Formation and Evolution Simulations of Saturn, Including Composition Gradients and Helium Immiscibility

The formation of Saturn is modeled by detailed numerical simulations according to the core-nucleated accretion scenario. Previous models are enhanced to include the dissolution of accreting planetesimals, composed of water ice, rock, and iron, in the gaseous envelope of the planet, leading to a non-uniform composition with depth. The immiscibility of helium in metallic hydrogen layers is also considered. The calculations start at a mass $0.5$ Earth masses and are extended to the present day. At 4.57 Gyr, the model, proceeding outwards, has the following structure: (i) a central core composed of $100$% heavy elements and molecules, (ii) a region with decreasing heavy element mass fraction, down to a value of $0.1$, (iii) a layer of uniform composition with the helium mass fraction $Y$ enhanced over the primordial value, (iv) a helium rain region with a gradient in $Y$, (v) an outer convective, adiabatic region with uniform composition in which $Y$ is reduced from the primordial value, and (vi) the very outer layers where cloud condensation of the heavy elements occurs. Models of the distribution of heavy elements as a function of radius are compared with those derived to fit the observations of the Cassini mission, with rough qualitative agreement. The helium mass fraction in Saturn's outer layers is estimated to be around $20$%. Models are found which provide good agreement with Saturn's intrinsic luminosity and radius.