Protoplanet Collisions: Statistical Properties of Ejecta

Abstract

The last phase of the formation of rocky planets is dominated by collisions among Moon- to Mars-sized planetary embryos. Simulations of this phase need to handle the difficulty of including the post-impact material without saturating the numerical integrator. A common approach is to include the collision-generated material by clustering it into few bodies with the same mass and uniformly scattering them around the collision point. However, this approach oversimplifies the properties of the collision material by neglecting features that can play important roles in the final structure and composition of the system. In this study, we present a statistical analysis of the orbital architecture, mass, and size distributions of the material generated through embryo-embryo collisions and show how they can be used to develop a model that can be directly incorporated into the numerical integrations. For instance, results of our analysis indicate that the masses of the fragments follow an exponential distribution with an exponent of $-2.21\pm 0.17$ over the range of $10^{-7}$ to $2\times 10^{-2}$ Earth-masses. The distribution of the post-impact velocities show that a large number of fragments are scattered toward the central star. The latter is a new finding that may be quite relevant to the delivery of material from the outer regions of the asteroid belt to the accretion zones of terrestrial planets. Finally, we present an analytical model for the 2D distribution of fragments that can be directly incorporated into numerical integrations.

10 pages, 13 figures, accepted for publication in MNRAS

References in corpus (9)

• The NumPy array: a structure for efficient numerical computation
• Debris from giant impacts between planetary embryos at large orbital radii
• The early instability scenario: terrestrial planet formation during the giant planet instability, and the effect of collisional fragmentation
• Chemical Diversity of Super-Earths As a Consequence of Formation
• Atmospheric Erosion by Giant Impacts onto Terrestrial Planets: A Scaling Law for any Speed, Angle, Mass, and Density
• Formation of compact systems of super-Earths via dynamical instabilities and giant impacts
• Transfer, loss and physical processing of water in hit-and-run collisions of planetary embryos
• Realistic collisional water transport during terrestrial planet formation: Self-consistent modeling by an N-body--SPH hybrid code
• Water worlds in N-body simulations with fragmentation in systems without gaseous giants