A Massive Core in Jupiter Predicted From First-Principles Simulations
  Hydrogen-helium mixtures at conditions of Jupiter's interior are studied with first-principles computer simulations. The resulting equation of state (EOS) implies that Jupiter possesses a central core of 14-18 Earth masses of heavier elements, a result that supports core accretion as standard model for the formation of hydrogen-rich giant planets. Our nominal model has about 2 Earth masses of planetary ices in the H-He-rich mantle, a result that is, within modeling errors, consistent with abundances measured by the 1995 Galileo Entry Probe mission (equivalent to about 5 Earth masses of planetary ices when extrapolated to the mantle), suggesting that the composition found by the probe may be representative of the entire planet. Interior models derived from this first-principles EOS do not give a match to Jupiter's gravity moment J4 unless one invokes interior differential rotation, implying that jovian interior dynamics has an observable effect on the measured gravity field. 
B. Militzer, W. B. Hubbard, J. Vorberger, I. Tamblyn, S.A. Bonev