Gas flow across gaps in protoplanetary disks

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 semianalytic, one-dimensional model that accounts for the effects of the planet as a mass sink and also carry out two-dimensional hydrodynamic simulations of a planet embedded in a disk. The predictions of the mass flow rate through the gap based on the semianalytic model generally agree with the hydrodynamic 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 similar to 1M(J) 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%-25% of the mass accretion rate outside the orbit of the planet, for planet-to-star mass ratios that range from 5 x 10(-5) to 1 x 10(-3).