Evolution of a Circumterrestrial Disk and Formation of a Single Moon

Abstract

We investigate the evolution of a circumterrestrial disk of debris generated by a giant impact on Earth and the dynamical characteristics of the moon accreted from the disk by using high-resolution N-body simulation. We find that in most cases the disk evolution results in the formation of a single large moon on a nearly circular orbit close to the equatorial plane of the initial disk just outside the Roche limit, which is consistent with the previous work by S. Ida et al. (1997, Nature 389, 353–357). The efficiency of incorporation of disk material into a moon is 10–55%, which increases with the initial specific angular momentum of the disk. These results hardly depend on the initial condition of the disk as long as the mass of the disk is 2 to 4 times the present lunar mass and most mass of the disk exists inside the Roche limit. The timescale of the disk evolution is determined mainly by the surface density of the disk because mass transfer to the outside of the Roche limit and formation of lunar seeds are regulated by collective behavior of disk particles. The evolution of the disk is summarized as follows: The disk contracts through collisional damping. As the velocity dispersion of disk particles decreases, particle clumps grow inside the Roche limit. The clumps become elongated due to Keplerian shear, which forms spiral arm-like structure. Particles are transfered to the outside of the Roche limit through the gravitational torque exerted by the spiral arms. When a tip of a spiral arm goes beyond the Roche limit, it collapses into a small moonlet. The rapid accretion of these small moonlets forms a lunar seed. The seed exclusively grows by sweeping up particles transfered over the Roche limit. When the moon becomes large enough to gravitationally dominate the disk, it pushes the rest of the inner disk to Earth. The formation timescale of the moon is of the order of 1 month if a particulate disk is assumed and the effect of melting/vaporization is not included.