Accretion rates of moonlets embedded in circumplanetary particle disks

摘要

We examine the gravitational capture probability of colliding particles in circumplanetary particle disks and accretion rates of small particles onto an embedded moonlet, using analytic calculation, three-body orbital integrations, and Y-body simulations. Expanding our previous work, we take into account the Rayleigh distribution of particles' orbital eccentricities and inclinations in our analytic calculation and orbital integration and confirm agreement between them when the particle velocity dispersion is comparable to or larger than their mutual escape velocity and the ratio of the sum of the physical radii of colliding particles to their mutual Hill radius (r?_p) is much smaller than unity. As shown by our previous work, the capture probability decreases significantly when the velocity dispersion is larger than the escape velocity and/or r?_p ≥ 0.7. Rough surfaces of particles can enhance the capture probability. We compare the results of three-body calculations with N-body simulations for accretion of small particles by an embedded moonlet and find agreement at the initial stage of accretion. However, when particles forming an aggregate on the moonlet surface nearly fill the Hill sphere, the aggregate reaches a quasi-steady state with a nearly constant number of particles covering the moonlet, and the accretion rate is significantly reduced compared to the three-body results.