- About PSI
Eileen V. Ryan and H.J. Melosh
In this paper, we study the effect of target size on the fragmentation outcome of rock targets using a 2D numerical hydrocode. After comparing our hydrocode calculations to laboratory data (including explosive disruption experiments) to validate the results, we use the code to calculate how the critical specific energy (Q*) needed to catastrophically fracture a body varies with target size in the regimes not accessible to experiment. Impact velocity is generally kept constant at about 2.0 krn s, although some higher velocity (~5 km s-1) simulations were run to determine a velocity dependence for the fragmentation outcome. To reflect the asteroid population, target diameters range from 10 cm to 1000 km, spanning the regimes where strength and self-gravity (radially varying lithostatic stress) each dominate resistance to fragmentation. We find that there is a significant difference in fragmentation outcome when the lithostatic stress is included in the computations. As expected, surface layers fragment more easily, while the strength of the central regions is greatly enhanced.
We derive the Q* versus size relationship for three materials, (basalt, strong, and weak cement mortar) each having different static compressive strengths, and representing a range of asteroid materials. The hydrocode results showed that Q* decreased with increasing target size in the strength regime, with slopes of 0.43, 0.59, and 0.6 for basalt, strong and weak mortar, respectively. This decrease is directly related to the decrease in strain rate as target size grows. In the gravity regime, Q* increases with increasing target size, with a slope equal to 2.6 for all three of the materials modeled. These values are much steeper than those previously derived from scaling theories.
Ejecta velocity distributions as a function of target size are examined as well. For large bodies, resultant ejecta speeds tend to be well below escape velocity, implying that these asteroids are likely to be reaccumulated rubble piles. In simulating the creation of the asteroid family Eos, we find that the code-calculated fragment size distribution is similar in character to the observed data, but secondary fragment sizes are significantly underestimated. More importantly, the determined ejecta speeds were too low for these fragments to have achieved escape velocity, and thus we fail to actually form the separate bodies comprising the Eos family, and are left instead with a single rubble-pile conglomerate.
S. J. Weidenschilling
Comets originated as icy planetesimals in the outer Solar System, as shown by dynamical studies and direct observation of objects in the Kuiper disk. Their nuclei have low strength consistent with "rubble pile" structure and inhomogeneities on scales of tens to hundreds of meters. These properties can be explained by their formation process in the solar nebula.
I present results of numerical simulation of the growth of cometesimals, beginning with a uniform mixture of microscopic grains in the nebular gas. Coagulation and settling yield a thin, dense layer of small aggregates in the central plane of the nebula. Shear between this layer and the pressure-supported gas produces turbulence that initially inhibits gravitational instability. Particles grow by collisional coagulation; relative velocities are dominated by radial motion due to orbital decay induced by gas drag. The radial velocity dispersion further delays gravitational instability until the mean particle size reaches tens of meters. Lack of damping in the swarm of macroscopic particles limits gravitational instability to 1arge scales that do not allow collapse to solid bodies. Collisional coagulation is responsible for growth even after instability occurs.
The size distribution of cometesimals growing by drag-induced collisions develops a narrow peak in the range tens to hundreds of meters. This occurs because drag-induced velocities decrease with size in this range, while gravitational focusing is negligible. Impact velocities have a minimum at the transition from drag-driven to gravitational accretion at approximately kilometer sizes. Bodies accreted in this manner should have low mechanical strength and macroscopic voids in addition to small-scale porosity. They will be composed of structural elements having a variety of scales, but with some tendency for preferential sizes in the range ~10-100 m. These properties are in good agreement with inferred properties of comets, which may preserve a physical record of their accretion.
Paolo Farinella and Donald R. Davis
Modeling results show that collisions among Edgeworth-Kuiper Belt Objects (EKOs), a vast swarm of small bodies orbiting beyond Neptune, have been a major process affecting this population and its progeny, the short-period comets. Most EKOs larger than about 100 kilometers in diameter survive over the age of the solar system, but at smaller sizes collisional breakup is frequent, producing a cascade of fragments having a power law size-frequency distribution. Collisions are also a plausible mechanism for injecting EKOs 1 to 10 kilometers in diameter into dynamical resonances, where they can be transported into the inner solar system to become short-period comets. The fragmental nature of these comets may explain their physical properties, such as shape, color, and strength.
D. R. Davis and P. Farinella
The Edgeworth-Kuiper Belt contains a population of objects ~103 times that of the main asteroid belt, spread over a volume ~103 larger and with relative speeds ~10 times lower. As for the asteroids, the size distribution of Edgeworth-Kuiper Belt objects has been modified by mutual impacts over Solar System history. We have modeled this collisional evolution process using a numerical code developed originally to study asteroid collisional evolution but modified to reAect collision rates in the Edgeworth-Kuiper Belt.
Our numerical simulations show that collisional evolution is substantial in the inner part of the Edgeworth-Kuiper Belt, but its intensity decreases with increasing distance from the Sun. In the inner belt, objects with diameters D > 50-100 km are not depleted by disruptive collisions; hence they reflect the original (formative) population (many of them, however, may have been converted into "rubble piles"). On the other hand, smal1er objects are mostly multigenerational fragments, although the original population must have contained a significant number of bodies down to at least a few tens of kilometers in size in order to initiate a collisional cascade. About 10 fragments, 1-10 km in size, are produced per year in the inner Edgeworth-Kuiper Belt, with a few percent of them inserted into chaotic resonant orbits. This is in rough agreement with the required influx rate of Jupiter-family comets. Both collisions and dynamical instabilities associated with resonances are processes that can inject comets into the "escape hatches," but our results indicate that most comets coming from the Edgeworth-Kuiper Belt would be fragments from larger parent bodies, rather than primitive planetesimals. However, this does not apply to Chiron-sized (D > 100 km) objects, which must be primordial and delivered to the outer Solar System by either dynamical processes or nondisruptive collisions.
S. J. Weidenschilling, D. Spaute, D. R. Davis, F. Marzari, and K. Ohtsuki
We use our multi-zone simulation code (D. Spaute, S. Weidenschilling, D. R. Davis, and F. Marzari, Icarus 92, 147-164, 1991) to model numerically the accretion of a swarm of planetesimals in the region of the terrestrial planets. The hybrid code allows interactions between a continuum distribution of small bodies in a series of orbital zones and a population of large, discrete planetary embryos in individual orbits. Orbital eccentricities and inclinations evolve independently, and collisional and gravitational interactions among the embryos are treated stochastically by a Monte Carlo approach. The spatial resolution of our code allows modeling of the intermediate stage when particle-in-a-box methods lose validity due to nonuniformity in the planetesimal sv arm. The simulations presented here bridge the gap between such early-stage models and N-body calculations of the final stage of planetary accretion.
The code has been tested for a variety of assumptions for stirring of eccentricities and inclinations by gravitational perturbations and the presence or absence of damping by gas drag. Viscous stirring, which acts to increase relative velocities of bodies in crossing orbits, produces so-called "orderly" growth, with a power-law size distribution having most of the mass in the largest bodies. Addition of dynamical friction, which tends to equalize kinetic energies and damp the velocities of the more massive bodies, produces rapid "runaway" growth of a small number of embryos. Their later evolution is affect perturbations between bodies in non-crossing orbits. Distant perturbations increase eccentricities while allowing inclinations to remain low, promoting collisions between embryos and reducing their tendency to become dynamically isolated. Growth is aided by orbital decay of smaller bodies due to gas drag, which prevents them from being stranded between orbits of the embryos.
We report results of a large-scale simulation of the region of terrestria1 planets, employing 100 zones spanning the range 0.5 to 1.5 AU and spanning 106 years of model time. The final masses of the largest bodies are several times larger than predicted by a simple analytic model of runaway growth, but a minimal-mass planetesimal swarm still yields smaller bodies, in more closely spaced orbits, than the actual terrestrial planets. Longer time scales, additional physical phenomena, and/or a more massive swarm may be needed to produce Earth-like planets.
Dominique Spaute, Stuart J. Weidenschilling, Donald R. Davis, and Francesco Marzari.
We describe a new simulation for planetary accretion which treats simultaneous accretion in many interacting heliocentric distance zones, rather than the single one characteristic of earlier models. The planetesimals are characterized by keplerian elements rather than a single "random velocity." This numerical code can follow the evolution of both the size distribution and the orbit element distribution of a planetesimal swarm from any initial distributions of sizes and orbits. It also can treat a small number of the largest bodies as discrete objects with individual orbits, rather than as part of the continuum size distribution. We describe the structure of this model, results of testing the code against two analytic solutions of the coagulation equation, and comparison of our results with those of other workers. We find that our accretion algorithm yields good agreement with the analytic solutions. We also find agreement with the results of Wetherill and Stewart (1989, Icarus 77, 330-357) for gravitational accretion of planetesimals with equivalent initial conditions. In addition, we demonstrate accretion in multiple heliocentric zones.
William K. Hartmann and Donald R. Davis
Exploratory calculations using accretionary theory are made to demonstrate plausible sizes of second-largest, third-largest, etc., bodies at the close of planet formation in heliocentric orbits near the planets, assuming asteroid-like size distributions at the start of the calculation. Many satellite-sized bodies are found to be available for capture, cratering, or collisional fragmentation. In the case of Earth-sized planets, the models suggest second-largest bodies of 500 to 3000 km radius, and tens of bodies larger than 100 km radius. Many of these interact with the planet before suffering any fragmentation events with each other. Collision of a large body with Earth could eject iron-deficient crust and upper mantle material, forming a cloud of refractory, volatile-poor dust that could form the Moon. Other satellite systems may have been affected by major capture or co1lision events of chance character.