  The formation of a circumplanetary disk and accretion of angular momentum
onto a protoplanetary system are investigated using 3D hydrodynamical
simulations. The local region around a protoplanet in a protoplanetary disk is
considered with sufficient spatial resolution: the region from outside the Hill
sphere to the Jovian radius is covered by the nested-grid method. To
investigate the thermal effects of the circumplanetary disk, various equations
of state are adopted. Large thermal energy around the protoplanet slightly
changes the structure of the circumplanetary disk. Compared with a model
adopting an isothermal equation of state, in a model with an adiabatic equation
of state, the protoplanet's gas envelope extends farther, and a slightly thick
disk appears near the protoplanet. However, different equations of state do not
affect the acquisition process of angular momentum for the protoplanetary
system. Thus, the specific angular momentum acquired by the system is fitted as
a function only of the protoplanet's mass. A large fraction of the total
angular momentum contributes to the formation of the circumplanetary disk. The
disk forms only in a compact region in very close proximity to the protoplanet.
Adapting the results to the solar system, the proto-Jupiter and Saturn have
compact disks in the region of r < 21 r_J (r < 0.028 r_HJ) and r < 66 r_S (r <
0.061 r_HS), respectively, where r_J (r_HJ) and r_S (r_HS) are the Jovian and
Saturnian (Hill) radius, respectively. The surface density has a peak in these
regions due to the balance between centrifugal force and gravity of the
protoplanet. The size of these disks corresponds well to the outermost orbit of
regular satellites around Jupiter and Saturn. Regular satellites may form in
such compact disks around proto-gas giant planets.
