Comparing planetary accretion in two and three dimensions

Two ways to speed up N-body simulations of planet formation are (i) to confine motion to 2 spatial dimensions, or (ii) to artificially enhance the physical radii of the bodies. These short cuts have the same effect of increasing the collision probability between objects. Here, I compare the results of four integrations using these approximations with two more realistic simulations. Each integration begins with 153 lunar-mass planetary embryos with semi-major axes 0.3 < a < 2.0 AU, plus Jupiter and Saturn. The two- and three-dimensional (2D and 3D) simulations have many differences. In 3D, orbital eccentricities objects remain on crossing orbits until accretion is complete, while centricities become larger than in 2D, there is more radial mixing of material, and a significant amount of mass falls into the Sun. In 3D, in 2D, embryos become isolated from-each other when similar to 10 bodies still remain. The nu (5) and nu (6) secular resonances affect evolution in the inner and outer parts of the terrestrial-planet region in SD, but are unimportant in 2D. The 2D integrations yield more final planets, with smaller eccentricities, than the 3D case. Stochasticity plays a minor role in 2D, while chance events dominate the outcome in 3D. Generally, the simulations with enhanced radii yield results intermediate between the 2D and the 3D cases, having more in common with the former. The differences between the 2D and the 3D integrations occur principally because in 3D, the collision timescale is large compared to the timescale for orbital evolution, while in 2D, these timescales are comparable. (C) 2001 Academic Press.