Formation of Isothermal Disks around Protoplanets. I. Introductory   Three-Dimensional Global Simulations for Sub-Neptune-Mass Protoplanets
  The regular satellites found around Neptune ($\approx 17~M_{\Earth}$) and Uranus ($\approx 14.5~M_{\Earth}$) suggest that past gaseous circumplanetary disks may have co-existed with solids around sub-Neptune-mass protoplanets ($< 17~M_{\Earth}$). These disks have been shown to be cool, optically thin, quiescent, with low surface density and low viscosity. Numerical studies of the formation are difficult and technically challenging. As an introductory attempt, three-dimensional global simulations are performed to explore the formation of circumplanetary disks around sub-Neptune-mass protoplanets embedded within an isothermal protoplanetary disk at the inviscid limit of the fluid in the absence of self-gravity. Under such conditions, a sub-Neptune-mass protoplanet can reasonably have a rotationally supported circumplanetary disk. The size of the circumplanetary disk is found to be roughly one-tenth of the corresponding Hill radius, which is consistent with the orbital radii of irregular satellites found for Uranus. The protoplanetary gas accretes onto the circumplanetary disk vertically from high altitude and returns to the protoplanetary disk again near the midplane. This implies an open system in which the circumplanetary disk constantly exchanges angular momentum and material with its surrounding prenatal protoplanetary gas. 
Hsiang-Hsu Wang, Defu Bu, Hsien Shang, Pin-Gao Gu
astro-ph.EP