Evolution of Jupiter and Saturn with helium rain

Institut für Astrophysik, Universität Zürich, Winterthurerstr. 190, CH8057 Zurich, Switzerland
e-mail: saburo.howard@uzh.ch

Received: 7 May 2024
Accepted: 12 July 2024

Abstract

The phase separation between hydrogen and helium at high pressures and temperatures leads to the rainout of helium in the deep interiors of Jupiter and Saturn. This process, also known as “helium rain”, affects their long-term evolution. Modeling the evolution and internal structure of Jupiter and Saturn (and giant exoplanets) relies on the phase diagram of hydrogen and helium. In this work, we simulated the evolution of Jupiter and Saturn with helium rain by applying different phase diagrams of hydrogen and helium and we searched for models that reproduce the measured atmospheric helium abundance in the present day. We find that a consistency between Jupiter’s evolution and the Galileo measurement of its atmospheric helium abundance can only be achieved if a shift in temperature is applied to the existing phase diagrams (−1250 K, +350 K or −3850 K depending on the applied phase diagram). Next, we used the shifted phase diagrams to model Saturn’s evolution and we found consistent solutions for both planets. We confirm that de-mixing in Jupiter is modest, whereas in Saturn, the process of helium rain is significant. We find that Saturn has a large helium gradient and a helium ocean. Saturn’s atmospheric helium mass fraction is estimated to be between 0.13 and 0.16. We also investigated how the applied hydrogen-helium equation of state and the atmospheric model affect the planetary evolution, finding that the predicted cooling times can change by several hundred million years. Constraining the level of super-adiabaticity in the helium gradient formed in Jupiter and Saturn remains challenging and should be investigated in detail in future research. We conclude that further explorations of the immiscibility between hydrogen and helium are valuable as this knowledge directly affects the evolution and current structure of Jupiter and Saturn. Finally, we argue that measuring Saturn’s atmospheric helium content is crucial for constraining Saturn’s evolution as well as the hydrogen-helium phase diagram.