zones with the following definitions: inner: q>1.3 au, a<2.5 au, sin(i)<0.3 middle: 2.50.3 The following applies to families identified in previous versions: 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 familieslist.tab 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 Trojans, - in the 400s include inner main belt families with 2.0 > a > 2.5 AU and i < 17.5, - in the 500s 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.c - The Nesvorny HCM code for synthetic proper elements (compile with nrutil.c and nrutil.h). The code was modified from the previous code (hcluster_syn.c) to read proper_catalog24.tab on input. The new code is called hcluster.c in the present distribution. 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) - synthetic proper elements used in previous versions, used as input to hcluster_syn.c proper_catalog24.tab - The synthetic proper 1.25 million main belt asteroids, used as input to hcluster.c. familylist.tab - catalog of 122 asteroid families from synthetic proper elements, with their cutoffs, numbers of members, and ranges of proper elements derived in the previous version. 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 a Fedora core. On other platforms, known compilation issues may arise with memory allocation routines. On input, the code asks to input a reference body and the velocity cutoff. The reference body is used to start the HCM chain. To avoid ambiguity of different asteroid naming conventions (e.g., MPC packed vs. normal name, capitalizing, spaces), the reference body is identified by the line number on which it appears in proper_catalog24.tab. For example, asteroid (6) Hebe appears on line number 6. To identify the Hebe family, the user enters 6 for the reference body and 80 for the cutoff. This will cluster 112 Hebe family members. The output file is family.list. The first row in family.list reports line numbers of family members. If needed, this needs to be linked with proper_catalog24.tab to obtain additional information about family members (e.g., proper frequencies, the number of oppositions). Modification History ==================== PDS3 Version 1.0 of this data set, archived in 2010, contained 55 families from the analytic proper elements of Milani and Knezevic. PDS3 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. PDS3 Version 3.0, archived in 2015, contains 122 families based on synthetic proper elements, including high-inclination families. That version was migrated to PDS4 V1.0 in August 2020. PDS4 V2.0 added 153 new families in 2024. The HCM analysis software has not been modified from PDS3 version 1.0 to PDS3 version 3.0. The HCM code has been modified in this release (PDS4 V2.0) to read the new catalog of proper elements (proper_catalog24.dat). See the description of hcluster.c above (section "Running the code"). References ========== Bottke, W.F., D. Vokrouhlicky, M. Broz, D. Nesvorny, and A. Morbidelli, Dynamical Spreading of Asteroid Families via the Yarkovsky Effect, Science 294, 1693-1696, 2001. doi:10.1126/science.1066760 Broz, M., Vokrouhlicky, D., Morbidelli, A., Nesvorny, D., Bottke, W. F., Did the Hilda collisional family form during the late heavy bombardment? Monthly Notices of the Royal Astronomical Society 414, 2716-2727, 2011. doi:10.1111/j.1365-2966.2011.18587.x Davis, D.R., D.D. Durda, F. Marzari, A. Campo Bagatin, and R. Gil-Hutton, 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, 2002. Hirayama, K., Groups of asteroids probably of common origin. Astron J. 31, 185-188, 1918. doi:10.1086/104299 Ivezic, Z. and 32 others, Solar System objects observed in the Sloan Digital Sky Survey commissioning data, AJ 122, 2749-2784, 2001. doi:10.1086/323452 Knezevic, Z., A. Lemaitre, and A. Milani, 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, 2002. Levison, H. F., Duncan, M. J., The Long-Term Dynamical Behavior of Short-Period Comets. Icarus 108, 18–36, 1994. doi:10.1006/icar.1994.1039 Milani, A., and Z. Knezevic, Asteroid Proper Elements and the Dynamical Structure of the Asteroid Belt, Icarus 107, 219-254, 1994. doi:10.1006/icar.1994.1020 Nesvorny, D. and D. Vokrouhlicky, New Candidates for Recent Asteroid Breakups. The Astronomical Journal 132, 1950-1958, 2006. doi:10.1086/507989 Nesvorny, D., D. Vokrouhlicky, and W.F. Bottke, The Breakup of a Main-Belt Asteroid 450 Thousand Years Ago. Science 312, 1490, 2006. doi:10.1126/science.1126175 Nesvorny, D., M. Broz, and V. Carruba, 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, 2015. doi:10.2458/azu_uapress_9780816532131-ch016 astroph: 10.48550/arXiv.1502.01628 Nesvorny, D., W.F. Bottke, L. Dones, and H.F. Levison, The recent breakup of an asteroid in the main-belt region. Nature 417, 720-771, 2002. doi:10.1038/nature00789 Nesvorny, D., R. Jedicke, R.J. Whiteley, and Z. Ivezic, Evidence for asteroid space weathering from the Sloan Digital Sky Survey. Icarus 173, 132-152, 2005. doi:10.1016/j.icarus.2004.07.026 Nesvorny, D., Roig, F., Vokrouhlicky, D., Broz, M., Catalog of Proper Orbits for 1.25 Million Main-belt Asteroids and Discovery of 136 New Collisional Families. ApJ Suppl. 274, id25, 19 pp. 2024. doi:10.3847/1538-4365/ad675c Quinn, T. R., Tremaine, S., Duncan, M., A Three Million Year Integration of the Earth's Orbit. The Astronomical Journal 101, 2287, 1991. doi:10.1086/115850 Wisdom, J., Symplectic Correctors for Canonical Heliocentric n-Body Maps. The Astronomical Journal 131, 2294–2298, 2006 doi:10.1086/500829 Zappala, V., A. Cellino, P. Farinella, Z. Knezevic, Asteroid Families, I. Identification by hierarchical clustering and reliability assessment, Astronomical Journal, 100, 2030-2046, 1990. doi:10.1086/115658 Zappala, V., A. Cellino, P. Farinella, and A. Milani, Asteroid families. II: Extension to unnumbered multiopposition asteroids. The Astronomical Journal 107, 772-801, 1994. doi:10.1086/116897 Caveats to the data user ======================== 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.