Grain sedimentation inside giant planet embryos

In the context of massive fragmenting protoplanetary discs, Boss suggested that grains can grow and sediment inside giant planet embryos formed at R similar to 5 au away from the star. Several authors since then criticized the suggestion. Convection may prevent grain sedimentation, and the embryos cannot even form so close to the parent star as cooling is too inefficient at these distances. Here we reconsider the grain sedimentation process suggested by Boss but inside an embryo formed, as expected in the light of the cooling constraints, at R similar to 100 au. Such embryos are much less dense and are also cooler. We make analytical estimates of the process and also perform simple spherically symmetric radiation hydrodynamics simulations to test these ideas. We find that convection in our models does not become important before a somewhat massive (similar to an Earth mass; this is clarified in a followup paper) solid core is built. Turbulent mixing slows down dust sedimentation but is overwhelmed by grain sedimentation when the latter grows to a centimetres size. The minimum time required for dust sedimentation to occur is a few thousand years, and is a strong function of the embryo's mass, dust content and opacity. An approximate analytical criterion is given to delineate conditions in which a giant embryo contracts and heats up faster than dust can sediment. As Boss et al., we argue that core formation through grain sedimentation inside the giant planet embryos may yield an unexplored route to form giant gas and giant ice planets. The present model also stands at the basis of Paper III, where we study the possibility of forming terrestrial planet cores by tidal disruption and photoevaporation of the planetary envelope.