  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. Therefore, modelling 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 simulate the evolution of Jupiter and Saturn with
helium rain by applying different phase diagrams of hydrogen and helium. We
find that consistency between Jupiter s evolution and the Galileo measurement
of its atmospheric helium abundance is achieved only if a shift in temperature
in the existing phase diagrams is applied (-1250 K, +350 K or -3850 K depending
on the used phase diagram). We next use the shifted phase diagrams to model
Saturn s evolution and find consistent solutions for both planets. We confirm
that demixing in Jupiter is modest while 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 investigate how the used hydrogen-helium equation of
state and atmospheric model affect the planetary evolution and find 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-state 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.
