Cometary nuclei internal structure from early aggregation simulations

Abstract

A new model for the aggregation of cometesimals in the primordial solar nebula is proposed. The simulation of the aggregation takes into account disruptive and sticking effects of impacts on the aggregates properties together with the temporal evolution of cohesive strength during accretion due to sintering processes. Different regimes of aggregation are obtained depending on the value of the homogeneity exponent, μ, that indicates the fraction of kinetic energy available for cohesive energy dissipation during an impact. Porous fractal aggregates with different cohesive strength blocks are formed for 0 < μ < 0.4, while they are compact with a layered structure of different strengths for 0.4 < μ < 0.6 and weak ‘rubble piles’ for 0.6 < μ < 1. Cohesive strength estimations of the final cometary nuclei obtained give values generally lower than 10 kPa. The layered aggregates present the highest global cohesive strength, increasing their probability to survive collisions or moderate tidal stress. These results compare well with the structural and cohesive properties of comets deduced from observations and laboratory simulations.

Introduction

Remote observations of cometary nuclei are limited: on the one hand, these small icy bodies (with sizes below a few kilometers) are reduced to bright spots in the field of view of large telescopes when they are far away from the Sun and thus the Earth, on the other hand, they are hidden under a coma of dust and gases when they get closer to the Sun and the Earth. As far as in situ studies are concerned, observations have been, up to now, made during the flybys of five nuclei, with images retrieved only for 1P/Halley, 19P/Borrelly, 81P/Wild 2 and 9P/Tempel 1, respectively, by Giotto and Vega in 1986 (Keller et al., 1986, Sagdeev et al., 1986), Deep Space 1 in 2001 (Soderblom et al., 2002, Britt et al., 2004), Stardust in 2004 (Brownlee et al., 2004) and Deep Impact in 2005 (A’Hearn et al., 2005, Thomas et al., 2007). Information about their internal structure can be tentatively inferred from an analysis of the surfaces features, as well as from estimations of the densities and the observation of study of fragmentation processes (see, e.g., Rickman et al., 1987, Boehnhardt, 2004, Levasseur-Regourd et al., 2006).

A comparison of images of the above-mentioned nuclei reveals a significant diversity in overall shapes, the nuclei of 81P/Wild 2 and 9P/Tempel 1 being much less elongated than those of 1P/Halley and 19/Borrelly. The highest resolution images yet obtained are those of 9P/Tempel 1, which reveal numerous unexpected topographic features such as crater-like depressions, extensive surface erosion, and very smooth terrains (Thomas et al., 2007). These latter features have been proposed to originate either in recent fluid flows (Thomas et al., 2007, Goguen et al., 2008) or to correspond to primitive layers that were originally laid down during the formation of the nucleus (Belton et al., 2007).

As far as the density is concerned, it has to be noticed that no significant gravitational perturbations from a nearby cometary nucleus have ever been detected on solar system bodies or spacecraft. The density of comet nuclei has actually been estimated through modeling of non-gravitational force induced by the sublimation of ices. This approach has allowed Rickman et al. (1987) to derive a bulk value below 500 kg m⁻³ for about 30 short-period comets. More recently, a density of (450 ± 250) kg m⁻³ has been derived for 9P/Tempel 1 (Davidsson et al., 2007), in agreement with the value of 400 (200–1000) kg m⁻³ derived from the modeling of the expansion of the cloud released by the impactor (Richardson et al., 2007). It is generally estimated that the densities of these icy bodies remain within the 100–1000 kg m⁻³ range (see, e.g., Weissman et al., 2004, Blum et al., 2006 and references therein). Thus, they present quite low a packing density and a very high micro- and/or macro-porosity (Levasseur-Regourd et al., 2009).

Numerous comets have been observed to fragment, i.e., to release active fragments that display mini-comae, while a couple of comets have disappeared after a complete disruption (see, e.g., Boehnhardt, 2004). The most conspicuous example of a complete disruption has been that of D/1993 F1 Shoemaker-Levy 9, which tidally split at its Jupiter periapsis in 1992 (Asphaug and Benz, 1994, Asphaug and Benz, 1996). Comet C/1999 S4 LINEAR also suffered a complete disruption after an outburst in brightness in July 2000 (see, e.g., Kidger, 2002 and references therein). The numerous condensations around its icy fragments (with sizes below about 50 m) survived for more than two weeks (Farnham et al., 2001, Weaver et al., 2001). Partial fragmentation of nuclei has been noticed for many comets. A noticeable example has been that of C/1996 B2 Hyakutake, while it was passing not too far from Earth. The study of the motion of the multiple evaporating icy fragments observed in the anti-solar direction has shown that the size of the biggest fragment was in a 60–160 m range and that it was accompanied by several fragments with sizes around 20 m (Desvoivres et al., 2000). More recently, cascading fragmentations have been observed for 73P/Schwassmann-Wachmann 3 (Crovisier et al., 1996, Toth et al., 2005).

Many cometary nuclei actually seem to be fragile and to present mechanical weakness and low tensile strengths. The surface layers of some nuclei may break off in meter or sub-meter sized fragments. Although the deep interior structure of the nucleus has not yet been probed, it may be suspected that some nuclei are gravitational aggregates of smaller bodies (so-called rubble piles), while other ones could be more compact (see, e.g., Weissman et al., 2004 and references therein).

Numerical simulations of aggregation of planetesimals in the early solar system nebula suggest that comets could have been formed by collisional coagulation rather than through gravitational instability. In the Weidenschilling (1997) one-dimensional model, the cometesimals that aggregate into the final comet nuclei follow a bimodal size distribution with small particles (size below 1 m) and large aggregates (with a preferential size within the range 10–100 m). The impact velocities between the cometesimals go from 10 to 100 m s⁻¹. In Weidenschilling (2004), a two-dimensional model of nebular accretion gives the same ranges of velocities and sizes with a more regular size distribution. However, a radial drift occurs and prevents the formation of large objects further than 50 AU from the Sun. The formation of the observed cometary nuclei, with sizes of a few kilometers, can be obtained from hierarchical accretion, resulting in ‘rubble pile’, i.e., gravitational aggregates structures (see, e.g., Sirono and Greenberg, 2000, Weissman et al., 2004 and references therein). These structures are most probably the result of collisions that occurred during ejection of the comets to the Oort cloud (Stern and Weissman, 2001) or collisions within the Kuiper belt (see, e.g., Duncan et al., 2004).

Numerical models of cometesimal rubble piles have previously been performed by random accretions of cometesimals, in order to explain the irregular shapes of the cometary nuclei (Jewitt and Meech, 1988). Such aggregation processes lead to the formation of fluffy aggregates (Donn, 1990) with irregular shapes, low internal density and significant internal density variations. It is expected that such fluffy aggregates dissipate kinetic energy efficiently during collision processes (see, e.g., Donn and Duva, 1994, Asphaug, 1999). This efficiency may be affected by sintering between the cometesimals constituting the aggregates (Sirono, 1999). To our knowledge, the consequences of sintering due to the kinetic energy dissipation on the internal structure and cohesive strength of collisional aggregates of cometesimals have not been studied up to now. The internal structure of such aggregates could present variations in cohesive strength, leading to the formation of layers of different strengths such as those that were observed on the surface of Comet 9P/Tempel 1, as discussed in Section 1.1.

Laboratory experiments conducted by Bridges et al. (1996) have shown a significant enhancement of energy loss and of sticking probability between particles during the collision process, when the particles are covered with low temperature volatile ice frost. These experiments suggested hard collisions in which part of the material is compressed and another part is ejected as a way to produce bound aggregates. Moreover, results from impact experiments between dust aggregates at about 25 m s⁻¹ by Wurm et al. (2005) have shown that for those kinds of velocities (realistic in the context of the protosolar nebula formation), almost half of the projectile mass rigidly sticks to the target after the collision. Such results show that in order to obtain a runaway growth of the planetesimals larger than 1 cm in size, both sticking and disruption of the impacting aggregates should be taken into account.

In the model presented here, the disruption of the aggregates is obtained by considering that some fraction of the kinetic energy is used to disrupt the aggregates around the impact location. Moreover, bonding between the constituents of the resultant aggregate appears because of sintering due to kinetic energy loss through the material. Such a sintering process between coalesced cometesimals is introduced for the first time in this paper and gives information on the values of the parameters for which realistic aggregates are obtained. The second section of this paper describes in details the hypotheses made and the algorithm implemented for the simulations. Then the results of the calculations for the aggregation of up to 50,000 cometesimals with quantitative estimations of the cometary material properties are presented. Finally, the results are discussed in the light of previous property determinations from simulations and observations.