  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.
