| Abstract
| - The formation of a circumplanetary disc and accretion of angular momentum on to a protoplanetary system are investigated using three-dimensional hydrodynamical simulations. The local region around a protoplanet in a protoplanetary disc 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 disc, various equations of state are adopted. Large thermal energy around the protoplanet slightly changes the structure of the circumplanetary disc. 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 disc 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 disc. The disc 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 discs in the region of r< 21rJup(r< 0.028 rH,Jup) and r< 66rSat(r< 0.061rH,Sat), respectively, where rJup(rH,Jup) and rSat(rH,Sat) 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 discs corresponds well to the outermost orbit of regular satellites around Jupiter and Saturn. Regular satellites may form in such compact discs around proto-gas giant planets.
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