Tidally Induced Gap Formation in Protostellar Disks: Gap Clearing and Suppression of Protoplanetary Growth

We present the results of numerical simulations of protostellar accretion disks that are perturbed by a protoplanetary companion that has a much smaller mass than the central object. We consider the limiting cases where the companion is in a coplanar, circular orbit and is initially embedded in the disk. Three independent numerical schemes are employed, and generic features of the flow are found in each case. In the first series of idealized models, the secondary companion is modeled as a massless, orbiting sink hole able to absorb all matter incident upon it without exerting any gravitational torque on the disk. In these simulations, accretion onto the companion induces surface density depression and gap formation centered on its orbital radius. After an initial transitory adjustment, the accretion rate onto the sink hole becomes regulated by the rate at which viscous evolution of the disk can cause matter to diffuse into the vicinity of the sink hole orbit, and thus the sink hole grows on a disk viscous timescale. In the second series of comprehensive models, the companion's gravity is included. When the tidal torque exerted by the companion on the disk becomes important, the angular momentum exchange rate between the companion and the disk induces the protoplanetary accretion to reduce markedly below that in the idealized sink hole models. Whether this process is effective in inhibiting protoplanetary accretion depends on the equation of state and disk model parameters. For polytropic or isothermal equations of state, we find, in basic agreement with earlier work, that when the mean Roche lobe radius of the companion exceeds the disk thickness and when the mass ratio, q, between the companion and the central object exceeds ~40/, where is the effective Reynolds number, a clean deep gap forms. Although precise estimation is rendered difficult due to the limitation of numerical schemes in dealing with large density contrasts, the generic results of three series of simulations indicate that accretion onto sufficiently massive protoplanets can become ineffective over the expected disk lifetimes in their neighborhood. We suggest that such a process operates during planetary formation and is important in determining the final mass of giant planets.