After protoplanets have acquired sufficient mass to open partial gaps in their natal protostellar disks, residual gas continues to diffuse onto horseshoe streamlines under effect of viscous dissipation, and meander in and out of the planets' Hill sphere. Within the Hill sphere, the horseshoe streamlines intercept gas flow in circumplanetary disks. The host stars' 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 super thermal planets. In weakly viscous disks, protoplanets' accretion rate steeply decreases with their masses above the thermal limit. As their growth timescale exceeds the gas depletion time scale, 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 observe mass distribution of known exoplanets, we suggest their natal disks had relatively low viscosity alpha sim 0.001, modest thickness H/R sim 0.03 to 0.05, and limited masses comparable to that of minimum mass solar nebula model.

中文翻译：

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受潮汐屏障约束的气态巨行星的吸积

在原行星获得足够的质量以打开它们出生时原恒星盘中的部分间隙后，残余气体在粘性耗散的作用下继续扩散到马蹄形流线上，并蜿蜒进出行星的希尔球。在希尔球体中，马蹄形流线拦截了环行星盘中的气流。宿主恒星的潮汐扰动在会聚流线的界面上产生了障碍。穿过这个潮汐屏障的角动量的粘性传递决定了质量从马蹄形流线到环行星盘的扩散率，并最终决定了原行星上的吸积率。我们进行了一系列数值模拟来测试这个潮汐屏障对超热行星的影响。在弱粘性盘中，原行星的 当它们的质量超过热极限时，吸积率急剧下降。由于它们的生长时间尺度超过了气体消耗的时间尺度，它们的质量达到了与木星相当的渐近值。在相对较厚且粘性较强的圆盘中，原行星的渐近质量超过木星的数倍。二维数值模拟表明，这种巨大的原行星强烈激发了附近马蹄形流线的偏心，破坏了有序流动，大大提高了穿过潮汐屏障的扩散速度，并提高了它们的生长速度，直到它们的出生盘严重耗尽。相比之下，偏心流线在三维模拟中保持稳定。基于已知系外行星观测质量分布的上限衰减，