Grain Sedimentation in a Giant Gaseous Protoplanet

We present a calculation of the sedimentation of grains in a giant gaseous protoplanet such as that resulting from a disk instability of the type envisioned by Boss (1998). Boss (1998) has suggested that such protoplanets would form cores through the settling of small grains. We have tested this suggestion by following the sedimentation of small silicate grains as the protoplanet contracts and evolves. We find that during the course of the initial contraction of the protoplanet, which lasts some $4\times 10^5$ years, even very small (> 1 micron) silicate grains can sediment to create a core both for convective and non-convective envelopes, although the sedimentation time is substantially longer if the envelope is convective, and grains are allowed to be carried back up into the envelope by convection. Grains composed of organic material will mostly be evaporated before they get to the core region, while water ice grains will be completely evaporated. These results suggest that if giant planets are formed via the gravitational instability mechanism, a small heavy element core can be formed due to sedimentation of grains, but it will be composed almost entirely of refractory material. Including planetesimal capture, we find core masses between 1 and 10 M$_{\oplus}$, and a total high-Z enhancement of ~40 M$_{\oplus}$. The refractories in the envelope will be mostly water vapor and organic residuals.