Tidal barrier and the asymptotic mass of proto-gas giant planets

According to the conventional sequential accretion scenario, observed extrasolar planets acquired their current masses via efficient gas accretion onto super-Earth cores with accretion timescales that rapidly increase with mass. Gas accretion in weak-line T Tauri disks may be quenched by global depletion of gas, but such a mechanism is unlikely to have stalled the growth in planetary systems that contain relatively low-mass, close-in planets together with more massive, longer period companions. Here, we suggest a potential solution for this conundrum. In general, supersonic infall of surrounding gas onto a protoplanet is only possible interior to both its Bondi and Roche radii. Above the critical mass where the Roche and Bondi radii are equal to the disk thickness, the protoplanet's tidal perturbation induces the formation of a gap. However, despite continued diffusion into the gap, the azimuthal flux across the protoplanet's Roche lobe will be quenched. Using two different schemes, we present the results of numerical simulations and analysis to show that the accretion rate increases rapidly with the ratio of the protoplanet's Roche to Bondi radii or equivalently to the disk thickness. Gas accretion is quenched, yielding relatively low protoplanetary masses, in regions with low aspect ratios. This becomes important for determining the gas giant planet's mass function, the distribution of their masses within multiple-planet systems, and for suppressing the emergence of gas giants around low-mass stars. Finally, we find that accretion rates onto protoplanets declines gradually on a characteristic timescale of a few Myr, during which the protracted accretion timescale onto circumplanetary disks may allow for the formation and retention of regular satellites.