The planet is assumed to be in a circular orbit about the central star and is not allowed to migrate. A gap is formed about the orbit of the planet, but there is a nonaxisymmetric flow through the gap and onto the planet. For a 1 M J planet and typical disk parameters, the accretion through the gap onto the planet is highly efficient. Following shocks near the L1 and L2 Lagrange points, disk material enters the Roche lobe in the form of two gas streams. Shocks occur within the Roche lobe as the gas streams collide, and shocks lead to rapid inflow towards the planet within much of planet's Roche lobe.
Shocks also propagate in the inner and outer disks that orbit the star.
The flow in the gap affects planetary migration. For the 1 M J planet case, mass can penetrate from the outer disk to the inner disk, so that the inner disk is not depleted. The results suggest that most of the mass in gas giant planets is acquired by flows through gaps.