Tidal Barrier and the Asymptotic Mass of Proto–Gas Giant Planets

Extrasolar planets found with radial velocity surveys have masses rangingfrom several Earth to several Jupiter masses. While mass accretion ontoprotoplanetary cores in weak-line T-Tauri disks may eventually be quenched by aglobal depletion of gas, such a mechanism is unlikely to have stalled thegrowth of some known planetary systems which contain relatively low-mass andclose-in planets along with more massive and longer period companions. Here, wesuggest a potential solution for this conundrum. In general, supersonic infallof surrounding gas onto a protoplanet is only possible interior to both of itsBondi and Roche radii. At a critical mass, a protoplanet's Bondi and Rocheradii are equal to the disk thickness. Above this mass, the protoplanets' tidalperturbation induces the formation of a gap. Although the disk gas may continueto diffuse into the gap, the azimuthal flux across the protoplanets' Roche lobeis quenched. Using two different schemes, we present the results of numericalsimulations and analysis to show that the accretion rate increases rapidly withthe ratio of the protoplanet's Roche to Bondi radii or equivalently to the diskthickness. In regions with low geometric aspect ratios, gas accretion isquenched with relatively low protoplanetary masses. This effect is importantfor determining the gas-giant planets' mass function, the distribution of theirmasses within multiple planet systems around solar type stars, and forsuppressing the emergence of gas-giants around low mass stars