Core Formation in Giant Gaseous Protoplanets
  Sedimentation rates of silicate grains in gas giant protoplanets formed by disk instability are calculated for protoplanetary masses between 1 M_Saturn to 10 M_Jupiter. Giant protoplanets with masses of 5 M_Jupiter or larger are found to be too hot for grain sedimentation to form a silicate core. Smaller protoplanets are cold enough to allow grain settling and core formation. Grain sedimentation and core formation occur in the low mass protoplanets because of their slow contraction rate and low internal temperature. It is predicted that massive giant planets will not have cores, while smaller planets will have small rocky cores whose masses depend on the planetary mass, the amount of solids within the body, and the disk environment. The protoplanets are found to be too hot to allow the existence of icy grains, and therefore the cores are predicted not to contain any ices. It is suggested that the atmospheres of low mass giant planets are depleted in refractory elements compared with the atmospheres of more massive planets. These predictions provide a test of the disk instability model of gas giant planet formation.   The core masses of Jupiter and Saturn were found to be ~0.25 M_Earth and ~0.5 M_Earth, respectively. The core masses of Jupiter and Saturn can be substantially larger if planetesimal accretion is included. The final core mass will depend on planetesimal size, the time at which planetesimals are formed, and the size distribution of the material added to the protoplanet. Jupiter's core mass can vary from 2 to 12 M_Earth. Saturn's core mass is found to be ~8 M_Earth. 
Ravit Helled and Gerald Schubert