The number of asteroids with accurately determined orbits increases fast, and this increase is also accelerating. The catalogs of asteroid physical observations have also increased, although the number of objects is still smaller than in the orbital catalogs. Thus it becomes more and more challenging to perform, maintain and update a classification of asteroids into families. To cope with these challenges 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), containing data for > 330 000 numbered asteroids. By selecting from the catalog a much smaller number of large asteroids, 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. This leads to a classification with 128 families and currently 87095 members; the number of members can be increased automatically with each update of the proper elements catalog. 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 in cases where we identify internal structures. The analysis of the plot above evidences some open problems but also the possibility of obtaining further information of the geometrical properties of the impact process. 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.The families formed by one or more cratering events are found to be more numerous than previously believed because the fragments are smaller. 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. 6 According to [Ivezić et al. 2001] the first principal component in the r − i vs g − r plane is defined as a * = 0.89(g − r) + 0.45(r − i) − 0.57. 7 Every asteroid is affected by chaotic effects over timescales comparable to the age of the solar system, but this does not matter for family classification.

To try to understand the dynamical and collisional evolution of the Hungaria asteroids we have built a large catalog of accurate synthetic proper elements. Using the distribution of the Hungaria, in the spaces of proper elements and of proper frequencies, we can study the dynamical boundaries and the internal structure of the Hungaria region, both within a purely gravitational model and also showing the signature of the non-gravitational effects. We find a complex interaction between secular resonances, mean motion resonances, chaotic behavior and Yarkovsky-driven drift in semimajor axis. We also find a rare occurence of large scale instabilities, leading to escape from the region. This allows to explain the complex shape of a grouping which we suggest is a collisional family, including most Hungaria but by no means all; we provide an explicit list of non-members of the family. There are finer structures, of which the most significant is a set of very close asteroid couples, with extremely similar proper elements. Some of these could have had, in a comparatively recent past, very close approaches with low relative velocity. We argue that the Hungaria, because of the favourable observing conditions, may soon become the best known subgroup of the asteroid population.

In this work we have estimated 10 collisional ages of 9 families for which for different reasons our previous attempts failed. In general, these are difficult cases that required dedicated effort, such as a new family classifications for asteroids in mean motion resonances, in particular the 1/1 and 2/1 with Jupiter, as well as a revision of the classification inside the 3/2 resonance.Of the families locked in mean motion resonances, by employing a numerical calibration to estimate the Yarkovsky effect in proper eccentricity, we succeeded in determining ages of the families of (1911) Schubart and of the "super-Hilda" family, assuming this is actually a severely eroded original family of (153) Hilda. In the Trojan region we found families with almost no Yarkovsky evolution, for which we could compute only physically implausible ages. Hence, we interpreted their modest dispersions of proper eccentricities and inclinations as implying that the Trojan asteroid families are fossil families, frozen at their proper elements determined by the original ejection velocity field. We have found a new family, among the Griquas locked in the 2/1 resonance with Jupiter, the family of (11097) 1994 UD1.We have estimated the ages of 6 families affected by secular resonances: families of (5) Astraea, (25) Phocaea, (283) Emma, (363) Padua, (686) Ger- suind, and (945) Barcelona. By using in all these cases a numerical calibration method, we have shown that the secular resonances do not affect significanly the secular change of proper a. For the family of (145) Adeona we could estimate the age only after removal of a number of assumed interlopers.With the present paper we have concluded the series dedicated to the determination of asteroid ages with a uniform method. We computed the age(s) for a total of 57 families with > 100 members. For the future work there remain families too small at present to provide reliable estimates, as well as some complex families (221, 135, 298) which may have more ages than we could currently estimate. Future improvement of some already determined family ages is also possible by increasing family membership, revising the calibrations, and using more reliable physical data.

We present a new classification of families identified among the population of high-inclination asteroids. We computed synthetic proper elements for a sample of 18,560 numbered and multi-opposition objects having sine of proper inclination greater than 0.295. We considered three zones at different heliocentric distances (inner, intermediate and outer region) and used the standard approach based on the Hierarchical Clustering Method (HCM) to identify families in each zone. In doing so, we used slightly different approach with respect to previously published methodologies, to achieve a more reliable and robust classification. We also used available SDSS color data to improve membership and identify likely family interlopers. We found a total of 38 families, as well as a significant number of clumps and clusters deserving further investigation.Comment: Accepted by Icaru

We present a transport model that describes the orbital diffusion of asteroids in chaotic regions of the three-dimensional space of proper elements. Our goal is to use a simple random-walk model to study the evolution and derive accurate age estimates for dynamically complex asteroid families. To this purpose, we first compute local diffusion coefficients, which characterize chaotic diffusion in proper eccentricity (e p ) and inclination (I p ), in a selected phase-space region. Then, a Monte Carlo type code is constructed and used to track the evolution of random walkers (i.e. asteroids), by coupling diffusion in (e p , I p ) with a drift in proper semimajor axis (a p ) induced by the Yarkovsky/YORP thermal effects. We validate our model by applying it to the family of (490) Veritas, for which we recover previous estimates of its age (∼8.3 Myr). Moreover, we show that the spreading of chaotic family members in proper element space is well reproduced in our random-walk simulations. Finally, we apply our model to the family of (3556) Lixiaohua, which is much older than Veritas and thus much more affected by thermal forces. We find the age of the Lixiaohua family to be 155 ± 36 Myr.