The Growth of Protoplanets via the Accretion of Small Bodies in Disks Perturbed by the Planetary Gravity

Abstract

Planets grow via the collisional accretion of small bodies in a protoplanetary disk. Such small bodies feel strong gas drag, and their orbits are significantly affected by the gas flow and atmospheric structure around the planet. We investigate the gas flow in the protoplanetary disk perturbed by the gravity of the planet by 3D hydrodynamical simulation. We then calculate the orbital evolutions of particles in the gas structure obtained from the hydrodynamical simulation. Based on the orbital calculations, we obtain the collision rate between the planet and centimeter-to-kilometer-sized particles. Our results show that meter-sized or larger particles effectively collide with the planet owing to the atmospheric gas drag, which significantly enhances the collision rate. On the other hand, the gas flow plays an important role for smaller particles. Finally, considering the effects of the atmosphere and gas flow, we derive the new analytic formula for the collision rate, which is in good agreement with our simulations. We estimate the growth timescale and accretion efficiency of drifting bodies for the formation of a gas giant solid core using the formula. We find that the accretion of sub-kilometer-sized bodies achieves a short growth timescale (∼0.05 Myr) and a high accretion efficiency (∼1) for the core formation at 5 au in the minimum-mass solar nebula model.