The effects of nebula surface density profile and giant-planet eccentricities on planetary accretion in the inner solar system

Abstract

We describe results of 32 N-body planetary accretion simulations that investigate the dependence of terrestrial-planet formation on nebula surface density profile σ and evolution of the eccentricities of Jupiter and Saturn eJ,S. Two surface density profiles are examined: a decaying profile with σ ? 1/a, where a is orbital semi-major axis, and a peaked profile in which σ increases for a < 2 AU and decreases for a > 2 AU. The peaked profiles are generated by models of coagulation in an initially hot nebula. Models with initial eJ,S = 0.05 (the current value) and 0.1 are considered. Simulations using the decaying profile with eJ,S = 0.1 produce systems most like the observed planets in terms of mass-weighted mean a and the absence of a planet in the asteroid belt. Simulations with doubled σ produce planets roughly twice as massive as the nominal case. Most initial embryos are removed in each simulation via ejection from the Solar System or collision with the Sun. The asteroid belt is almost entirely cleared on a timescale of 10-100 Ma that depends sensitively on eJ,S. Most initial mass with a < 2 AU survives, with the degree of mass loss increasing with a. Mass loss from the terrestrial region occurs on a timescale that is long compared to the mass loss time for the asteroid belt. Substantial radial mixing of material occurs in all simulations, but is greater in simulations with initital eJ,S = 0.05. The degree of mixing is equivalent to a feeding zone of half width 1.5 and 0.9 AU for an Earth mass planet at 1 AU for the cases eJ,S = 0.05 and 0.1 respectively. In simulations with eJ,S = 0.05, roughly 1/3 and 5-10% of the mass contained in final terrestrial planets originated in the region a > 2.5 AU for the decaying and peaked profiles respectively. In the case eJ,S = 0.1, the median mass accreted from a > 2.5 AU is zero for both profiles.