Diverse Impact Outcomes and Compositional Changes during the End Stage of Terrestrial Planet Formation

Numerical simulations of the end stage of planet formation typically begin with a population of planetary embryos and planetesimals that grow into planets by merging. In these simulations, the growth of Earth-mass planets is dominated by giant impacts between embryos. We analyze the impact parameters of collisions leading to the growth of terrestrial planets from recent N-body simulations that assumed perfect merging^1,2 and predict the actual collision outcomes using a new analytic model³. We find that collision outcomes are diverse and span all possible regimes: hit-and-run, merging, partial accretion, partial erosion, and catastrophic disruption. The primary outcomes of giant impacts between planetary embryos are approximately evenly split between partial accretion, merging, and hit-and-run events. In hydrocode simulations of partial accretion events, the target body grows by preferentially accreting the iron core of the projectile and the escaping fragments are derived primarily from the silicate mantles of both bodies^4,5. Thus, the bulk composition of a planet can evolve via stochastic giant impacts. In addition, the time scale for planet growth may be significantly longer than found in current N-body studies. Here, we model terrestrial planet growth with a Monte Carlo technique using the distribution of impact parameters from N-body simulations. We calculate the probability distribution of final planet masses and core-to-mantle mass ratios using the new collision outcome model. The projectiles in hit-and-run events are assumed to collide again at a lower impact velocity⁶. To investigate the largest effect of partial accretion events on changing bulk composition, we assume that no collision fragments are accreted at a later time. Starting with 0.025 M_Earth embryos, fewer planets reach masses greater than 0.5 M_Earth (20%) using the collision outcome model compared to simulations that assume every collision results in perfect merging (50%). For final planets with masses of 0.5-1.5 M_Earth, 80% are enriched in their core-to-mantle mass fraction by >5% compared to the initial embryo composition and 50% of planets are enriched by 10-30%. The Earth's bulk Fe/Mg ratio is 10-30% greater than solar^7,8; if the initial Fe/Mg ratios in planetary embryos were solar, the observed iron enrichment is in good agreement with our predictions of compositional changes during the giant impact phase of terrestrial planet formation. ¹O'Brien, D., et al., Icarus 184, 39, 2006. ²Raymond, S., et al., Icarus 203, 644, 2009. ³Leinhardt, Z. M., and S. T. Stewart, Mon. Not. Roy. Ast. Soc., submitted (arXiv:1106.6084v1). ⁴Marcus, R., et al., Astrophys. J. Lett. 700, L118, 2009. ⁵Marcus, R., et al., Astrophys. J. Lett. 719, L45, 2010. ⁶Kokubo, E., and H. Genda, Astrophys. J. Lett. 714, L21, 2010. ⁷O'Neill, H., and H. Palme, Phil. Trans. R. Soc. A 366, 4205, 2008. ⁸Jurewicz, A., et al., LPSC 42, Abs. 1917, 2011.