Late-stage planetary accretion including hit-and-run collisions and fragmentation

Abstract

To date, most simulations of the final accretion of the terrestrial planets have assumed that all collisions lead to mergers. Recent hydrodynamic simulations of impacts between planetary mass bodies (Leinhardt, Z.M., Stewart, S.T. [2012]. Astrophys. J. 745, 79; Genda, H., Kokubo, E., Ida, S. [2012]. Astrophys J. 744, 137) have parameterized the outcome of planetary collisions in terms of the masses and velocities of the colliding bodies. Using these results, it is now possible to simulate late-stage planetary growth using a more realistic model for collisions. Here, we describe results of eight N-body simulations of terrestrial planet formation that incorporate collisional fragmentation and hit-and-run collisions. The results are compared to simulations using identical initial collisions in which all collisions were assumed to result in mergers (Chambers, J.E. [2001]. Icarus 152, 205–224). The new simulations form 3 to 5 terrestrial planets moving on widely spaced orbits with growth complete by 400My. The mean time for Earth-like planets to reach half their final mass is 17My, comparable to the time in simulations without fragmentation. However, the prolonged sweep up of collision fragments lengthens the mean time required for Earth analogues to become fully formed to 159My. The final planets have somewhat smaller masses m and eccentricities e when fragmentation is included. Masses are particularly reduced in the region now occupied by Mars. The final distributions of m, e and semi-major axis are similar to the terrestrial planets of the Solar System, but the strong concentration of mass in the narrow zone occupied by Earth and Venus is not reproduced. Collisional fragmentation is likely to preferentially eject silicate-rich mantle material leaving a target enriched in iron-rich core material. However, large bodies often reaccrete silicate-rich mantle fragments at a later time, leaving their final composition largely unchanged. The final core mass fractions of all but one planet formed in the simulations lie in the range 0.25–0.37 assuming an initial mass fraction of 0.3.