Towards initial mass functions for asteroids and Kuiper Belt Objects

Our goal is to understand primary accretion of the first planetesimals. Some examples are seen today in the asteroid belt, providing the parent bodies for the primitive meteorites. The primitive meteorite record suggests that sizeable planetesimals formed over a period longer than a million years, each of which being composed entirely of an unusual, but homogeneous, mixture of millimeter-size particles. We sketch a scenario that might help explain how this occurred, in which primary accretion of 10-100 km size planetesimals proceeds directly, if sporadically, from aerodynamically-sorted millimeter-size particles (generically “chondrules”). These planetesimal sizes are in general agreement with the currently observed asteroid mass peak near 100 km diameter, which has been identified as a “fossil” property of the pre-erosion, pre-depletion population. We extend our primary accretion theory to make predictions for outer Solar System planetesimals, which may also have a preferred size in the 100 km diameter range. We estimate formation rates of planetesimals and explore parameter space to assess the conditions needed to match estimates of both asteroid and Kuiper Belt Object (KBO) formation rates. For parameters that satisfy observed mass accretion rates of Myr-old protoplanetary nebulae, the scenario is roughly consistent with not only the “fossil” sizes of the asteroids, and their estimated production rates, but also with the observed spread in formation ages of chondrules in a given chondrite, and with a tolerably small radial diffusive mixing during this time between formation and accretion. As previously noted, the model naturally helps explain the peculiar size distribution of chondrules within such objects. The optimum range of parameters, however, represents a higher gas density and fractional abundance of solids, and a smaller difference between Keplerian and pressure-supported orbital velocities, than “canonical” models of the solar nebula. We discuss several potential explanations for these differences. The scenario also produces 10-100 km diameter primary KBOs, and also requires an enhanced abundance of solids to match the mass production rate estimates for KBOs (and presumably the planetesimal precursors of the ice giants themselves). We discuss the advantages and plausibility of the scenario, outstanding issues, and future directions of research.     

Asteroid rotation and shapes from numerical simulations of gravitational re-accumulation

We present simulations of the gravitational collapse of a mono-disperse set of spherical particles for studying shape and spin properties of re-accumulated members of asteroid families. Previous numerical studies have shown that these “gravitational aggregates” exhibit properties similar to granular continuum models described by Mohr-Coulomb theory. A large variety of shapes is thus possible, in principle consistent with the observed population of asteroid shapes.However, it remains to be verified that the re-accumulation following a catastrophic disruption is capable of naturally producing those shapes. Conversely, we find that fluid equilibrium shapes (flattened two-axis spheroids, in particular) are preferentially created by re-accumulation. This is rather unexpected, since the dynamical system used could allow for other stable configurations. Jacobi three-axial ellipsoids can also be created, but this seems to be a less common outcome.The results obtained so far seem to underline the importance of other non-disruptive shaping factors during the lifetime of rubble-pile asteroids.     

Itokawa's cratering record as observed by Hayabusa: Implications for its age and collisional history

In this paper, we study cratering and crater erasure processes and provide an age estimate for the near-Earth Asteroid (25143) Itokawa, the target of the mission Hayabusa, based on its crater history since the time when it was formed in the main belt by catastrophic disruption or experienced a global resetting event. Using a model which was applied to the study of the crater history of Gaspra, Ida, Mathilde and Eros [O'Brien, D.P., Greenberg, R., Richardson, J.E., 2006. Icarus 183, 79–92], we calculate the time needed to accumulate the craters on Itokawa's surface, taking into account several processes which can affect crater formation and crater erasure on such a low-gravity object, such as seismic shaking. We use two models of the projectile population and two scaling laws to relate crater diameter to projectile size. Both models of the projectile population provide similar results, and depending on the scaling law used, we find that the time necessary to accumulate Itokawa's craters was at least ∼75 Myr, and maybe as long as 1 Gyr. Moreover, using the same model and similar parameters (scaled accordingly), we provide a good match not only to Itokawa's craters, but also to those of Eros, which has also been imaged at high enough resolution to give crater counts in a similar size range to those on Itokawa. We show that, as for Eros, the lack of small craters on Itokawa is consistent with erasure by seismic shaking, although for Itokawa, the pronounced deficiency of the smallest craters (<10 m in diameter) requires another process or event in addition to just seismic shaking. A small body such as Itokawa is highly sensitive to specific events that may occur during its history. For example, the two parts of Itokawa, called head and body, may well have joined each other by a low-velocity impact within the last hundred thousand years [Scheeres, D.J., Abe, M., Yoshikawa, M., Nakamura, R., Gaskell, R.W., Abell, P.A., 2007. Icarus 188, 425–429]. In addition to providing an erasure mechanism for small craters, the proposed timescale of that event is consistent with the timescale necessary in our model to form the current, depleted population of just a few small (<10 m) craters on Itokawa, suggesting that it may be the explanation for the discrepancy between Itokawa's cratering record and that obtained from our equilibrium seismic shaking model. Other explanations for the depletion of the smallest craters on Itokawa, such as armoring by boulders lying on the surface, cannot be ruled out.     

Combined effect of YORP and collisions on the rotation rate of small Main Belt asteroids

The rotation rate distribution of small Main Belt asteroids is dominated by YORP and collisions. These mechanism act differently depending on the size of the bodies and give rise to non-linear effects when they both operate. Using a Monte Carlo method we model the formation of a steady state population of small asteroids under the influence of both mechanisms and the rotation rate distribution is compared to the observed one as derived from Pravec et al. (Pravec, P. et al. [2008]. Icarus 197, 497-504). A better match to observations is obtained with respect to the case in which only YORP is considered. In particular, an excess of slow rotators is produced in the model with both collisions and YORP because bodies driven to slow rotation by YORP have a random walk-like evolution of the spin induced by repeated collisions with small projectiles. This is a dynamical evolution different from tumbling and it lasts until a large impact takes the body to a faster rotation rate. According to our model, the rotational fission of small asteroids is a very frequent event and might explain objects like P/2010 A2 and its associated tail of millimeter-sized dust particles. The mass loss during fission of small asteroids might significantly influence the overall collisional evolution of the belt. Fission can in fact be considered as an additional erosion mechanism, besides cratering and fragmentation, acting only at small diameters.     

Catastrophic disruption of pre-shattered parent bodies

In this paper, we analyze the effect of the internal structure of a parent body on its fragment properties following its disruption in different impact energy regimes. To simulate an asteroid breakup, we use the same numerical procedure as in our previous studies, i.e., a 3D SPH hydrocode to compute the fragmentation phase and the parallel N-body code pkdgrav to compute the subsequent gravitational re-accumulation phase. To explore the importance of the internal structure in determining the collisional outcome, we consider two different parent body models: (1) a purely monolithic one and (2) a pre-shattered one which consists of several fragments separated by damaged zones and small voids. We present here simulations spanning two different impact energy regimes—barely disruptive and highly catastrophic—corresponding to the formation of the Eunomia and Koronis families, respectively. As we already found for the intermediate energy regime represented by the Karin family, pre-shattered parent bodies always lead to outcome properties in better agreement with those of real families. In particular, the fragment size distribution obtained by disrupting a monolithic body always contains a large gap between the largest fragment and the next largest ones, whereas it is much more continuous in the case of a pre-shattered parent body. In the latter case, the ejection speeds of large fragments are also higher and a smaller impact energy is generally required to achieve a similar degree of disruption. Hence, unless the internal structure of bodies involved in a collision is known, predicting accurately the outcome is impossible. Interestingly, disrupting a pre-shattered parent body to reproduce the Koronis family yields a fragment size distribution characterized by four almost identical largest objects, as observed in the real family. This peculiar outcome has been found before in laboratory experiments but is obtained for the first time following gravitational re-accumulation. Finally, we show that material belonging to the largest fragments of a family originates from well-defined regions inside the parent body (the extent and location of which are dependent upon internal structure), despite the many gravitational interactions that occur during the re-accumulation process. Hence fragment formation does not proceed stochastically but results directly from the velocity field imparted during the impact.