A. Cellino

Wavy size distributions for collisional systems with a small-size cutoff

Abstract Dohnanyis [ J. geophys. Res . 74 , 2531–2554, 1969; in Physical Studies of Minor Planets (edited by T. Gehrels), pp. 263–295. NASA-SP 267, 1971] theory predicts that a collisional system such as the asteroid population should rapidly relax to a power-law equilibrium size distribution, provided all the collisional response parameters are independent of size. However, we have found that Dohnanyi did not include in a consistent way in the theory the possible occurrence of a small-size cutoff in the distribution. We have carried out a number of numerical simulations of the collisional evolution process, showing that the cutoff results in a wavy pattern superimposed on Dohnanyis equilibrium power law, which affects the distribution up to sizes of tens of km. The pattern arises because particles just above the cutoff are not removed by catastrophic impacts by smaller projectiles, and therefore are created by break-up of larger bodies faster than they are eliminated; larger particles are increasingly depleted up to the size where the smallest shattering projectile exceeds the cutoff, and beyond that the removal rate is reduced and the distribution flattens. Thus, to be effective in producing the waves, the cutoff (or any other persisting “discontinuity” in the particle properties) must be sharp over a size range corresponding to the threshold projectile-to-target ratio for fragmentation. The presence of a small-size cutoff in the real asteroid belt is an open question, since it may be generated by poorly known non-gravitational effects acting on μm-sized dust, and may be affected by influx of cometary debris. However, the observational evidence for a variable characteristic exponent of the size distribution of interplanetary bodies is now strong, and the cutoff effect may provide a simple explanation for this finding.

Asteroid families classification: Exploiting very large datasets

Abstract 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 a large catalog of 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 satellite 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 87,095 members. The number of members can be increased automatically with each update of the proper elements catalog; changes in the list of families are not automated. 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.

THE STATISTICAL ASTEROID MODEL. I. THE MAIN-BELT POPULATION FOR DIAMETERS GREATER THAN 1 KILOMETER

We describe the creation of a model of the main asteroid belt whose purpose is to describe the main-belt asteroid size frequency distribution and simulate the number of main-belt asteroids and their fluxes at visual through mid-infrared (~0.3–70 μm) wavelengths in any area of sky for an arbitrary date. This model is based on a population of ~1.9 × 106 asteroids obtained from the complete known asteroid sample, plus extrapolation of the size-frequency distributions of 15 asteroid dynamical families and three background populations, to a diameter limit of 1 km. The model is compared with data and other models, example applications are given, planned refinements and extensions to the model are presented, and some implications of the resulting size frequency distribution are discussed.

Asteroid photometric and polarimetric phase curves: empirical interpretation

Abstract A method for interpretation of asteroid phase curves, based on empirical modeling and laboratory measurements, is outlined and preliminary results are presented. A linear–exponential function is used to describe the opposition peaks and negative polarization surges of various asteroids and laboratory samples and a statistical algorithm is used in parameter estimation. The linear–exponential function describes well the phase curves, but dense phase angle coverage, particularly at small phase angles must be obtained to improve the results. Major emphasis should also be put on laboratory study: with an extensive library of laboratory measurements, a stronger connection between the phase curve properties and surface characteristics is possible.

Families among high-inclination asteroids

Abstract 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.

The formation of binary asteroids as outcomes of catastrophic collisions

Abstract A semi-empirical model of catastrophic break-up processes among asteroids is used to investigate the possibility that binary asteroids could be formed by collisional events. In particular, numerical integrations of the dynamical evolution of fragments under the effect of mutual gravitational interactions after ejection are performed for a set of simulations, in order to detect the possible formation of binary systems. The results suggest that the occurrence of binaries formed by couples of fragments of comparable mass is fairly rare. Therefore it is estimated that such systems could exist but they should not be very frequent in the asteroid belt. On the other hand, binaries with very small mass ratios, like the Ida-Dactyl binary system, might be more frequent. However, in these cases fragments are dealt with in a size range which is poorly sampled by the model. For this reason, some more detailed analysis seems necessary for assessing more reliably the efficiency of break-up phenomena as sources of Ida-Dactyl-like systems.

Flattening, pole, and albedo features of 4 vesta from photometric data

Abstract A number of large asteroids show irregular lightcurves of relatively small amplitude and/or ambiguous rotational periods. These observations and the fact that their strong gravitational binding probably results in quasi-equilibrium shapes lead to model these bodies as axisymmetric, biaxial ellipsoids covered by albedo markings. We developed a general numerical algorithm for obtaining simulated lightcurves of “spotted” asteroids and varied the most critical geometrical and physical parameters (albedo contrast, size, and position of the spots; polar coordinates, and shape of the asteroid). We then analyzed the case of 4 Vesta by assuming an axisymmetric ellipsoidal shape with a large brighter region on one hemisphere, in agreement with the results of photometric and polarimetric observations. Fitting the numerical simulations to the available data, we obtained the flattening of the ellipsoid (0.79 ± 0.03), the albedo contrast and geometry of the brighter region, and the orientation of the polar axis. If the derived flattenning corresponds to the equilibrium shape of a nearly homogeneous body, a density of 2.4 ± 0.3 g cm −3 can be inferred. These results show satisfactory agreement with values by different techniques. We plan to apply the same method both to other large asteroids and to smaller, irregularly shaped ones; in the latter case, this will allow us to test the uncertainties in current pole determination methods.

Rotational properties of outer belt asteroids

Abstract We present new photometric observations of 13 asteroids (153, 190, 225, 279, 334, 420, 483, 528, 588, 692, 721, 940, 1583) orbiting in the outer part of the belt, beyond the Hecuba gap at 3.3 AU from the Sun. The resulting periods and amplitudes are then used to compare the properties of a main-belt asteroid sample and an outer-belt sample at similar sizes. The outer-belt sample includes objects which are likely to have been affected less by collisional evolution and to have retained a better record of their “primordial” features. The distributions of rotational periods are not different at a statistically significant level; however, the outer-belt sample does not include the “population” of show rotators which make the main-belt distribution markedly non-Maxwellian. As already pointed out by L. M. French (1987 Icarus 72,325) and W. K. Hartmann and coworkers (1988, Icarus 73, 487) for Trojans and Hildas, amplitudes in the outer belt are clearly higher than in the main belt. We suggest that elongated shapes might have been frequent among planetesimals in the outer belt, as a consequence of smaller impact velocities and lower densities than for the present main-belt asteroids.

Asteroid shapes and lightcurve morphology

Abstract In order to systematically analyze the influence on asteroidal photometric lightcurves of large-scale deviations from triaxial ellipsoidal shapes, a general model is needed for which the variation of a few parameters can describe a wide range of irregular but “realistic” shapes. We adopted a model formed by merging together eight octants of ellipsoids having different semiaxes, with the constraint that adjacent octants must have two equal semiaxes in common. The corresponding lightcurves can then be computed by approximating the surface with a polyhedron formed by a finite number of plane facets. In several cases very irregular lightcurves are obtained, showing intriguing analogies with some puzzling lightcurves of real asteroids. In particular, the variation of lightcurve morphology with aspect angle can lead to changes in the number of extrema and/or an inversion of them, possibly implying an incorrect estimate of the spin axis direction and of the rotation period.

RUBBLE-PILE RESHAPING REPRODUCES OVERALL ASTEROID SHAPES

There have been attempts in the past to fit the observed bulk shapes (axial ratios) of asteroids to theoretical equilibrium figures for fluids, but these attempts have not been successful in many cases, evidently because asteroids are not fluid bodies. So far, however, the observed distribution of asteroid macroscopic shapes has never been attributed to a common cause. Here, we show that a general mechanism exists, capable of producing the observed shape distribution. We base our approach on the idea that aggregates of coherent blocks held together mostly by gravity (gravitational aggregates) can change their shape under the action of external factors, such as minor collisions, that break the interlocking of the constituent blocks, thus allowing them to asymptotically evolve toward fluid equilibrium. We show by numerical simulations that this behavior can produce a shape distribution compatible with the observations. Our results are shown to be consistent with a simple interpretation based on the topology of the potential energy field for rotating bodies. Also, they suggest that most asteroids have an internal structure that is at least partially fragmented, consistent with constraints derived from large asteroids (diameters >100 km) with satellites.