Phase separation in giant planets: inhomogeneous evolution of Saturn

We present the first models of Jupiter and Saturn to couple their evolution to both a radiative-atmosphere grid and to high-pressure phase diagrams of hydrogen with helium and other admixtures. We find that prior calculated phase diagrams in which Saturnʹs interior reaches a region of predicted helium immiscibility do not allow enough energy release to prolong Saturnʹs cooling to its known age and effective temperature. We explore modifications to published phase diagrams that would lead to greater energy release, and propose a modified H–He phase diagram that is physically reasonable, leads to the correct extension of Saturnʹs cooling, and predicts an atmospheric helium mass fraction Yatmos=0.185, in agreement with recent estimates. We also explore the possibility of internal separation of elements heavier than helium, and find that, alternatively, such separation could prolong Saturnʹs cooling to its known age and effective temperature under a realistic phase diagram and heavy element abundance (in which case Saturnʹs Yatmos would be solar but heavier elements would be depleted). In none of these scenarios does Jupiterʹs interior evolve to any region of helium or heavy-element immiscibility: Jupiter evolves homogeneously to the present day. We discuss the implications of our calculations for Saturnʹs primordial core mass.