Planetesimal Evolution and the Formation of Terrestrial Planets

Title of Dissertation: Planetesimal Evolution and the Formation of Terrestrial Planets Zoë Malka Leinhardt, Doctor of Philosophy, 2005 Dissertation directed by: Dr. Derek C. Richardson Department of Astronomy To create an accurate numerical model of solar system formation it is necessary to understand how planetesimals, the planetary building blocks, evolve and grow into larger bodies. Traditionally, numerical simulations of planet formation have used extrapolations of impact experiments in the strength regime to model the effects of fragmentation in planetesimal collisions (e.g. Greenberg et al. 1978; Beaugé & Aarseth 1990; Wetherill & Stewart 1993). However, planetesimals, which are large enough to decouple from the gaseous nebula, are dominated by self-gravity not material strength (Holsapple 1994). As a result, such extrapolations may give misleading results since much more energy is needed to disperse than to disrupt a planetesimal in the gravity regime. Moreover, the effects of impact angle, spin, and impactor mass ratio are often not taken into account. In order to determine the effects of various collision parameters, I have completed several parameter-space studies of collisions between kilometer-sized planetesimals. The planetesimals are modeled as “rubble piles”—gravitational aggregates of indestructible particles bound together purely by gravity. These rubble pile planetesimals have no tensile strength. I find that as the ratio of projectile to target mass departs from unity the impact angle has less effect on the collision outcome. At the same time, the probability of planetesimal growth increases. Conversely, for a fixed impact energy, collisions between impactors with mass ratio near unity are more dispersive than those with mass ratio far from unity. Net accretion dominates the outcome in slow head-on collisions while net erosion dominates for fast off-axis collisions. The dependence on impact parameter is almost as important as the dependence on impact speed. Off-axis collisions can result in fast-spinning elongated remnants or contact binaries while fast collisions result in smaller fragments overall. Clumping of debris escaping from the post-collision remnant can occur, leading to the formation of smaller rubble piles. In the cases tested, less than 2% of the system mass ends up orbiting the remnant. Initial spin can reduce or enhance collision outcomes, depending on the relative orientation of the spin and orbital angular momenta. For an average mass ratio of 1:5, the accretion probability is ∼ 60% over all impact parameters. Results are presented from a dozen direct N -body simulations of terrestrial planet formation with various initial conditions. In order to increase the realism of the simulations and investigate the effect of fragmentation on protoplanetary growth, a self-consistent planetesimal collision model was developed that includes fragmentation and accretion of debris. The collision model is based on the rubblepile planetesimal model developed and investigated in the parameter space studies summarized above. The results are compared to the best numerical simulations of planet formation in the literature (Kokubo & Ida 2002) in which no fragmentation is allowed—perfect merging is the only collision outcome. After 400,000 years of integration our results are virtually indistinguishable from those of Kokubo & Ida (2002). We find that the number and masses of protoplanets, and time required to grow a protoplanet, depends strongly on the initial conditions of the disk and is consistent with oligarchic theory. The elasticity of the collisions, which is controlled by the normal component of the coefficient of restitution, does not significantly affect planetesimal growth over a long timescale. In contrast to the suggestion by Goldreich et al. (2004), it appears that there is negligible debris remaining at the end of oligarchic growth, where “debris” is defined to be those particles smaller than our resolution that are modeled semi-analytically. I have also looked to the small bodies currently in our solar system to help constrain its evolution. Asteroids and comets are the closest remnants in our solar system to the original building blocks of planets. Understanding the dynamics and evolution of these objects will also place constraints on the initial conditions of planet formation models. The most can be learned from binary and multiple systems since they provide mass and density information. High-resolution simulations of binary asteroid formation produce a tremendous amount of data, making it difficult to look for binary and multiple systems. I present a new code (companion) that identifies bound systems of particles in O(N logN) time. In comparison, brute-force binary search methods scale as O(N2) while full hierarchy searches can be as expensive as O(N3), making analysis highly inefficient for multiple data sets with N > 10. A simple test case is provided to illustrate the method. Timing tests demonstrating O(N logN) scaling with the new code on real data are presented. The method is applied to data from asteroid satellite simulations (Durda et al. 2004) and previously unknown multi-particle configurations are noted. Planetesimal Evolution and the Formation of Terrestrial Planets