Gas Flow across Gaps in Protoplanetary Disks

Abstract

We analyze the gas accretion flow through a planet-produced gap in a protoplanetary disk. We adopt the α-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 ~1MJ 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 5×10-5 to 1×10-3.