General Analytic Solutions for Circumplanetary Disks during the Late Stages of Giant Planet Formation

Abstract

Forming giant planets are accompanied by circumplanetary disks, as indicated by considerations of angular momentum conservation, observations of candidate protoplanets, and the satellite systems of planets in our Solar System. This paper derives surface density distributions for circumplanetary disks during the final stage of evolution when most of the mass is accreted. This approach generalizes previous treatments to include the angular momentum bias for the infalling material, more accurate solutions for the incoming trajectories, corrections to the outer boundary condition of the circumplanetary disk, and the adjustment of newly added material as it becomes incorporated into the Keplerian flow of the pre-existing disk. These generalizations lead to smaller centrifugal radii, higher column density for the surrounding envelopes, and higher disk accretion efficiency. In addition, we explore the consequences of different angular distributions for the incoming material at the outer boundary, with the concentration of the incoming flow varying from polar to isotropic to equatorial. These geometric variations modestly affect the disk surface density, but also lead to substantial modification to the location in the disk where the mass accretion rate changes sign. This paper finds analytic solutions for the orbits, source functions, surface density distributions, and the corresponding disk temperature profiles over the expanded parameter space outlined above.