  We analyze the nonlinear, two-dimensional response of a gaseous, viscous
protoplanetary disk to the presence of a planet of one Jupiter mass (1 M_J) and
greater that orbits a 1 solar mass star by using the ZEUS hydrodynamics code
with high resolution near the planet's Roche lobe. 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. The gap partitions the disk into an inner
(outer) disk that extends inside (outside) the planet's orbit. For a 1 M_J
planet and typical disk parameters, the accretion through the gap onto the
planet is highly efficient. For typical disk parameters, the mass doubling time
scale is less than 10^5 years, considerably shorter than the disk lifetime.
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. For higher mass planets (of order 6 M_J), the
flow rate onto the planet is considerably reduced, which suggests an upper mass
limit to planets in the range of 10 M_J. This rate reduction is related to the
fact that the gap width increases relative to the Roche (Hill sphere) radius
with increasing planetary mass. 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.
