Long-Term Orbital Evolution of Protoplanets

Abstract

We investigated the stability of systems of ten protoplanets using three-dimensional N-body simulations. We found that the timescale of instability T depends strongly on the initial random velocities v (eccentricities e and inclinations i) and orbital separations Δa of protoplanets. For v = 0, we confirmed the result of Chambers et al. (1996) that T is proportional to exp(Δa). For v > 0, we found that T depends strongly on the initial random velocities. The relation between T and Δa is still expressed as log T = bΔa + c. However, both b and c depend on initial random velocities and the slope, b, decreases with v. Even for relatively small initial eccentricities such as e ~ 2r _H/a, where r _H is the Hill radius, the timescale can be reduced by a factor of 10 compared with the case of the zero random velocity. Therefore, the timescale of the formation of inner planets might be much shorter than implied by Chambers et al..