  In the context of massive fragmenting protoplanetary discs, Boss (1998)
suggested that grains can grow and sediment inside giant planet embryos formed
at R ~ 5 AU away from the star. Several authors since then criticised 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
(1998) but inside an embryo formed, as expected in the light of the cooling
constraints, at R ~ 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 (~ 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 grow 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 (2002), 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.
