The stability of protoplanet systems

We investigated the stability of 10 protoplanet systems using three-dimensional N-body simulations. We found that the time scale of instability T depends strongly on the initial random velocities v (eccentricities e and inclinations i) and orbital separations Delta a. For zero initial random velocities, we confirmed the result of Chambers et al. (1996, Icarus 119, 261-268) that Tis proportional to exp(Delta a). For finite random velocities, we found that T depends strongly on the initial random velocities. The relation between T and Delta a is still expressed as log T = b + c Delta a. However, both b and c depend on initial random velocities and the slope, b, becomes smaller for larger v. Even for relatively small initial eccentricities such as e similar to 2r(H)/a, where r(H) is the Hill radius, the time scale can be reduced by a factor of 10 compared with the case of the zero random velocity. Therefore, the time scale of the formation of inner planets might be much shorter than what implied by Chambers et al. (C) 1999 Academic Press.