2023MNRAS.526.5346L

We perform a series of 3D simulations to study the accretion of giant planet embedded in protoplanetary discs (PPDs) over gap-opening time-scales. We find that the accretion mass flux mainly comes from the intermediate latitude above the disc mid-plane. The circumplanetary disc (CPD) for a super-thermal planet is rotation-supported up to ∼20-30 per cent of the planet Hill radius. While both mass inflow and outflow exists in the CPD mid-plane, the overall trend is an outflow that forms a meridional circulation with high-latitude inflows. We confirm the absence of accretion outburst from disc eccentricity excited by massive planets in our 3D simulations, contrary to the consensus of previous 2D simulations. This suggests the necessity of 3D simulations of accretion even for super-Jupiters. The accretion rates of planets measured in a steady state can be decomposed into the 'geometric' and 'density depletion' factors. Through an extensive parameter survey, we identify a power-law scaling for the geometric factor $\propto q_{\rm th}^{2/3}$ for super-thermal planets (q_th being the thermal mass ratio), which transform to $\propto q_{\rm th}^{2}$ for less massive cases. The density depletion factor is limited by the disc accretion rate for mildly super-thermal planets and by gap-opening for highly super-thermal ones. Moderate planetary eccentricities can enhance the accretion rates by a factor of 2-3 by making the gap shallower, but it does not impact the flow geometry. We have applied our simulations results to accreting protoplanet system PDS 70 and can satisfactorily explain the accretion rate and CPD size in observations.