Mass flow and accretion through gaps in accretion discs

We study the structure and dynamics of the gap created by a protoplanet in an accretion disc. The hydrodynamic equations for a flat, two-dimensional, non-self-gravitating protostellar accretion disc with an embedded, Jupiter-sized protoplanet on a circular orbit are solved. To simulate possible accretion of mass on to the protoplanet we continually remove mass from the interior of the planet's Roche lobe, which is monitored. First, it is shown that consistent results independent of numerical issues (such as boundary or initial conditions, artificial viscosity or resolution) can be obtained. Then, a detailed parameter study delineates the influence of the disc viscosity and pressure on the magnitude of the accretion rate. We find that, even after the formation of a gap in the disc, the planet is still able to accrete more mass from the disc. This accretion occurs from regions of the disc that are radially exterior and interior to the planet's orbital radius. The rate depends on the magnitude of the viscosity and vertical thickness of the disc. For a disc viscosity alpha = 10(-3) and vertical thickness H/r = 0.05 we estimate the time-scale for the accumulation of one Jupiter mass to be of the order of a hundred thousand years. For a larger (smaller) viscosity and disc thickness this accretion rate is increasing (decreasing). For a very small viscosity alpha less than or similar to 5 x 10(-4) the mass accretion rate through the gap on to the planet is markedly reduced, and the corresponding accretion time-scale becomes larger than the viscous evolution time of the disc.