  We analyze the gas accretion flow through a planet-produced gap in a
protoplanetary disk. We adopt the alpha disk model and ignore effects of
planetary migration. We develop a semi-analytic, one-dimensional model that
accounts for the effects of the planet as a mass sink and also carry out
two-dimensional hydrodynamical simulations of a planet embedded in a disk. The
predictions of the mass flow rate through the gap based on the semi-analytic
model generally agree with the hydrodynamical simulations at the 25% level.
Through these models, we are able to explore steady state disk structures and
over large spatial ranges. The presence of an accreting Jupiter-mass planet
significantly lowers the density of the disk within a region of several times
the planet's orbital radius. The mass flow rate across the gap (and onto the
central star) is typically 10% to 25% of the mass accretion rate outside the
orbit of the planet, for planet-to-star mass ratios that range from 5e-5 to
1e-3.
