Delivery of pebbles from the protoplanetary disk into circumplanetary disks

Small bodies likely existed in the late stage of planet formation either as remnants of the planetesimal formation stage or as fragments of larger planetesimals. Recent studies suggest that they may have played an important role in the formation of regular satellites of giant planets, but their delivery process into the circumplanetary disk has been poorly understood. Using orbital integration that incorporates the gas flow around the planet obtained by hydrodynamic simulation, we examine delivery of small bodies in the protoplanetary disk into circumplanetary disks. We find that large bodies can be captured when they experience strong gas drag near the midplane of the circumplanetary disk, while particles with Stokes number near unity tend to settle toward the midplane of the protoplanetary disk and can be captured near the outer edge of the circumplanetary disk. On the other hand, small particles coupled to the gas can be delivered into the circumplanetary disk with the vertically accreting gas and are captured near the surface of the circumplanetary disk over a wide radial region, if they are sufficiently stirred off the midplane of the protoplanetary disk. However, if the turbulence in the protoplanetary disk is not sufficiently strong, delivery of small particles by such a mechanism would not be efficient. Also, gas depletion in the vicinity of the planet's orbit reduces the efficiency of the delivery. In these cases, larger bodies directly captured by gas drag from the circumplanetary disk would be the major building blocks of regular satellites.