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Asteroid families classification: exploiting very large data sets

Andrea Milani, Alberto Cellino, Zoran Knezevic, Bojan Novakovic, Federica Spoto, Paolo Paolicchi

arXiv:1312.7702v2astro-ph.EP

TL;DR

Rapidly expanding asteroid catalogs make conventional family classification difficult because large samples create overlapping groupings and chaining. The paper combines HCM with member attribution, iterative removal and reclustering, age analysis from V-shapes, and physical-property checks. The enlarged dataset produces qualitative changes, including internal family structures, while some merging decisions and age estimates remain constrained.

  • Problem

    Rapidly growing orbital catalogs create overlapping groupings and chaining, making straightforward HCM classification problematic for large asteroid samples.

  • Method

    The paper combines HCM, iterative member attribution and reclustering, V-shape age analysis, and physical-property information to classify and interpret asteroid families.

  • Results

    The enlarged dataset produces qualitative changes in family classifications and reveals many internal family structures.

  • Takeaways & Limitations

    Large proper-element catalogs support classifications that can be repeatedly updated and supplemented with physical data to examine overlapping or intersecting families.

  • Takeaways & Limitations

    Merging intersecting families cannot be fully automated, and V-shape ages contain errors from size-dependent Yarkovsky drift and spin evolution.

Abstract

from arXiv · show

The number of asteroids with accurately determined orbits increases fast. The catalogs of asteroid physical observations have also increased, although the number of objects is still smaller than in the orbital catalogs. We developed a new approach to the asteroid family classification by combining the Hierarchical Clustering Method (HCM) with a method to add new members to existing families. This procedure makes use of the much larger amount of information contained in the proper elements catalogs, with respect to classifications using also physical observations for a smaller number of asteroids. Our work is based on the large catalog of the high accuracy synthetic proper elements (available from AstDyS). We first identify a number of core families; to these we attribute the next layer of smaller objects. Then, we remove all the family members from the catalog, and reapply the HCM to the rest. This gives both halo families which extend the core families and new independent families, consisting mainly of small asteroids. These two cases are discriminated by another step of attribution of new members and by merging intersecting families. By using information from absolute magnitudes, we take advantage of the larger size range in some families to analyze their shape in the proper semimajor axis vs. inverse diameter plane. This leads to a new method to estimate the family age (or ages). The results from the previous steps are then analyzed, using also auxiliary information on physical properties including WISE albedos and SDSS color indexes. This allows to solve some difficult cases of families overlapping in the proper elements space but generated by different collisional events. We analyze some examples of cratering families (Massalia, Vesta, Eunomia) which show internal structures, interpreted as multiple collisions. We also discuss why Ceres has no family.

1. Introduction

Asteroid-family classification can reveal collisional and dynamical evolution, but reliable interpretation requires large, accurate datasets and a distinction between dynamical groupings and collisionally formed families. The paper therefore develops an openly available classification designed for continual updating as asteroid catalogs grow.

  • Correctly identified asteroid families constrain parent-body properties, generating collisions, and subsequent dynamical evolution.
  • Family membership and boundaries are intrinsically uncertain because background asteroids create interlopers and marginal density contrasts prevent sharp borders.
  • A useful classification needs enough members, size range, and parameter accuracy to estimate family events, ages, parent sizes, fragment distributions, composition, and orbital transport.
  • Proper dynamical elements contain more information than physical observations because they are available for larger catalogs or with better relative accuracy.
  • 336 219 numbered asteroids had synthetic proper elements by November 2012, and the catalog grew 5.4% in five months to 354 467 objects.
  • The proposed workflow defines dynamical families from proper elements, uses physical data for confirmation or rejection, and automatically attaches newly numbered objects to existing families.

2. Dataset

The dataset combines a large synthetic proper-elements catalog with absolute magnitudes, albedos, colors, resonance information, and chaos indicators. These sources expand classification coverage but differ substantially in accuracy and availability, especially for physical measurements and difficult dynamical regions.

  • Synthetic proper elements a, e, and sin i were computed for 336 319 asteroids, with extra integrations targeting sparse high-eccentricity and high-inclination regions.
  • Proper-element instabilities at high proper e and sin I can make family classification dubious.
  • Absolute magnitudes span 15.7 magnitudes, but their accuracy is difficult to estimate because incidental photometry is heterogeneous.
  • Systematic photometric effects and lightcurve variability mean the 336 219 absolute-magnitude values have no reliable accuracy estimate, with guessed standard deviation 0.3 ÷ 0.5 magnitudes.
  • WISE provides albedos for 94 632 asteroids but has moderate relative accuracy, while SDSS colors are filtered by magnitude-error thresholds before analysis.
  • SDSS colors support broad C-, S-, and V-type discrimination and can help identify multiple collisional families or escaping objects, but are not reliable for individual-object colors.
  • Lyapunov exponents identify asteroids affected by comparatively short-timescale chaos, while resonance catalogs identify the specific mean-motion resonances involved.
  • Analytical proper elements degrade for e2 + sin2 I > 0.3 and beyond a > 3.2 au, so extended synthetic catalogs are recommended there.

3. Method for large dataset classification

The classification combines HCM with a multistep procedure designed for very large asteroid catalogs, reducing chaining and separating halo extensions from independent families. It uses zoned proper-element analysis, statistical thresholds, family intersections, and later updates to maintain a classification as new data arrive.

  • The asteroid belt is divided into heliocentric-distance zones, with some zones further split by proper inclination and bounded by dynamical structures.The zones use important mean-motion resonances and, where appropriate, inclination boundaries or stability gaps.
  • HCM identifies groups whose members are linked below a mutual-distance threshold, while minimum membership and critical-distance levels control candidate-family selection.The critical distance is estimated using quasi-random populations matched to the real distributions of proper a, e, and sin I.
  • The study extends the classical HCM approach with a multistep procedure that analyzes manageable subsets and links results across steps.The procedure addresses the difficulty of applying earlier HCM workflows directly to much larger asteroid samples.
  • After HCM processing, intersecting families are examined statistically; 34 of 77 step-3 families were classified as halos, while 43 remained independent families dominated by smaller asteroids.The number of multiply classified asteroids decreased from 1,042 to 29 after mergers.
  • The classification can automatically attach newly numbered asteroids, but decisions about mergers and possible statistical flukes remain non-automated and require reassessment as intersections change.An update adding 18,149 records produced 3,586 new step-4 members and increased double-family intersections from 29 to 36.
  • The resulting large-asteroid datasets are intended to preserve a stable public classification while improving analysis of small-asteroid phenomena, including cratering-family structure.The authors identify handling large numbers of small asteroids as a specific advantage of their datasets and methods.

4.1. Large families

Large families are expanded beyond core members by attaching smaller asteroids and halo families, revealing complex structures shaped by collisions and resonances. Several cases remain uncertain because family intersections and boundaries cannot be resolved automatically.

  • Scope: More than 1,000 members define a large family; 19 such families are reported.Table 3 lists their zones, QRL distances, step-wise membership counts, totals, and proper-element boundaries.
  • Classification growth: Attaching individual asteroids extends families toward smaller objects, while attaching smaller-asteroid families extends them in proper semimajor axis.The procedure can greatly increase membership beyond the core.
  • Classification growth: The Astraea core grows from 27 to 2,120 members through steps 2–5, with nearly all added members having H > 14.This illustrates how the procedure recovers many small asteroids around a small core.
  • Internal structures: Hertha contains disruption products from two parents, whereas Vesta reflects two or more cratering events on one parent body.Their complex projected shapes are difficult to model as single collisional events.
  • Resonances and halos: Massalia expands on both semimajor-axis sides through halo families, producing a bilobate shape associated with the 1/2 resonance with Mars.Chaotic orbits and diffusion along the resonance mark the dynamical influence.
  • Halo problems: Koronis has no halo because it lies between Jupiter’s 5/2 and 7/3 resonances, while Eunomia–Ino merging remains unreliable because only four intersections are found.Other ambiguous cases include Eos continuations and the unmerged 2076–883 and Baptistina cases.
  • Halo problems: The authors report 29 asteroids at family intersections and emphasize that halo attachment is neither automatic nor an absolute truth.Hoffmeister’s merger with family 14970 yields a shape difficult to reconcile with standard disruption followed by Yarkovsky evolution.

4.2. Medium families

Medium families contain enough members to represent real phenomena but often lack sufficient data for detailed structural and age analyses. Their interpretation is therefore family-specific and expected to improve as larger proper-element catalogs become available.

  • Scope: Medium families contain more than 100 and at most 1,000 members; 41 families are listed in Table 4.The table uses the same categories as Table 3 for this smaller membership range.
  • Interpretation: Their data may be insufficient for detailed age, size-distribution, internal-structure, and outlier analyses, although they are unlikely to be statistical flukes.Caution remains necessary when interpreting individual families.
  • Future growth: Families near the lower membership boundary are expected to grow as AstDyS applies the classification procedure to expanding proper-element datasets.Additional members may enable more information about their collisional histories.
  • Classification: Fourteen medium families were generated in step 3 from the intermediate background after removing step 1 and 2 members.These families are formed roughly from smaller asteroids.
  • Remarkable families: Hungaria, Phocaea, Euphrosyne, and Hansa are the largest high-inclination families, with membership near 1,000.Their high counts may support studies of collisional processes at higher relative velocities.
  • Data limitations: For family 480, paradoxical libration complicates proper-element computation, but the authors report no effect on family membership.The issue particularly affects proper e and the proper frequency g.
  • Remarkable families: Sylvia is well defined but has a central gap corresponding to Jupiter’s 9/5 resonance, and its dominant largest member is consistent with a cratering-event interpretation.The number of fragments removed by resonances remains unknown.

4.3. Small families

Small families are evaluated as provisional clusters whose membership may change as larger catalogs reveal halo relationships, independent status, or statistical weakness.

  • Small families contain 30–100 members, with data for 43 families presented in Table 5.
  • 29 of 41 small families were added in step 3 rather than absorbed as halo families.
  • Statistical tests identify these families as unlikely flukes, but most still require confirmation because small-number statistics limit available evidence.
  • The update procedure can confirm families, validate them physically or through modeling, attach them to larger halos, or reject them as non-collisional.
  • Overlapping proper-element boxes identify possible future mergers, including 12 complete inclusions and 17 additional cases exceeding 20% overlap.
  • A significant fraction of small families may join larger halos, while others may remain independent or be dismissed.

4.4. Tiny families

Tiny families have fewer than 30 members and are concentrated in low-density or high-inclination regions, where statistical reliability and observational completeness remain limited.

  • Tiny families contain fewer than 30 members, and Table 6 presents 25 such families.
  • The 25 tiny families occur mainly in low-density regions: 3 in zone 5, 1 in zone 6, 12 in zone 4 high inclination, and 9 in zone 3 high inclination.
  • Although these groups satisfy the standard HCM statistical requirements, low object counts make the minimum-member threshold especially influential.
  • Each tiny group remains only a proposed family because low densities reflect both fewer asteroids and strong observational biases.
  • 14 of 25 tiny families increased membership in the update, usually by only 1–2 objects.

5. Use of absolute magnitude data

Absolute magnitudes provide size estimates for asteroid-family members, enabling analyses of family volume, collisional age, and fragment size distribution when albedo information is available.

  • Diameter estimates from absolute magnitudes require albedo data, so accurate sizes are available mainly for asteroids with physical observations such as WISE or polarimetric measurements.
  • Family diameter statistics support estimation of total volume, collisional age, and fragment size distribution.

5.1. The volume of the families

Family-volume estimates use diameter and albedo assumptions to constrain parent-body or crater sizes, with Vesta and Hygiea illustrating the approach for cratering events.

  • For total fragmentation, family volume provides a lower bound on parent-body size; for cratering, it constrains the corresponding crater from below.
  • Vesta’s known family volume is estimated at 32 500–54 500 km3 depending on the assumed albedo, enabling identification of a possible source crater.
  • Hygiea’s family volume is 550 000 km3, implying a crater at least as large as Rheasilvia, although the family represents only 1.3% of Hygiea’s volume.

5.2. Family Ages

The paper estimates asteroid-family ages from V-shape slopes in proper semimajor axis versus inverse diameter, using automated fitting and Yarkovsky-based interpretation. Examples show that asymmetric slopes, resonances, substructures, and multiple collisional events can materially affect the age estimates.

  • Age estimation: Family ages are estimated from V-shape slopes in the proper semimajor axis versus inverse diameter plane, where Yarkovsky drift produces the size-dependent spread.Diameters are inferred from absolute magnitudes assuming a common geometric albedo; the Yarkovsky drift scales approximately as 1/D.
  • Multiple events: The method assumes all family members share one age, but superimposed V-shapes can reveal multiple collisional events with different ages.Agnia contains an inner subfamily V-shape inside the wider family V-shape.
  • Automated fitting: The new procedure fits both V-shape sides by iterative least-squares regression with automatic rejection of points whose residual exceeds 3σ.Rejected points may be interlopers or family members with inaccurate diameters.
  • Limitations and calibration: Age interpretation remains limited because fragment ejection velocities cannot be fully ignored, and Yarkovsky calibration is uncertain.The authors use asteroid (101955) Bennu as the benchmark because its Yarkovsky measurement and physical properties are best known.
  • Vesta: Vesta’s different fitted slopes indicate two collisional-event ages, with the event defining the high-a boundary older; overlapping substructures prevent measuring two additional slopes.The common albedo used for the Vesta fit was 0.423.
  • Resonance effects: Resonance truncation limits the usable size range and can make one slope less robust, although the Vesta age ordering remains reliable and its age ratio is approximately 2/1.The high-a side is affected by the 3/1 resonance and the low-a side by the 7/2 resonance.
  • Family examples: Eunomia’s two slopes differ by 31%, while Massalia’s age estimates from both slopes agree closely with an independent method.Eunomia’s outer-side fit is less accurate because the 8/3 resonance restricts the fitted range.
  • Agnia and Jitka: Agnia’s Jitka subfamily has inverse slopes more than nine times lower than the wider family, consistent with a much younger event if compositions are similar.The central depletion in Jitka’s V-shape is interpreted as a YORP-effect signature.

5.3. Size distributions

Size-distribution fits can indicate collisional evolution, but their interpretation is highly sensitive to the diameter range, incompleteness, small-number statistics, and family structure.

  • Methodological cautions: Size-distribution estimates are delicate because small diameters suffer incompleteness, large diameters suffer small-number statistics, and complex families require extra caution.These limitations make diameter-range selection central to interpreting family size distributions.
  • Family 20: Family 20 has a differential distribution proportional to 1/D5 and a cumulative distribution proportional to 1/D4, suggesting it has not reached collisional equilibrium.The result supports a comparatively young age, while the deficit below D < 1 km indicates observational incompleteness.
  • Interpretation: Concavity in cratering-family size distributions agrees with fragmentation models and depends qualitatively on the parent-body-to-largest-member size ratio.A larger ratio provides more volume for producing larger fragments, while slopes above 4 cannot persist to arbitrarily small diameters.

6. Refinement with physical data

Physical observations refine dynamical family classifications by distinguishing internal populations and overlapping families, although available data do not always resolve ambiguous boundaries.

  • Role of physical data: WISE albedos and SDSS colors help distinguish family subsets, families from local backgrounds, and overlapping dynamical families when catalogs are sufficiently consistent and complete.These physical data complement classifications based only on proper elements.
  • Hertha–Polana–Burdett: The Hertha dynamical family contains 11,428 members and a distinctive >-shape in proper a, e caused by two partly overlapping collisional families.The shape becomes more pronounced after adding smaller halo asteroids.
  • Hertha–Polana–Burdett: Hertha’s WISE albedo distribution is bimodal, separating 611 dark asteroids with albedo < 0.09 from 568 bright asteroids with albedo > 0.16.The two populations correspond to the Polana and Burdett components, while Hertha itself has intermediate albedo.
  • Hertha–Polana–Burdett: The Polana and Burdett components overlap significantly in high a, low e, and resonance-driven erosion leaves only portions of their original fragment clouds visible.Albedo data imply parent-body diameters greater than 76 km for Polana and 30 km for Burdett.
  • Hertha–Polana–Burdett: SDSS colors independently reproduce the two-component split, with 184 low-a∗ and 835 high-a∗ asteroids among 1,019 objects with usable colors.Negative a∗ corresponds to the low-albedo population and positive a∗ to the high-albedo population.
  • Limits of refinement: Hertha’s exclusion from both collisional families is not proven from the listed data alone and requires taxonomic information and suitable modeling.The paper identifies Hertha’s different composition as the basis for the presumption.
  • Limits of refinement: Physical observations do not always resolve dynamical ambiguities: Eos, Laodica, and 1999 NA41 remain difficult to separate, and neither merging nor keeping all families separate is fully satisfactory.The available observations do not support attaching families 507 and 31811 to 221 Eos.

7. Cratering families

The classification reveals internal structures in several cratering families, indicating multiple collisional events and complicating age interpretation. Physical data help identify interlopers and distinguish family components, but measurement limits remain important.

  • Accurate proper elements for small asteroids produce a classification containing many families formed by cratering events.
  • Massalia: Massalia’s asymmetric eccentricity and inclination distributions, together with low relative ejection velocities, argue against a single cratering event.
  • Massalia: Massalia’s dynamical family likely contains multiple collisional components, including a lower-e subfamily distinct from the denser high-e family.
  • Vesta: Vesta’s family is bounded by Jupiter’s 3/1 and 7/2 resonances, while an additional Mars 1/2 resonance helps define its low-e portion.
  • Vesta: Vesta’s high-e subfamily contains 2 538 members after excluding the low-e component and two identified interlopers.
  • Vesta: The two discordant Vesta ages correspond to different cratering events, although their uncertainties are dominated by the poorly known Yarkovsky calibration constant.
  • Vesta interlopers: V-type asteroids outside dynamical family 4 outnumber those inside by at least two to one, supporting widespread dispersal of older Vestoids.
  • Eunomia: Eunomia’s gap near a = 2.66 au and asymmetric family structure indicate that a single collision is insufficient, but separate ages are poorly constrained.

8. Binaries and couples

The paper examines whether binary asteroids concentrate in families and provides a large catalog of very close asteroid couples. Binary systems are not especially frequent among families overall, while close-couple statistics may reveal split-binary origins.

  • Binaries: Among 88 known main-belt binary or multiple asteroids, 17 are family members according to the classification.
  • Binaries: Family membership occurs for about 20% of binary asteroids, so binaries cannot be concluded to be particularly frequent among families.
  • Binaries: Binaries tend to be more abundant in the Koronis, Hungaria, and Themis families and among some families’ largest members.
  • Very close couples: The authors offer a dataset of 14 627 asteroid couples with proper-element distances below 10 m/s.
  • Very close couples: The distance histogram combines a quadratic component associated with random pairs and a linear component associated with phenomena such as split-binary drift.

9. Conclusions and Future Work

The enlarged dataset and multistep procedure produce qualitatively richer asteroid-family classifications while enabling ongoing updates. The analysis reveals clearer family structures, supports age estimation and cratering-family identification, and leaves merging and some physical interpretations as important limitations.

  • 9. Conclusions and Future Work: An enlarged dataset produces qualitative changes in family classifications, including internal structures revealed by larger numbers, smaller objects, and improved accuracy.The authors argue these changes are not merely an increase in the number of identified families.
  • 9. Conclusions and Future Work: The procedure retains HCM by combining it with a more complex multistep classification process.This addresses the chaining effect that can join distinct families when large proper-element datasets are used.
  • 9. Conclusions and Future Work: The method adds many smaller asteroids to core-family haloes without expanding families with larger members, yielding well-defined V-shapes and small-object cratering families.These V-shapes provide a basis for estimating family ages.
  • 9. Conclusions and Future Work: Merging remains subjective and non-automated, while future work includes collisional modeling, substructure searches, and testing family interpretations against spacecraft data.The Ceres interpretation remains plausible rather than uniquely established, pending further observations.
  • 9.4. Yarkovsky effect and ages: For most families large enough for statistically significant shape analysis, the V-shape is clearly visible, and the authors propose a more objective age method accounting for diameter errors from the common-albedo assumption.The method is presented as an improvement over previous age-estimation approaches.
  • 9. Conclusions and Future Work: Physical data can resolve overlapping dynamical families, as in the Hertha/Polana/Burdett complex, but incomplete physical coverage leaves classifications incomplete.The authors therefore prioritize dynamical parameters because they are more widely available and accurate.
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