No abstract

We analyse the non‐linear, three‐dimensional response of a gaseous, viscous protoplanetary disc to the presence of a planet of mass ranging from 1 Earth mass (1 M⊕) to 1 Jupiter mass (1 MJ) by using the zeus hydrodynamics code. We determine the gas flow pattern, and the accretion and migration rates of the planet. The planet is assumed to be in a fixed circular orbit about the central star. It is also assumed to be able to accrete gas without expansion on the scale of its Roche radius. Only planets with masses Mp≳ 0.1 MJ produce significant perturbations in the surface density of the disc. The flow within the Roche lobe of the planet is fully three‐dimensional. Gas streams generally enter the Roche lobe close to the disc mid‐plane, but produce much weaker shocks than the streams in two‐dimensional models. The streams supply material to a circumplanetary disc that rotates in the same sense as the orbit of the planet. Much of the mass supply to the circumplanetary disc comes from non‐coplanar flow. The accretion rate peaks with a planet mass of approximately 0.1 MJ and is highly efficient, occurring at the local viscous rate. The migration time‐scales for planets of mass less than 0.1 MJ, based on torques from disc material outside the Roche lobes of the planets, are in excellent agreement with the linear theory of type I (non‐gap) migration for three‐dimensional discs. The transition from type I to type II (gap) migration is smooth, with changes in migration times of about a factor of 2. Starting with a core which can undergo runaway growth, a planet can gain up to a few MJ with little migration. Planets with final masses of the order of 10 MJ would undergo large migration, which makes formation and survival difficult.

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 ∼ 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% to 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 . Subject headings: accretion, accretion discs -hydrodynamics -planets and satellites: generalThis 2-column preprint was prepared with the AAS L A T E X macros v5.0, modified by Gennaro D'Angelo.

No abstract