  We examine the comparative thermal evolution of Jupiter and Saturn applying
recent theoretical results for helium's immiscibility in fluid metallic
hydrogen. The redistribution of helium in their interiors proceeds very
differently for the two planets. We confirm that based on Jupiter's atmospheric
helium depletion as observed in situ by the Galileo entry probe, Jupiter's
interior helium has differentiated modestly, and we present models reconciling
Jupiter's helium depletion, radius, and heat flow at the solar age. Jupiter's
recently revised Bond albedo implies a lower intrinsic flux for the planet,
accommodating more luminosity from helium differentiation such that mildly
superadiabatic interiors can satisfy all constraints. The same phase diagram
applied to the less massive Saturn predicts dramatic helium differentiation to
the degree that Saturn inevitably forms a helium-rich shell or core, an outcome
previously proposed by Stevenson & Salpeter and others. The luminosity from
Saturn's helium differentiation is sufficient to extend its cooling time to the
solar age, even for adiabatic interiors. This model predicts Saturn's
atmospheric helium to be depleted to Y=0.07+/-0.01, corresponding to a He/H_2
mixing ratio 0.036+/-0.006. We also show that neon differentiation may have
contributed to both planets' luminosity in the past. These results demonstrate
that Jupiter and Saturn's thermal evolution can be explained self-consistently
with a single physical model, and emphasize that nontrivial helium
distributions should be considered in future models for Saturn's internal
structure and dynamo.
