Formation of Terrestrial Planets from Protoplanets. II. Statistics of Planetary Spin

The final stage of terrestrial planet formation is known as the giant impact stage, where protoplanets collide with one another to form planets. The initial spin state of terrestrial planets is determined at this stage. We statistically investigate the spin parameters of terrestrial planets assembled from protoplanets using N-body simulations. As initial conditions, we adopt the oligarchic growth model of protoplanets. For the standard disk model, typically two Earth-sized planets form in the terrestrial planet region. We find that the spin angular velocity of the planets is well expressed by a Gaussian distribution, and their obliquity is well expressed by an isotropic distribution. The typical spin angular velocity is given by the critical spin angular velocity for rotational instability under the assumption of perfect accretion in collisions. We show the dependencies of the spin parameters on the initial protoplanet system parameters. The initial orbital separation and velocity anisotropy of protoplanets barely affect the spin parameters. The bulk density of protoplanets does not affect the obliquity distribution, while the spin angular velocity increases with the bulk density.