  The properties of hydrogen-helium mixtures at Mbar pressures and intermediate
temperatures (4000 to 10000 K) are calculated with first-principles molecular
dynamics simulations. We determine the equation of state as a function of
density, temperature, and composition and, using thermodynamic integration, we
estimate the Gibbs free energy of mixing, thereby determining the temperature,
at a given pressure, when helium becomes insoluble in dense metallic hydrogen.
These results are directly relevant to models of the interior structure and
evolution of Jovian planets. We find that the temperatures for the demixing of
helium and hydrogen are sufficiently high to cross the planetary adiabat of
Saturn at pressures around 5 Mbar; helium is partially miscible throughout a
significant portion of the interior of Saturn, and to a lesser extent in
Jupiter.
