On the accretion of distant planets

We consider the accretion time scale of planetary objects at large stellar distances such as Neptune. The shallow stellar potential well inhibits the formation of large, distant companions in three important ways: (1) orbital periods are longer, and so more remote regions are dynamically younger; (2) the volume occupied by accreting material is larger, contributing to low collision frequencies; and (3) the low gravitational binding energy to the star makes it easier for a planetary embryo to scatter planetesimals out of the system. We suggest that resonant damping of embryo dispersion velocities by a dissipating remnant of their precursor gas disk may mitigate this situation and make the existence of large, outer planets like Neptune easier to explain. Disk torques dynamically cool a system of embryos at the expense of more remote regions of the gas disk by driving acoustic waves at coorbiting Lindblad resonance sites. This lowers embryo eccentricities and inclinations; the smaller dispersion velocities increase the embryos' collision cross sections, which in turn shortens accretion times and results in less material ejected from the system. If the gas surface density has decreased to the point in which it is comparable to that of the condensed solids, the embryo's equilibrium eccentricities become comparable to the normalized scale height of the gas disk. In such a case, the disk torques causing orbit migration are significantly weakened and the protoplanet could be relatively stable against type I decay.