Tidally induced gap formation in protostellar disks: Gap clearing and suppression of protoplanetary growth

We present the results of numerical simulations of protostellar accretion d isks that are perturbed by a protoplanetary companion that has a much small er mass than the central object. We consider the limiting cases where the c ompanion is in a coplanar, circular orbit and is initially embedded in the disk. Three independent numerical schemes are employed, and generic feature s of the flow are found in each case. In the first series of idealized mode ls, the secondary companion is modeled as a massless, orbiting sink hole ab le to absorb all matter incident upon it without exerting any gravitational torque on the disk. In these simulations, accretion onto the companion ind uces surface density depression and gap formation centered on its orbital r adius. After an initial transitory adjustment, the accretion rate onto the sink hole becomes regulated by the rate at which viscous evolution of the d isk can cause matter to diffuse into the vicinity of the sink hole orbit, a nd thus the sink hole grows on a disk viscous timescale. In the second seri es of comprehensive models, the companion's gravity is included. When the t idal torque exerted by the companion on the disk becomes important, the ang ular momentum exchange rate between the companion and the disk induces the protoplanetary accretion to reduce markedly below that in the idealized sin k hole models. Whether this process is effective in inhibiting protoplaneta ry accretion depends on the equation of state and disk model parameters. Fo r polytropic or isothermal equations of state, we find, in basic agreement with earlier work, that when the mean Roche lobe radius of the companion ex ceeds the disk thickness and when the mass ratio, q, between the companion and the central object exceeds similar to 40/R, where R is the effective Re ynolds number, a clean deep gap forms. Although precise estimation is rende red difficult due to the limitation of numerical schemes in dealing with la rge density contrasts, the generic results of three series of simulations i ndicate that accretion onto sufficiently massive protoplanets can become in effective over the expected disk lifetimes in their neighborhood. We sugges t that such a process operates during planetary formation and is important in determining the final mass of giant planets.