Accretion of Gas Giants Constrained by the Tidal Barrier

Abstract

Abstract After protoplanets have acquired sufficient mass to open partial gaps in their natal protostellar disks, residual gas continues to diffuse onto horseshoe streamlines under the effect of viscous dissipation, and to meander in and out of the planets’ Hill sphere. Within the Hill sphere, the horseshoe streamlines intercept gas flow in circumplanetary disks. The host star’s tidal perturbation induces a barrier across the converging streamlines’ interface. Viscous transfer of angular momentum across this tidal barrier determines the rate of mass diffusion from the horseshoe streamlines onto the circumplanetary disks, and eventually the accretion rate onto the protoplanets. We carry out a series of numerical simulations to test the influence of this tidal barrier on superthermal planets. In weakly viscous disks, the protoplanets’ accretion rate steeply decreases with their masses above the thermal limit. As their growth timescale exceeds the gas depletion timescale, their masses reach asymptotic values comparable to that of Jupiter. In relatively thick and strongly viscous disks, protoplanets’ asymptotic masses exceed several times that of Jupiter. Two-dimensional numerical simulations show that such massive protoplanets strongly excite the eccentricity of nearby horseshoe streamlines, destabilize orderly flow, substantially enhance the diffusion rate across the tidal barrier, and elevate their growth rate until their natal disk is severely depleted. In contrast, eccentric streamlines remain stable in three-dimensional simulations. Based on the upper falloff in the observed mass distribution of known exoplanets, we suggest that their natal disks had relatively low viscosity (α ∼ 10−3) and modest thickness (H/R ∼ 0.03–0.05).